A Thesis

entitled

Corona Induced Electrohydrodynamics: A Contactless Method to Manipulate

Liquids

by

Md Ashraful Haque

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the

Master of Science Degree in

Mechanical Engineering

______Dr. Hossein Sojoudi, Committee Chair

______Dr. Sorin Cioc, Committee Member

______Dr. Ana C. Alba Rubio, Committee Member

______Dr. Cyndee Gruden, Dean College of Graduate Studies

The University of Toledo

December 2018

Select copyright license. 2018 Md Ashraful Haque

This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

An Abstract of

Corona Induced Electrohydrodynamics: A Contactless Method to Manipulate Liquids

by

Md Ashraful Haque

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering

The University of Toledo December 2018

The dynamics of dielectric liquid and liquid drops suspended in another fluid medium subjected to electric field has captivated researchers ever since electro-fluid dynamics was introduced in 17th century. While there has been much work in uniform electric field, recent trends have moved towards the study of how non-uniformity of electric field would induce the motion. The purpose of this thesis is to investigate the response of dielectric liquids and droplets under an ionization technique creating non-uniform electric field. The method applied is corona discharge whose electrical parameters are first studied to understand the behavior of the source impulse. We advocate for the method for it is contactless and enlighten the area of applications considering the limitations of other methods. While studying the behavior of droplet to this electrical signal, their physical changes are tracked down to relate its intrinsic property to this extrinsic discharge phenomena. The dynamic behavior is modeled with the insights of spring-damper analogy and this model is found to capture the different states of deformation while droplet move from one place to other. One distinct feature of this works is to explain how the combined effects of electrophoresis and di-electrophoresis induce the motion and an analogy to

iii differentiate them serves as valuable inputs to carry out electrohydrodynamic(EHD) research. We configured our geometry to address the applicability of this technique to drive very viscous liquids in attempts to see the potentials of the technique being used as EHD pumping. Apart from experiments, we have carried numeric simulations to conclude on the coupled interactions of Electro-Fluid dynamics.

iv

Acknowledgements

I am ever grateful to my family for their great sacrifices. My research advisor, Dr.

Hossein Sojoudi, will carry a big influence in my days ahead who reshaped my entire journey to the process of graduation. And last but not the least are my co-workers in research lab and friends. They are the true inspiration of this work.

v

Table of Contents

Abstract ...... iii

Acknowledgements ...... iv

Table of Contents ...... vi

List of Tables ...... x

List of Figures ...... xi

List of Abbreviations ...... xiii

List of Symbols ...... xiv

1 Fundaments of Electrohydrodynamics ...... 1

1.1 Introduction ...... 1

1.2 Maxwell’s Equation: Foundation of EHD ...... 3

1.2.1 Maxwell’s Equation ...... 3

1.2.2 Non-dimensionalizing ...... 6

1.2.3 Classification of EHD based on Maxwell’s Equation ...... 7

1.2.3.1 Electro and Magnetostatics ...... 7

1.2.3.2 Stationary Fields (DC current) ...... 8

1.2.3.3 Quasi- Stationary Fields (AC current) ...... 8

1.2.3.4 Rapidly changing EM (EM waves)...... 9

1.2.4 Electro-quasistatics of moving fluid ...... 9

1.3 Electrical conduction in liquids ...... 11

vi 1.3.1 Conduction……...... 11

1.3.2 Transport of charge carriers ...... 12

1.3.3 Ion mobilities in liquids and gases ...... 13

1.3.4 Ion injection …...... 15

1.4 Polarization of Dielectrics...... 16

1.4.1 Interfacial Polarization ...... 17

2 Corona discharge phenomena ...... 19

2.1 Plasma ...... 19

2.2 Ionization of air ...... 22

2.2.1 Thermal ionization ...... 22

2.2.2 Photo ionization ...... 23

2.2.3 Particle impact ionization ...... 23

2.2.4 Nuclear emission ...... 24

2.2.5 Electric field ionization ...... 24

2.3 Corona Discharge...... 25

2.3.1 A brief history ...... 25

2.3.2 Mechanism ...... 26

2.3.3 Corona properties ...... 28

2.3.4 Glow discharge vs Arc discharge vs Corona discharge ...... 31

2.3.5 Application of corona discharge ...... 33

2.3.6 Corona discharge research ...... 34

3 Dielectrophoretic motion of conducting droplet in low conducting medium ...... 39

vii 3.1 Introduction ...... 40

3.2 Experimental Set Up ...... 42

3.2.1 Sequential voltage source ...... 42

3.2.2 Electrode device ...... 43

3.2.3 Experimental procedure ...... 43

3.3 Mathematical modeling ...... 46

3.4 Results and Discussions ...... 50

3.4.1 Generation of non-uniform E & parameters effect ...... 50

3.4.2 Electroquasistatics of sessile droplet & deformation pattern ...... 53

3.4.3 Electroquasistatics of moving droplet & deformation effect ...... 56

3.4.4 Analogy of contact charging effect from spring-damper model ...... 61

3.4.5 Statistical analysis of random droplet motion in electroconvection ..69

3.4.6 Rayleigh-Plateau instability of dielectric-dielectric system ...... 72

3.4.7 Translation of droplet in multiple electrode...... 74

3.5 Repeatability of experiment data ...... 76

3.6 Conclusions ...... 76

4 Instability of DL under Atmospheric Air Corona ...... 78

4.1 Introduction ...... 79

4.2 Bulk instability ...... 83

viii 4.2.1 Experimental design and methodology ...... 83

4.2.2 Results and Discussions ...... 91

4.3 EHD pump ...... 105

4.3.1 Experiment set up ...... 105

4.3.2 Theory and characterization ...... 106

4.3.3 Results and discussions ...... 106

5 Conclusions and guidelines for future work ...... 111

5.1 Summary of Thesis ...... 111

5.2 Directions of future work ...... 112

References ...... 114

ix

List of Tables

3.1 Property of water droplet ...... 44

3.2 Property of silicone oil investigated ...... 44

3.3 Physical and electrical property of the system ...... 46

3.4 Relative variation of polarization strength in different locations ...... 62

x

List of Figures

1 – 1 Zero dipole moment and induced dipole moment ...... 17

1 – 2 Effect of dipole potential on interface ...... 18

2 – 1 Various kind of plasma on basis of density and temperature ...... 21

2 – 2 Deep space glows in photoionization ...... 23

2 – 3 Electron avalanche formation ...... 26

2 – 4 Glow of corona ...... 27

2 – 5 Current density at point plane configuration ...... 29

2 – 6 Reaction regions and reaction channels ...... 30

2 – 7 V-I characteristics of different discharges ...... 32

2 – 8 EHD lifters for levitation ...... 35

2 – 9 A Martian particle analyzer ...... 36

2 – 10 Different configurations of EHD gas pumps ...... 37

3 – 1 Schematic diagram for droplet manipulation ...... 45

3 – 2 Numeric simulation displaying electric parameters ...... 52

3 – 3 Prolate and oblate deformation of droplets ...... 54

3 – 4 Relation of contact angle and vertex angle to droplet deformation ...... 55

3 – 5 Medium property effects on deformation ...... 58

3 – 6 Interfacial polarization effects on droplet ...... 60

3 – 7 Electric field and velocity distribution of moving droplet ...... 62

xi

3 – 8 Schematic of spring damper ideology for droplet deformation ...... 64

3 – 9 Conjugate effects of radius and viscosity on motion of droplet ...... 67

3 – 10 Mobility coefficient and result validation ...... 69

3 – 11 Statistical analysis of random behavior of droplet about pathline ...... 70

3 – 12 Statistical analysis of random behavior of droplet about distribution ...... 72

3 – 13 Rayleigh-Plateau instability developed for castor-water ...... 73

3 – 14 Rayleigh-Plateau instability developed for castor-castor ...... 73

3 – 15 Successive position of single droplet in multiple electrode ...... 75

3 – 16 Successive position of multiple droplet in multiple electrode ...... 75

4 – 1 Schematic diagram of experiment ...... 88

4 – 2 Current distribution in realm of Electro-hydrostatics ...... 89

4 – 3 Corona wind optimization study ...... 91

4 – 4 Capacitive model developed for cell and upward pumped movement ...... 94

4 – 5 Qualitative idea of electro-convection in Dielectric silicone oil ...... 95

4 – 6 Time delay effect on electroconvection ...... 97

4 – 7 Nonlinear instability analysis from an extension of steady state convection ...... 98

4 – 8 Instability parameter and spectra of current flowing ...... 100

xii

List of Abbreviations

DEP ...... Dielectrophoresis EP ...... Electrophoresis EM...... Electromagnetic EHD ...... Electrohydrodynamics

xiii

List of Symbols

α ...... Aspect ratio β ...... Semi- vertex angle 훶 ...... Surface tension of multi-phase 휇 ...... Ion mobility 휂 ...... Dynamic viscosity 휎 ...... Conductivity 휆 ...... Viscosity ratio constant θ ...... Contact angle 휗 ...... Ionic velocity Λ ...... Relative strength of electro-convection ힽ ...... Any time scale of the system

휑퐵 ...... Magnetic flux induction 0 ...... Permittivity of vacuum 0 ...... Permeability of vacuum 휒푒 ...... Electric susceptibility 휒푚 ...... Magnetic susceptibility 휏푒 ...... Charge relaxation time 휏푚 ...... Magnetic field diffusion time 휏푒푚 ...... Transit time of Electromagnetic wave 휏푐 ...... Time to start volume instability 휇푚 ...... Dynamic viscosity of medium 휇푑 ...... Dynamic viscosity of droplet 휎푠 ...... Surface charge density

퐵⃗ ...... Magnetic induction vector 퐷⃗⃗ ...... Displacement field vector 퐻⃗⃗ ...... Magnetic field vector

xiv 퐹퐷 ...... Drag force 퐹퐸 ...... Electrophoretic force 퐹퐺 ...... Gravity force 퐹𝑖 ...... Inertia force force 퐹퐷퐸푃 ...... Dielelectrophoretic force 푅ℎ ...... Equivalent hydrodynamic radius 푇푟 ...... Transit time 푉푠 ...... Surface potential

푞푠푏 ...... Surface bound charge

푃 ...... Polarization strength T ...... Instability parameter C ...... Injection strength Ce ...... Electric capillary number

K ...... Clausius -Mossotti factor P ...... Diameter-thickness constant M ...... Viscosity ratio constant R ...... Conductivity ratio constant S ...... Permittivity ratio constant

Ch ...... Vertical displacement of deformed cell Ns ...... Deformation frequency j ...... Current density t ...... Thickness of liquid a ...... Radius of droplet c ...... DEP motion constant h...... Distance between corona electrode and ground electrode t ...... Time

xv

xvi Chapter 1

Fundaments of Electrohydrodynamics

This chapter aims to discuss a concise introduction of electro-hydrodynamics (EHD) phenomena. To align with the purpose of this thesis, the subject matter would be related to dynamics of liquids and droplets.

1.1 Introduction

Electrohydrodynamics (EHD) is the study of electro-fluid-dynamics (EFD). It is a science that deals with the studies of motion of ionized particles or molecules and their interaction with electric fields and surrounding fluid. EHD falls into wide spectrum categories of electrostrictive hydrodynamics (ESHD). Transport mechanism like: electrophoresis (EP), dielectrophoresis (DEP), electrokinetics, electro-osmosis, electrorotation sum up ESHD.

In any dielectric media, the electrostatic fields (ESF’s) create hydrostatic pressure.

Consequently, a flow is produced if the media is fluid. The direction of the flow can be controlled by electrode configuration. Flow even can be directed against electrodes capable

1

of moving them. The practical examples are EHD thrusters, EHD air ionizer, EHD cooling system where the moving systems act as electric motors.

EHD started its journey in the hands of Nicolo Cabeo in 1629, who noticed that sawdust would be attracted towards a electrified body, touch it and then get repelled.4 For Cabeo not being sure of the effect and aftermath, the first official discovery of EHD goes to F.

Hauksbee who reported the existence of weak wind blowing due to a charge. Newton renamed this weak wind as electric wind that continued for a century until it starts being known as ionic wind until it got popularity being known as ionic wind.5 Wilson could even successfully demonstrate electric wind as a driving mechanism of rapid rotary pinwheel. It took about 30 years to have the first qualitative theory of EHD from experimental observations by study of Cavallo who analyzed the motion of a fly.6 There was, later, a significant progress in Faradays work describing the wind as a resultant of collision/friction between charged and uncharged gas particles.7 It was Maxwell who first brought the qualitative analysis of electric wind from his gaseous discharge studies despite his limited ideas on gaseous electronics.8

The first quantitative study of ionic wind was done by Chattock.9 His 19th century work verified a relationship between pressure and ionic current for parallel electrode configuration. Peek later published a book on dielectric phenomena in high voltage engineering describing a big volume of information. 10 The work laid a foundation for future researchers with a vast information’s on corona effects and mechanism. The contributions of Thomas Townsend Brown while working with Coolidge X- Ray tube is also held high with his claim of mechanical force and together with P. Biefeld, his concepts for ionized particles earned the name “ Biefeld-Brown” effect.11 A point to note is brown’s 2

work has seen little scientific recognition due to his misinterpretation of the phenomenon for anti-gravity effects.

Interest in EHD rejuvenated several years later, credited to Lob, who extended Chattock’s study to other geometries.12 The thrust property all of a sudden became a core of interest and a captain from United States Air Force (USAF), named Harney, examined electrical parameters of corona discharge and its effect on some aerodynamic performance. 13

Stuetzar later extended and summarized both Lob’s and Harney’s work which earned a recognition of complete framework to that time.14

1.2 Maxwell’s Equation: Foundation of EHD

There are two limits of Maxwell’s equation: first Galilean limit of Maxwell’s equations known as Electroquasistatics and second Galilean limit of Maxwell’s equations known as

Magnetoquasistatics. Most EHD studies are conducted within first Galilean limit.

1.2.1 Maxwell’s Equation

There are four basic equations, called Maxwell equations, which form the axioms of electrodynamics. The so called local forms of these equations are the following:

⃗⃗ 휕퐷⃗⃗ ⁄ ∇ × 퐻 = 푗 + 휕푡 (1.1)

⃗ 휕퐵⃗ ⁄ ∇ × 퐸 = − 휕푡 (1.2)

∇퐵⃗ = 0 (1.3)

∇퐷⃗⃗ = 휌 (1.4)

3

Here curl is the so called vortex density, 퐻⃗⃗ is vector of the magnetic field strength, 푗 is the

휕퐷⃗⃗ ⁄ ⃗⃗ current density vector, 휕푡 is the time derivative of the electric displacement vector 퐷,

⃗ 휕퐵⃗ ⁄ 퐸is the electric field strength, 휕푡 is the time derivative of the magnetic induction vector

퐵⃗ , div is the so called source density and 휌 is the charge density.

While the above local or differential forms are easy to remember and useful in applications, they are not so easy to understand as they use vector calculus to give spatial derivatives of vector fields like curl 퐻⃗⃗ or div 퐷⃗⃗ . Maxwell equations have more complicated forms in.

The global or integral output. The good part is they can be understood by using path, surface, and volume integrals without knowing vector calculus. They are:

∮ 퐻⃗⃗ . 푑푟 = 퐼 + 퐼푑𝑖푠푝 (1.5)

⃗ −휕휑퐵⁄ ∮ 퐸. 푑푟 = 휕푡 (1.6)

∮ 퐵⃗ . 푑퐴 = 0 (1.7)

∮ 퐷⃗⃗ . 푑퐴 = ∮. 휌푑푉 (1.8)

Where

퐼 is the electric current, 퐼 = ∮ 푗. 푑퐴

푑𝑖푠푝 푑𝑖푠푝 휕퐷⃗⃗ ⁄ 퐼 is the displacement current, 퐼 = ∮( 휕푡). 푑퐴

휑퐵 is the flux of magnetic induction, 휑퐵 = ∮ 퐵. 푑퐴

It is important to realize that there are two variables to describe the electric properties of the electromagnetic field namely 퐸⃗ and 퐷⃗⃗ , and also two variables for the magnetic properties of the field 퐻⃗⃗ and 퐵⃗ . This is necessary when some materials are present with

4

oriented electric and magnetic dipoles. If the electric dipole density is denoted by 푃⃗ , and the magnetic dipole density by 푀⃗⃗ , then we can use the following definitions for 퐵⃗ and 퐷⃗⃗ :

퐷⃗⃗⃗ = 휀표퐸⃗ + 푃⃗

퐵⃗⃗⃗ = µ표퐻⃗⃗ + 푀⃗⃗ (1.9)

Here 0 and 0 are the permittivity and the permeability of the vacuum, respectively. If we are in vacuum (푃⃗ = 0, 푀⃗⃗ = 0) then the Maxwell equations can be written in the following form:

⃗ ⃗⃗ 휕휀표퐸⁄ ∇ × 퐻 = 푗 + 휕푡 (1.10)

⃗⃗ ⃗ 휕µ표퐻⁄ ∇ × 퐸 = − 휕푡 (1.11)

∇퐻 = 0 (1.12)

∇퐸 = 휌/휀표 (1.13)

Thus, we can see that in this case there are only one variable for the electric field 퐸⃗ , and another variable 퐻⃗⃗ for the magnetic field. In other words, the introduction of two more variables 퐷⃗⃗ and 퐵⃗ (or 푃⃗ and 푀⃗⃗ ) is necessary only if we have not only vacuum, but some material is also present. To determine j, P and M for a certain material we use the so-called material equations:

푗 = 휎퐸⃗ (1.14)

푃 = 휒푒휀표퐸⃗ (1.15)

푀 = 휒푚µ표퐻⃗⃗ (1.16)

5

where  is the electric conductivity, e is the electric and m is the magnetic susceptibility.

Thus, the governing equations of electromagnetism include the 4 Maxwell equations and the 3 material equations. Finally, one more equation is needed to establish a connection with mechanics e.g.

푓 = 휌. 퐸⃗ + 푗 × 퐵⃗⃗⃗ (1.17) where 푓 is the mechanical force density (force acting on the unit volume). Another possibility to establish the connection to mechanic is

휌퐸퐸 = 1/2(퐸⃗ . 퐷⃗⃗ + 퐻⃗⃗ . 퐵⃗ ) (1.18) where EE is the electromagnetic energy density, that is the energy stored by the electric and magnetic fields in the unit volume.

1.2.2 Non-dimensionalizing

If we consider a physical system of characteristic size, l, in the presence of an electromagnetic field, then depending on the phenomena we are interested, we may have a set of different characteristic times corresponding to thermal, chemical, mechanical, electrical and magnetic subprocesses taking place in the system. In addition, we also assume that there is only one characteristic time, 휏, and consequently a characteristic velocity, u.

The scales l and T will then be used to nondimensionalize the coordinates and time.

Since we are interested in electromagnetic phenomena there is always another

1 characteristic velocity, c, which is the velocity of light in the system, c = . Associated √휀µ

6

with this velocity there is a characteristic time given by the transit time of an electromagnetic wave across the system, 휏푒푚=l/c.

Now the various states of electrodynamics come with the relative strength of electromagnetic field (EM). We need to compare the relative magnitude of the electric to the magnetic field to find a scale to nondimensionalize the EM fields. For radiation fields, such as plane waves, it is well known that E = cB with E the magnitude of the electric field, c the velocity of light, and B the magnitude of the magnetic field. Also, it is well known from relativistic electromagnetism that, 퐸2 − 푐2퐵2, is a Lorentz invariant that may be positive, zero or negative. Alternatively, for those people not familiar with relativity, it may be easier to think in terms of energies. We have:

휀퐸2/2 퐸2 = (1.19) 퐵2/2휇 푐2퐵2

1.2.3 Classification of Electrodynamics Based on Maxwell’s Equation

The four Maxwell equations can be simplified omitting certain terms regarding the dynamics of the process.

1.2.3.1 Electro- and Magnetostatics

This is the condition when the charge remain stationary and there is no movement.no 휕퐵⃗ ⁄ current: 푗 = 0, no change in the magnetic induction 휕푡 = 0 , no change in the electric 휕퐷⃗⃗ ⁄ inductions 휕푡=0. Thus, basic equations of electrostatics

푗 = 0 (1.20)

∇ × 퐸⃗ = 0 (1.21)

7

∇퐷⃗⃗ = 휌 (1.22)

Equations of magnetostatics:

∇ × 퐻⃗⃗ = 0 (1.23)

∇퐵⃗ = 0 (1.24)

As we can see in statics there is no connection between the equations of electricity and magnetism.

1.2.3.2 Stationary fields (DC current)

We have already current: 푗 ≠ 0, but the magnetic and the electric fields are not changing:

휕퐵⃗ ⁄ 휕퐷⃗⃗ ⁄ 휕푡 = 0 and 휕푡=0.

In this case the Maxwell equations can be simplified to the following form:

∇ × 퐸⃗ = 0 (1.25)

∇퐷⃗⃗ = 휌 (1.26)

∇ × 퐻⃗⃗ = 푗 (1.27)

∇퐵⃗ = 0 (1.28)

1.2.3.3 Quasi- Stationary fields (e. g AC current)

We have already current: 푗 ≠ 0, but the magnetic field is changing:

휕퐵⃗ ⁄ 휕퐷⃗⃗ ⁄ 휕푡 ≠ 0 and the rate of change of electric field can be neglected 휕푡=0.

In this case the Maxwell equations can be simplified to the following form:

⃗ 휕퐵⃗ ⁄ ∇ × 퐸 = 휕푡 (1.29)

∇퐷⃗⃗ = 휌 (1.30)

∇ × 퐻⃗⃗ = 푗 (1.31) 8

∇퐵⃗ = 0 (1.32)

1.2.3.4 Rapidly changing EM (EM waves)

In this case we have to regard all terms of the Maxwell equations. There is a special situation, however, when electromagnetic waves are propagating in vacuum. In this case the following simplifications can be applied: No current: 푗 =0 (no electron beam or other particles conducting current), and 휌 = 0 (no charge in the space)

Thus, the Maxwell equations for electromagnetic waves:

⃗ ⃗⃗ 휕휀표퐸⁄ ∇ × 퐻 = 휕푡 (1.33)

⃗⃗ ⃗ 휕µ표퐻⁄ ∇ × 퐸 = − 휕푡 (1.34)

∇퐻 = 0 (1.35)

∇퐸 = 0 (1.36)

The wave equations can be derived from above equation.

1.2.4 Electro-quasistatics of moving fluids

Before discussing the relationship, we have to have some ideas on some length scale and time scale.

휀 The characteristics time for relaxation of charge due to ohmic conduction, 휏 = 푒 휎

2 The characteristics time for diffusion of magnetic field, 휏푚 = 푙 휎휇

푙 The characteristics time for transit of EM waves, 휏 = 푒푚 푐

We want to discuss the case of fluids subjected to electroquasistatic fields a little further. If we assume that the fluid is subjected to a time varying electric field of frequency 9

We add a note that the condition to convert Maxwell's equations to the set of electroquasistatics equations, is that 휏푒푚 < 휏. is true where 휏 is any characteristic time associated with electrical or mechanical processes taking place in the fluid. In particular, for a time varying electric field we may take as 휏 the period, 푇, of the electric field, and therefore we must have:

푙 푙푤 ~ ≪ 1 (1.37) 푐푇 푐

The condition w « (c/l) ensures that the magnetic field generated by the displacement current, which is of order 퐵0 ≅ 휇휀푙푤퐸0 satisfies automatically the condition c퐵0 « 퐸0.

Another condition for the physical system in order to be quasi electrostatic, is that the magnetic field due to the current density in the system, regardless of its origin, i. e. injection, dissociation or current due to particles, must also satisfy the condition c퐵0 « 퐸0.

Also, from the fourth Maxwell's equation the scale for 퐵0 ≅ 휇푙퐽0 can be considered due to the current density. Finally, we have:

푐퐵 푐휇푙퐽 0 = 0 (1.38) 퐸0 퐸0

And eventually,

휀1 퐽 ≪ 퐸 √ (1.39) 0 0 휇푙

Now most of the experiments those are conducted in the laboratory are:

푙 ≈ 10−2푚, 휇 ≈ 10−6퐻/푚, 휀~10−11퐹/푚,

So we must have

퐽0 ≪ 3퐸0 (1.40)

10

Moreover, in insulating/dielectric liquid, this condition are amply satisfied as 퐽0 are microamps/cm^2 and 퐸0 is several kV/cm.

To come to final remarks: The Maxwell equations, in EHD, reduces to

∇ × 퐸⃗ = 0 (1.41)

∇.⃗⃗⃗퐷⃗ = 휌 (1.42)

휕푞⁄ 휕푡 + ∇. 퐽 = 0 (1.43)

⃗⃗ 휕퐷⃗⃗ ⁄ ∇ × 퐻 = 푗 + 휕푡 (1.44)

∇.⃗⃗⃗퐵⃗ = 0 (1.45)

1.3 Electrical Conduction in Liquids

Conduction in liquid comes with understanding of transport and generation of free charge carriers in a fluid which is subjected to an electric field.

1.3.1 Conduction

When a d.c. electrical potential difference is applied across a fluid by means of two electrodes, an electrical current flow between them. This current is composed of two terms

• one is due to transport of free charge carriers present in the liquid,

휕퐷⃗⃗ ⁄ • and the other is the displacement current, which is given by 휕푡 .

11

The conduction current, the first term, depends on the type and number of charged species, its velocity and the chemical reactions that they may undergo. We have to mention that the current density J will refer only to the conduction current.

The charged species act in a way that there can’t be no net generation of charge in the liquid and it follows the conservation equation of the following form:

휕푞 +∇. 퐽 = 0 (1.46) 휕푡

1.3.2 Transport of charge carrier

Generally, electrons and ions are charge carriers. And electrons behave in a different way with respect to gas and liquids. The potential source of ions are ionizing collisions with the neutral molecules and ions, injection from the cathode, photoionization, secondary emission at the cathode, etc. The velocity of ions depends on the local electric field. We can safely assume that only positive and negative ions are charge carriers inside the fluid due to the reasons that most cases, electrons get trapped by electronegative impurities or molecules of fluids. It is then possible to approximate the behavior of these ions as spheres moving in a continuum, following the laws of an ideal gas of particles in the volume occupied by the fluid.

If we consider an ion of charge 푒𝑖, there exists 3 forces on it:

• The Coulomb force, 푒𝑖퐸, due to the presence of the electric field E.

12

• The friction force due to the surrounding fluid, which, in our approximation, is

given by the Stokes law, 6휋휂푅ℎ푢𝑖

where '휂 is the dynamic viscosity of the fluid, Rh the equivalent hydrodynamic radius of the ion, and 푢𝑖; the relative velocity of the ion with respect to the liquid.

Finally, we have the force acting upon the ion due to the partial pressure of other ions, which according to the ideal gas law is given 푏푦 푝 = 푛𝑖푘푇 with 푛𝑖; the number density of ions of the type i per unit volume.

Consequently the Newton’s law can be written as :

푑푢 푚 𝑖 = 푒 퐸 − 6휋휂푅 푢 − 1/푛 (∇푛 푘푇) (1.47) 푑푡 𝑖 ℎ 𝑖 𝑖 𝑖

Some simplification can show that, the velocity of an ion in a fluid at constant temperature as:

1 푢 = 휇 퐸 − 퐷 ∆푛 (1.48) 𝑖 𝑖 𝑖 푛

푒𝑖 Where, mobility 휇𝑖 = and 퐷𝑖 is the molecular diffusion coefficient. 6휋휂푅ℎ

1.3.3 Ion mobilities in liquids and gases

Due to different of structure of liquid and gases, ion mobility is different in the cases of liquids and gases. Ion mobility is related to the viscosity and follows how the viscosity changes in liquids and gases. The momentum transfer happens, in gases, across a plane by the molecules which are above and below the plane within a distance of mean free path and this momentum increases the viscosity. But for liquid, the momentum transfer is

13

carried by the molecules which are adjacent to the plane due to their relative closed packed positions. For gases, at constant pressure, the momentum transfer rises due to increase of temperature as a result of that each velocity of molecule follows 푘푇1/2. In other words, viscosity increases with increased temperature and consequently mobility decreases. The pressure has constant effect on viscosity on constant temperature i.e, viscosity does not increase even we increase the pressure. The reason can be related to the fact that even we can increase the no. of molecules participating in momentum transfer, but their mean free path decreases accordingly.

For liquids, viscosity is inversely related to temperature. So we can increase the mobility of ions in liquids by increasing the temperature. Also, if we consider liquid incompressible, the mobility is independent of pressure.

Now what happens if the fluids are in motion?

The ions would be advected along with the motion of the fluid. Consequently, the charge carrier would be moving in the liquid with a flow velocity u. So, we will end up having the expression:

1 푢 = 휇 퐸 − 퐷 ∆푛 + 푢 (1.49) 𝑖 𝑖 𝑖 푛

Now the expression of current density is the multiplication of velocity with the charge.

So the expression of current density is:

퐽 = 퐽′ + 푞푢 (1.50)

Where 퐽′ is the current density when there is no liquid motion.

The charge carriers, discussed above, in most cases, originate from either dissociation or injection. Based on the context of this research, only injection method would be highlighted

14

1.3.4 Ion Injection:

It is a process where the ions of same polarity as the electrode are created and injected into the fluid. This injection can happen from each of the electrodes present in the system meaning there can be unipolar injection or bipolar injection. In gases, the Schottky emission or field emission are the dominant mechanisms. It is to mention that, current is limited to flow owing to space-charge limitation of the electric field. The easier way to interpret is that, if the electric field is above a certain a threshold value, the molecules of the gas will be ionized by the high energetic electrons resulting to large number of positive and negative carriers. It is very likely to happen breakdown in the gas if the field is uniform.

But in any non-uniform field like needle or wire, the region of ionization is very limited to the neighborhood with smaller curvature. The space charge is created between the electrode because of drifting of ions of same polarity to opposite ends. This space charge decreases the value of electric field. When the field values come down to a critical value, it is onset of ionization or corona onset. Eventually when the space charge has drifted to the opposite electrode, emission starts. There will be an oscillation situation till it reaches to a stationary equilibrium condition where the value of electric field is constant and equal to onset of ionization. (Peeks law).10

In liquids, it is very unlikely to happen the field emission unless there is an extensive electric field. If there is field emission in liquids, the electrical double layer is destroyed and there is created a tunnel through which the electron can move back and forth between the electrodes. Nonetheless, in most EHD problem with practical interest, the electric field

15

is not strong enough to create the tunneling. So there will be the existence of electrical double layer and it will mediate the electronic transfer at the interface.

Now in non-polar liquids, the ion injection process may be described by two processes:

The ions, first, are to be created at the electrodes and those ions are then escaped out and directed to a certain direction.

1.4 Polarization of Dielectrics

Dielectrics can be considered as substances whose resistivity is greater than 106 Ohm/m.

Under an electric field, the nuclei are pushed with field that increase positive charge on one side while electron clouds are pulled against to make an negative charge on other side.

The phenomena is known as polarization and there are two methods by which dielectrics are polarized: stretching and rotation.

Generally polar molecules (water) stretch and rotate where non-polar molecules (silicone oi, air, liquid gases, kerosene etc.) only stretch. In polar dielectrics, there is their own dipole moment and in non-polar dielectrics, molecules have a symmetrical distribution of positive and negative charges which result to zero net charge. Now under an external electric field, all molecules stretch whether they rotate or not. One should remember that stretching and rotation are not end of the story for polarization. The microscopic electrostatic strain in response to a macroscopic electrostatic stress can be termed as polarization of dielectric material. When the external field is applied to a dielectric, it can't cause charges move macroscopically, but it can result stretching and distorting them microscopically. They can be pushed into un uncomfortable position and when released, they are allowed to fall back

16

to a relaxed state. So we see that eliminating the stress does not release the strain and this

property make it different to stretching an elastic body like spring. Records reveal that

some insulators will remain in their polarized state for hours, days, years, or even centuries.

Different materials polarize to different degrees- a property that is expressed as electric

susceptibility represented by 휒푒. Also, the stronger the Electric field, the stronger the

polarization. So, we can use a proportion constant,휀0. Together we can write:

푃 = 휀0휒푒퐸 (1.50)

E→ Type equation here.

E=0 E≠0

Figure 1-1: Zero dipole moment in absence of E (left). Induced dipole moment in presence of E

1.4.1 Interfacial Polarizations:

If there is a non-uniform composition, like there is interfaces between two layers of

different dielectrics. It can be solid-liquid or liquid-liquid. For such cases, ions would be

stopped at the interface and this charge give rise to interfacial polarization. The effect goes

after the name “Maxwell-Wagner” effect.

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No free Charge Free positive charge

(a) (b) Air Air 퐷1,푛 퐷1 퐷1,푛 퐷1 퐷1,푡 퐷1,푡

Liquid Liquid 퐷2,푛 퐷2 퐷2,푛 퐷2 퐷2,푡 퐷2,푡

Interface condition

퐷2,푛- 퐷1,푛 = 휀0휀2퐸2,푛 − 휀0휀2퐸1,푛 = 푞푓 퐷2,푛- 퐷1,푛 = 0 퐷2,푡- 퐷1,푡 = 0 퐸2,푡- 퐸1,푡 =0

Figure 1-2: Effect of dipole potential on interface

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Chapter 2

Corona discharge phenomena

Concepts and application of corona discharge comes with an understanding of ionization techniques and plasma sciences. The purpose of this chapter is to highlight some insights of plasma and ionization techniques

2.1 Plasma

Plasma is the fourth state of matter in addition to solid, liquid and gas. The definition of plasma was brought metaphorically by S. Eliezer in his book “The fourth state of Matter:

An introduction to plasma Science:

“We are witnessing a dance competition. The conductor and the orchestra are ready to begin. The participants are well organized in pairs in a nice symmetrical way. This first phase is our solid—the competition has not yet begun, and the atmosphere is cold. As the music begins and the pairs perform their first dance, a slow, we enter into our second phase—the liquid; the temperature is low as they dance to the soft music. The music picks up tempo. The dancers are doing the rock and roll and we enter the third phase—the gas; the temperature is getting warmer. Now the music blares as the pop tunes begin. The girls

19

leave their partners and everyone is jumping and dancing by himself or herself. This is the last phase—the plasma; the temperature is very hot and everyone is jumping around all over the place. This example allows us to make an analogy in which the conductor is the physicist in the laboratory; the music is the ‘heat’ which changes the phases from solid, to liquid, to gas to plasma; and our dancers are the different particles of matter. The pair represent an atom (or molecule) which is the basic unit composing solids, liquids and gases.

The girls represent electrons while their partners symbolize ions.”15

When blood is cleared of its various corpuscles there remains a clear liquid, named

"plasma" by the great Czech medical scientist, Johannes Purkinje (1787-1869). The use of the term "plasma" for an ionized gas started in 1927 with Irving Langmuir (1881-1957), a 1932 Nobel Laureate, whose achievements ranged from the chemistry of surfaces to cloud seeding for promoting rain. The idea initiated from Langmuir’s work place in

General motor while he was working with electronic devices based on ionic gases. He found a correlation between the way the electrified fluid carried high velocity electrons, ions and impurities and the way blood plasma carried red and white corpuscles and germs.

Ever since then, the development of plasma has been carried successively through different means. The advent of radio brought ionosphere while astrophysics found that

99 % of the universe is plasma. The quest for alternative energy sources took humankind to thermonuclear fusion that needs enormous temperatures and pressures, like those found at the center of the Sun. When satellites discovered the radiation belt and began exploring the magnetosphere, space plasma physics, a fourth dimension opened with the success of satellite. Plasma can be categorized on the basis of temperature, thermodynamic 20

equilibrium, pressure and degree of ionization and each of them can be interpreted on electron temperature and plasma density.

Figure 2-1:The figure here illustrates where many plasma systems occur in terms of typical density and temperature conditions. Plasma temperatures and densities range from relatively cool and

tenuous (like aurora) to very hot and dense (like the central core of a star.1

Plasmas are common in nature and found nearly everywhere. All of the following are examples where plasmas are to be found:

• Lightning

• The Sun—from Core to Corona

• Fluorescent Lights and Neon Signs

• Nebulae - Luminous Clouds in Space

• The Solar Wind

• Primordial Fusion during the evolution of the Universe

• Magnetic Confinement Fusion Plasmas

• Inertially Confined Fusion Plasmas 21

• Flames as Plasmas

• Auroras - the Northern and Southern Lights

• Interstellar Space - it's not empty, it's a plasma!

• Quasars, Radio galaxies, and Galaxies—they emit plasma radiation and

microwaves

• Large Scale Structures of Galaxies—their filamentary and magnetized!

• Dense Solid-State Matter—when shocked by nuclear explosion or earthquakes,

emit both light and radio emission.

2.2 Ionization of air

A gas was thought to be ideal electrical insulator, prior to the 18th century, that electric charges of either sign could not be made to pass through it and that electric currents could not flow in a circuit which contained a gap. In 1750, Coulomb explained how two metal spheres which carried opposite electric charges lost their charges by electric leakage through the gas and not by leakage along the surface of insulators in the torsion balance. It took a lot of experiments to validate his claim, hence afterwards, the electrical conductivity of gas was established. There are various methods of way air or gas can be ionized. The methods heavily employed are Thermal ionization, Photo ionization, Particle Impact ionization, Nuclear emission and Electric field ionization.

2.2.1 Thermal ionization

It is a surface ionization or contact ionization process atoms are desorbed from the hot surface. The energies of gas particles can be made so high, by raising the temperature, that

22

they can induce ionization in the medium. The process is limited due to the byproducts of air contaminants.16

2.2.2 Photo ionization

Photoionization involves a radiative bound-free transition from an initial state consisting of n photon-sand an atom, molecule, or ion in a bound state to a final continuum state consisting of a residual ion and m free electrons. It can be shown as:

푛ℎ휈 + 푋 = 푋푚+ + 푚푒− (2.1)

Though it works on the argument that a photon with energy (ℎ휈), higher than the energy of the the atom, can ionize the individual atom, the ionization possibility reduces if energy of photon is much higher.

Figure 2-2:Photoionization is the process that makes once-invisible filaments in deep space glow1

2.2.3 Particle impact ionization

An atom can be struck by an electron or ion. An imparted electron might get absorbed to

23

an atom or can cause atom losing another electron. Subsequently the released electron can lead to secondary ionization. The heavier ions needs accelerator or strong magnetic

/electric field to accelerate in attaining required ionization energy. The target atom generally loss or gain charge depending upon the amount of energy transferred. The threshold energy has to be greater than eV where e (1.6x10-19 Coulombs)

2.2.4 Nuclear emission

The process takes place in the form of fission and fusion. Hydrogen would emit 퐻+ and

퐻푒+ ions under action of fusion. In fission, a large heavier atom split into smaller species and act as a source of secondary ionization. Due to sensitivity of radio activity, the reaction can not be performed in any arbitrary environment.

2.2.5 Electric field ionization

An ionized electrode can affect the gas. The constitutes of the gas attains or lose charge when they are in close proximity of the electrode. The factors controlling this phenomenon are strength of electric field, geometry and shape electrode, configuration. There are a minor effects of environment factors like temperature and humidity and pressure.

An increased intensity can cause the breakdown of the gases and discharge happens in the form of arc. There is a heavy flow of current and higher dissipation of energy. The output can be so intense with a potential threat to damage the appliances despite its high yielding of ion generation. Contrary to it, corona discharge is a subtle process with lower density ionization at expense of few mW power, making it a lucrative subject of interest to academia and industry. 24

2.3 Corona discharge

Corona discharge is a non-local thermodynamic equilibrium (non-LTE) plasma which may be in air atmosphere or in atmosphere of various inert or active gases.17

2.3.1 A brief history

The term “corona” comes from the French word crown. The history of corona is very ancient with an perception of supernatural properties attributed to it. Corona had an interesting name by “St. Elmos’s fire, in Europe, after St. Erasmus, the patron saint of sailors as it the sailors often found it on top of masts and sails of ships in the form of bluish- white flame, after a thunder storm, and hence seen as good sign of gods. Even names like

Julius Caesar, C Darwin, Columbus are found to mention of its existence through their historic voyages. “The tempest” by William Shakespeare is found to carry it between its lines.

Corona effect is also known as crown effect, that appears when electric potential exceeds a critical value without development of Electric arc. The crown effect, 50 years ago, drew a large audience in the Western World, rediscovered by a couple of scientists, the

Kirlians.18 This technique based on the Corona Effect is in tune with a classic theory of physics about the electromagnetic and electrostatic fields of energy. From 1860, this effect was well-known as the "Lichtenberg Effect". A Russian scientist Narkiewicz, in 1889, formulated the basic principles while French photographers, Durville, in 1880 and Baraduc

(in 1896) took the first pictures.19

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2.3.2 Mechanism

Corona discharge is a resultant of chain reaction under a very strong electric field:

Electrons in air collide with atoms with high enough energy to ionize them. This high energy is the ionizing potential of the particular atom /molecule of gas, expressed in eV.

The opposite charged species, accelerated by Electric field, will move in different directions preventing their recombinations. With higher charge/mass ratio for electron, they are likely to gain high energy from their accelerated speed, making them capable of creating another electron/positive ion. The reaction takes place in following form:

퐴 + 푒 = 퐴+ + 2푒 (2.2)

Figure 2-3: Electron avalanche formation

The extra electron liberated ( 2푒 − 1푒 ) will always impart certain energy to its colliding particle, even it does not have the required ionization potential, in the following form:

퐴 + 푒 + 퐾퐸 = 퐴∗ + 푒 (2.3)

Also, electrons, thus created undergo through a chain reaction called electron avalanche.

Both kind of corona, either positive or negative, rely on electron avalanches. While 26

electrons are attracted inward toward nearby positive electrode and ions are repelled outward for positive corona, its vice-versa for negative corona.

The glow of corona happens due to recombination of electrons with positive ions to form neutral atoms and getting back to ground states. The kinetic energy released in (2.3), due to change of energy state emerges as glow discharge in form of photons. The photon get absorbed (when its energy is below ionization potential) by other atoms, otherwise it will help generating one/more electron maintaining a chain reaction. The photons thus maintain the state of avalanche.

Figure 2-4: Glow of corona

There is a significant influence of wind on redistributions of ion cloud which impacts the emitted current.20 The wind not only increases the corona current but also localizes the

27

corona. At outer edge of corona, where the strength of E. field is too low to transmit energy capable of creating new species. The ions here move freely through the air.

Corona is found to occur at certain voltage, known as corona threshold voltage, in the forms of spots/brushes/streamers etc. Above threshold voltage, current rises against voltage proportionally maintain Ohmic regime. Outside this region, there is breakdown potential creating sparking or arcing.

2.3.3 Corona properties2

A corona discharge is a gas discharge process where the ionization is limited to very high field regions by geometric configuration. The polarity of electrodes, either positive, negative, bipolar, AC, DC, defines the geometry. The corona current can be of unipolar or bipolar depending on whether one or both ion polarities are taking part in the actions.

A separating feature of corona is the presence of a low field drift region joining ionization regions with passive electrodes (eventual electrodes). Corona species, ions, electrons, drift and react with the neutrals only in the drifting regions. It is to mention that both energy and density remains too low that they cannot react with other ionized corona species. There can not be any plasma in unipolar conduction corona. Characteristics like and corona voltage- current (V-I), current density (J) distribution will be determined by space charge field in drifting regions.

There are two most different types of DC coronas in air or most other gases: Unipolar conduction corona and bipolar (streamer) conduction coronas.

28

Figure 2-5: A point-plane configuration. The outer limit of ionization is ` marked by α = 0 and the production of electrons by ionisation balanches the loss of attachment.2

Unipolar one also go with the positive glow coronas, negative glow coronas, negative

Trichel pulse coronas. The ionization region for all remain very concentrated to active electrodes. The ions which are created exactly follow the kind of polarity of the electrode; positive ions from positive electrode and vice-versa. The non-uniformity of field distribution reduces with higher current. Also, the higher voltage increases the electron/negative ion ratio by sharply increasing the drift region field. We observe that there exists a rapid pulsation of ionization region that may cause sputtering resulting an affect in drift region.

On the other hand, streamer (bipolar) corona, at higher current with positive polarity, produces a conduction plasma faster than the plasma can be absorbed by point electrode. 29

A plasma filament, consequently grows out of point to the plane that carries plasma along with it, hence a ionization region ahead of it, at speed of atmospheric air density air. 10^6 m/s. Subsequently, a cathode spot may be produced, when streamer hits the plane, producing a plasma channel. The channel, eventually, dies out or reproduces to thermally ionized spark channel. A point to note down is both form of corona may co-exist together.

A 45 휇퐴 positive corona might consist of diffusively distributed 15 휇퐴 continuous unipolar current over the plane and a 30 휇퐴 streamer current hitting the plane opposite of the point.

Figure 2-6: Main reaction regions and reaction channels.2

The shape of electrode implies effect on corona effect highly. The electric field intensity,

E expressed as:

퐸 = 푄/4휋휖0푟 (2.4) 30

So, with r decreasing, E increases and eventually the process of avalanche, as described above, happens.

Moisture content in air initiates breakdown at lower potential by increasing conductivity in it. Bedsides common air components: nitrogen, oxygen, argon, carbon-di-oxide, water

+ − 2− + − vapor, there are particulate like dust or pollen. Ions of oxygen (푂 , 푂 , 푂 , 푂2 , 푂3 , ) combine to form ozone. Ions like OH, O, H of both positive and negative charges comes from moisture content. The supposed early breakdown is found to happen during thunderstorms making frequent lightning. There are also free electrons in ionized air but electrons are absorbed by heavier particles due to their short life spans, resulting more electrons. Like moisture, there is effect of dust particles in ionization explained by Malter effect.21

Some of the conclusions about corona discharge are:

(a) Most of electrical energy input (about 90-95 %), for unipolar positive corona, goes

into neutral gas only leaving rest for directed gas motion

(b) Though initially chemical inputs, excitation energy, thermal energy are transported by

corona wind, it is charge that is the most important quantity transported to passive

electrode for unipolar corona.

2.3.4 Glow discharge vs Arc discharge vs Corona discharge

Different kind of discharge are found due to passing of current through gas as shown by following figure.22

31

Figure 2-7: V-I characteristics of different discharges

So corona discharge happens in dark discharges of Townsend region at high electric fields near sharp points, edges or wires before electric breakdown. For low current, there happens a dark corona while at higher currents, corona discharge can be of glow discharges.

Generally arc discharge is high power discharge with high heat.

The heating resulted by corona are is not as severe as arc. While corona dissipatres power in range of mW, an arc discharge consumes hundreds or thousands W of power. In most of dark discharge cases, gas is ionised by a radiation source like ultraviolet light or cosmic rays. In arc discharge, gas is ionised by any kind of thermal means and electron leaves the cathode by thermoionic emission and field emission.

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2.3.5 Application of Corona discharge

Corona can be used for chemical synthesis of many chemical products. Ozone, the most important one is used for treatment of water in purification. Ozone, having large oxidation oxidation power, carries high potentials to be used in paper and textile industries to engineer the surface energies.23

Modifying polymer surfaces using atmospheric pressure air corona is of great industrial importance. The process introduces polar groups that see a significant improvement on surface energy, adhesion properties and wettability. Ever since the introduction of corona discharges to modify upper layer of polymers in 1960s, the technique has seen a wide range of application with target goals of:

(1) To increase the inherent low surface energy of polyolefins when they are used as

substrate for effective adhesion.

(2) To increase fiber- resin adhesivity of Polyester Fabrics.24-25

(3) To improve anti-fouling properties of ultrafiltration polymer membrane for

emulsion separation.26-27

(4) To enhance permeability and selectivity of modified membrane for gas separation

application.28-29

(5) Disinfection and sterilization of medical packaging materials using impact of

ozone.30

Mobilities of ions can be used in “Plasma Chromatograph”- to diagnose gas in detecting contaminants. The radicals of corona discharge can be used categorizing them on basis of

33

similar properties. Also, it is a small paradox that many of the gases used in corona ionization are subject of heavy usages for electrical insulation.

Corona discharge hold huge prospect in electrostatic applications. There remain ions of one sign in drift region for unipolar corona and consequently the application of corona discharge can be extended as chargers in electrostatic apparatus like voltage generators, precipitators, paint guns, fertilizer projectors etc.

In semi-conductor industry, this discharge properties can be used in device manufacturing, in failure analysis, in quality control of insulators, and in understanding electrical properties. The technique of generating ions via this process is becoming a reliable subjects of ion propulsion. On that note, EHD thrusters, Lifters or any other ionic wind devices see an application of corona discharge mechanism.

2.3.6 Corona discharge research

It is a history of about 300 years when corona discharge created EHD flow was discovered, but until recently of few decades extensive research is going on to comprehend this complex phenomenon.

Adamaik et al studied corona discharge electrostatic precipitator using a single wire and parallel collecting plates.31 Ever since Brown proposed an EHD lifters with a thin tungsten wire, researchers are continuously looking to analyze the space charge in corona system between the electrodes.31-34

Corona discharge has seen a wide range of researches in EHD gas pump fields due to promising applications of EHD phenomenon. A sliding discharge type EHD gas pump with

34

a discrete saw-toothed- plate electrode against conventional plate electrode is shown to generate higher gas flow velocity.35 Qiu et al showed the use of serial staged EHD pump , that increases the active area of gas pump, configuration to increase the velocity.36 In microelectronics, an EHD push-fan-type gas pump with non-parallel electrode configuration is studied for advanced thermal management.37 Other reported configuration

(a)

(b)

Figure 2- 8: (a) EHD lifters for levitation. (b) Forces acting on levitation.3

35

like needle-cylindrical, wire rod, needle ring clearly show the continuous pursuit of researchers to explore corona discharge studies.38-40 The capacity of corona wire to suck dust particles in any harsh environment like Mars is studied by Mazumder et all, Zhao et al.41-43

Figure 2-9: A Martian particle analyzer.3

With growing interest, people have come out with some other applications of corona discharge involved EHD like:

• EHD enhanced water evaporation.44-45

• Free convection heat transfer.46

• Microelectronics cooling.47-48

36

• Ionic breeze air cleaners.49

• Automobile engine combustion and diesel exhaust treatment.50

• Ignition of fuels in ramjets in supersonic air-propane mixtures.51

• De-icing.52

• Increasing efficiency of catalytic converter in gasoline/diesel engine.53

• Reducing drag over flat surface.54

3 Figure 2-10: Different configuration of EHD gas pumps. 37

Like the heavy usages of corona discharge in gas pump, the technology using liquid has also embraced this ionisation process to manipulate , control and achieve desired goals.

The purpose of my work to is to analyze such effects, discussed in the Chapetr 3 and

Chapter 4.

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Chapter 3

Dielectrophoretic motion of conducting droplet in low conducting medium

Use of Electrical field, di-electrophoresis (DEP) particularly, for droplet-based transport system has surfaced immense promise to chemical and bio-medical applications for no moving parts and di-electrophoretic nature of particles. No surprise to exponential rise of number of publications for last 15 years, however, patent numbers which do not correspond to that tally is transcending the importance of exploring alternative paths. We herein present a novel method of DC-DEP via atmospheric air corona discharge unlike to conventional AC source. A micro-controlled 3-D platform is built that can manipulate both the translational and vertical movement of droplet through successive switch on-off of array of corona and ground electrode. The feasibility of the platform is investigated by carrying experiments with conducting droplet in different liquid medium of low conductivity. Due to intricacies of the coupled electrohydrodynamic (EHD) system, separate studies is carried both for carrier and medium. We have also carried mathematical analogy to validate our experimental findings. The di-electrophoresis (DEP) of flow medium is visualized by distributing Electric field lines through solution of poisons equation where the dynamics of fully submerged droplet motion is modeled by estimating

39

natural characteristic coefficients of non-linear equations. The velocity measuring technique undertaken not only relate the electrohydrodynamic properties between droplet and medium, but also depicts the potential of it as characterization tool.

3.1 Introduction

Biology, material sciences, medicine, petroleum - what they have in common? An underlying method of characterization through manipulation of motion of small particles- a technique that has connected the common dots among them apart from their significant applications in our daily lives. From colloidal dispersions of μm particle in another liquid to mm droplet coalescence-particles are trapped, fractioned, actuated, manipulated. Droplet based transport has some advantages over traditional continuous flow systems due its compatibility with wall less structure and higher utilization of sample. Methods like Air pressure, Thermo-capillary, Electrochemical, Structured surfaces, Photochemical are being used to actuate droplet under wide range of purposes.55 The complementary significance of electricity to control shape and size of any droplets on any substrate, ever since the work of G Lippmann in 1875, is continuously fueling the thrust to explore.56 Moreover the success of electro-hydrodynamics (EHD) particularly in electrospray, ink-jet printing, transport sciences is feeding ground to the urge of fundaments and applied aspects of EHD.

The electrical modeling of particle/cells and medium, thanks to the integrated circuit (IC) production technology, has surfaced a great promise of understanding behavior by studying electrical properties such as permittivity and conductivity. It exploits two electrical phenomena: Electrophoresis (EP), a both polarity and charge dependent mechanism, and

40

Di-electrophoresis (DEP) whose motion is independent of Electric field (E) polarity. So,

EP is limited to the condition that particles have to be opposite charged or be same charged possessing different amount, that is different charge-to-mass ratio. Consequently, aggregation is likely to happen for opposite charged particles when they are dispersed in the medium. For same polarity particles with different amount, there should be significant separation length owing to very higher voltage to ensure the same E, making it less feasible to operate. On top of that, constant net charge is a paradox as particles will undergo dynamic charge transfer with surroundings, leaving little room to lean on EP for separation/such application. It is of no surprise, therefore, how DEP has emerged as an alternative answer for cell manipulation and an exponential rise of number of publications for last 15 years arguably speaks of it.

There are different methods of DEP where creating different electrode configuration is the most recurrent approach to create a non-uniform electric field.57-58 The reported configuration in literature so far can be listed as ratchet electrodes59, quadruple electrodes60, castellated electrodes61, concentric electrodes62-63 for direct DEP; spiral electrodes64, parallel electrodes65 for travelling wave DEP. All these configurations can offer at best two-dimensional (2-D) motion if not entirely limited to one -dimensional (1-

D) motion. Another observed trend lies in the fact that, non-uniformity in the field is created by alternating current (AC) source. With continuation of previous emphasis on potential effectiveness of DEP on a circumstantial scenario, we can also track that number of patents has not been proportional to number of publications.66 There is, therefore, an inevitable urge to pursue different paths to make it a more established science.

41

So this chapter aims-(1) To propose a contactless DEP actuation via ion injection. (2) To imply EHD phenomena in understanding the effect of carrier fluid and particle size in motion. (3) To investigate liquid layer as pseudo-electrode in comparison to metal electrode. (4) Exploring the potential effectiveness of this ionization technique in scopes of droplet motion leading to coalescence formation.

With above target goals, we have carried out experiments with different droplet radius in different medium. We have carried background study of AC voltage source, in comparison to DC, with low frequency, and same voltage ranges for this kind of ion injection process.

In addition, Newton’s equation of motion was formulated considering for low Reynolds number flow to model the motion and deformation of the droplet. The second order electric field distribution appears close approximation for DEP force. The mobility coefficient is found to deviate in the regime where contact charging initiates electrophoresis to DEP. The mathematical model is found to maintain same order of accuracy with experimental results.

3.2 Experiment set up

The experiment is a good embodiment of digital fluidics system that handle liquid in droplet forms. It has several units as follows:

3.2.1 Sequential voltage source

We constructed a microcontroller system that applies a sequential voltage signal to control the motion of droplets Figure 3-1. A high voltage supply is connected to a component

42

board formed of relays and pins. The pins are connected to terminal blocks joined with electrode through electrical switch according to their polarity. The applied voltage is sequenced through a program built in Arduino and is operated using personal computer. A voltage in the range of 2-10 kV was applied by a DC power supply with the help of a 10 kV TREK Model 10/10B-HS high -voltage amplifier. Injected ions create a variable corona current which is computed by ammeter.

3.2.2 Electrode device

The platform has 2 segments: the upper one comprises of a single needle electrode capable of ionizing the air thus creating the corona discharge and a bottom chamber holding the array ground electrodes, There were two sets of bottom electrode devices used to conduct the experiment. A transparent rectangular acrylic test cell (Figure 3-1.a) internal dimensions 50 ∗ 50 ∗ 25 mm3 is made to hold an array of 3*3 matrix copper electrodes with diameter 1.4 mm. To see the EHD effect on periodic droplet closely, we had another simplified version (Figure 3-1.b)with just one copper electrode on substrate.

3.2.3 Experimental procedure

The non uniformity of DEP is understood by observing carrier droplet in another medium of following intrinsic and extrinsic property.

43

Carrier Radius, Conductivity Delectric Viscosity constant 휂 (cst) a (mm) 휎 (S/m) 휀 Deionized water 1.001 2.4*10^-6 78.8 1 0.89 2.4*10^-6 78.8 1

Table 3.1: Property of water droplet

Medium Thickness Conductivity Delectric Viscosity constant 휂 (cst) t (mm) 휎 (S/m) 휀

Silicone oil 10 2.4*10^-12 2.75 3000 Silicone oil 10 2.4*10^-12 2.75 450

Table 3.2: Property of silicone oil investigated

First the distance between the tip of needle electrode and upper layer of medium fluid is decided by doing experiments as the ionized air here act as source of energy and air thickness has an effect on efficiency. From our own results, supplied as supplementary, at air thickness of 15 mm, The drop-dynamics is observed using Nikon stereoscopic zoom microscope (Nikon, USA). To record the movement and deformation of the drop, a high- speed camera (Phantom V12.1, Vision Research, USA) is mounted on the microscope. The drop is illuminated using Nikon C-FI230 Fiber illuminator (Nikon, USA). To conduct the experiments, the container is filled with continuous phase. A drop of dispersed phase is carefully injected between the electrodes. DC Electric field is then applied and the voltage which is varied using a function generator is amplified using an amplifier. The drop motion

44

(a) (c)

(c) (d)

퐹푑푒푝 퐹푒 퐹푔 10

퐹푑푒푝 퐹푔

퐹푑

30

Figure 3-1: Schematic diagram of experimental arrangements for droplet manipulation. (a)Multiple ground electrode. (b)Single ground electrodes(c) Schematic of ion generation from tip of needle and their direction of movement. (d) Direction of all the forces acting on the droplet two different locations.

45

is recorded at 4× optical magnification and at a frame speed of 10-25 frames per second.

These images are analyzed using the image processing software ImageJ.

Table 3.3: Physical and Electrical property of the system

3.3 Mathematical modeling

The forces acting on the droplet under a non uniform Electric field are as shown (Figure 3-

1.d). At any moment of motion, at z-direction we can write :

∑ 퐹푧 = 0

퐹퐷퐸푃 + 퐹퐷 − 퐹퐺 − 퐹퐸 − 퐹𝑖 = 0

Where 퐹퐷퐸푃, 퐹퐷, 퐹퐺, 퐹퐸, 퐹𝑖 are dielectrophoretic, drag, electrophoretic and inertial forces. We can develop expression of 퐹퐷 on the idea of the polarization effect in non- 46

uniform electric field. In the non-uniform electric field, one side of dipole is exposed to higher electric field than other. In this case the net force is not zero and dipole moves toward the place of the greatest electric field. It can be expressed by

퐹퐷퐸푃 = 휇 ∙ 훻퐸 ……………………………………………………………………… (3.1)

The induced dipole moment, when drops exposed to a strong electric field, can be expressed as:

휇 = 휈 푃⃗⃗ ……………………………………………………………………………… (3.2)

Where 푃 is a polarization or moment per unit volume and 휈 is a volume. For spherical 4 drops 휈 = 휋푎3 and 푃⃗⃗ = (휖 − 휖 )휖 퐸⃗⃗⃗⃗⃗ where 푎 is a drop radius and 퐸⃗⃗⃗⃗⃗ is the internal 3 푑 푐 0 푖푛 푖푛

3휖푐 field in the sphere and it can be found from 퐸⃗⃗⃗푖푛⃗⃗ = 퐸⃗ , 휖0 is the permittivity of free 휖푑+2휖푐 space, 휖푐 is the dielectric constant of the continuous phase, 휖푑 is dielectric constant of the disperse phase and 퐸⃗ is an external electric field. Substituting in (3.2) we can have dipole moment for the drop:

3 (휎푑−휎푐) 휇 = 4휋푎 휖0휖푐 퐸⃗⃗⃗ 푖 ------(3.3) 휎푑+2휎푐

(휎푑−휎푐) Where is Clausius-Mossotti factor and replacing this with 퐾푐, we get 휎푑+2휎푐

3 휇 = 4휋푎 휖0휖푐퐾푐퐸⃗⃗⃗ 푖 ------(3.4)

Combining (3.4) with (3.2) we have,

3 (휎푑−휎푐) 퐹⃗⃗⃗푑푒푝⃗⃗⃗⃗⃗ = 4휋푎 휖0휖푐 퐸∇퐸 ------(3.5) 휎푑+2휎푐

3 (휎푑 − 휎푐) 2 퐹푑푒푝 = 2휋푎 휖푐휖0 훻퐸 휎푑 + 2휎푐

The electric field lines from needle-plane electrode resemble the second order polynomial shape electrode geometry resulting

47

(푉 −푉 )2 훻퐸2 = 8 2 1 √푧2 + 푥2------(3.6) 4푑4 where z, x is the location of the droplet and d stands for radius of the region which is medium thickness for our case. Motion being only in z-direction, (5) and (6) results to

2 3 (휎푑−휎푐) (푉2−푉1) 퐹푑푒푝 = 4휋푎 휖푐휖0 4 푧------(3.7) 휎푑+2휎푐 푑

Hadamard-Rybczynski solution of drag gives:

푑푧 퐹 = 4휋휇 푎푐( ) ------(3.8) 푑 푚 푑푡

For any drop suspended in another medium, the gravitational force can be written as

4 퐹 = ( ) 휋푎3푔휌------(3.9) 푔 3

Electrophoretic force, 퐹푒 only when the droplet touches either the top layer or the bottom electrode can be modeled as time response in the form of 퐹푒(푇) (please see results and discussions for explanation)

Considering all expressions of forces, we can conclude to

퐹푑 ∝ 푣푒푙표푐푖푡푦 = 퐾1푣

퐹푑푒푝 ∝ 푑푖푠푡푎푛푐푒 = 퐾2푧

퐹푒 = 퐹푒(푡)

퐹푔 = 푐표푛푠푡푎푛푡 = 푆

푑2푧 퐾 푣 − 퐾 푧 − 푆 − 퐹 (푡) = 푚 1 2 푒 푑푡2

Rearranging the above expressions, we get

푑2푧 푑푧 푚 +퐾 + 퐾 z+ S=퐹 (푡)------(3.10) 푑푡2 1 푑푡 2 푒

Taking use of Laplace transform, this differential equation can be converted to algebraic form. If we consider that the droplet was sitting at rest at t=0, we get the following form in s domain:

2 [M푠 + 퐾1푠 + 퐾2]푍(푠) = 퐹푒(푠) 48

Or B(s)Z(s)= 퐹푒(푠)

We may define a system transfer function

퐻(푠)=1/ 퐵(푠)

푍(푠) 1/푀 = = 퐾1 퐾2 ------(3.11) 퐹푒(푠) 푠2+( )푠+( ) 푀 푀

At this point, we got the characteristic equation of the system in the form of denominator of

Eq.3.11.

Eventually we can find the roots as:

퐾 퐾 2 퐾 푐 = -( 1) ± √(( 1) − ( 2)4) 1,2 푀 푀 푀

=-ζ ±√(ζ2 − 1)ώ …………………………………………………………….. (3.12)

The solution of Eq. 3.12 describes dynamic behavior of the droplet. The coefficients can be found using the Eq. 3.7 and Eq.3.8. Non dimensionalizing against 퐹푒(푡), this system of equation are solved in MATLAB-Simulink to comprehend the behavior of droplet.

In addition, in absence of electrophoresis, the droplet is assumed to move with constant velocity, and, thereby, expression 3.10 converts to

푑푧 퐾 + 퐾 z+ S= 퐹 (푡)……………………………………………...... (3.13) 1 푑푡 2 푒

Eq.3.10 is a linear-homogenous constant coefficient.

At initial condition, 푦 → 푦0, 푡 → 푡0 the problem reduces to initial value problem which has a solution

The integrating factor of the problem (1) is in the form 퐼. 퐹 = 푒∫ −푝푑푡 = 푒−푝푡

Multiplying the I.F with Eq. 3.1 results to

푑푧 푒−푝푡 − 푝푦푒−푝푡 = 푒−푝푡 푑푡 49

∫(푦푒−푝푡)′ 푑푡 = ∫ 푝푒−푝푡푑푡

푏 푦푒−푝푡푑푡 = − 푒−푝푡 + 푑 푝

푏 푦 = − +푑 푒푝푡 ……………………………………………………………(3.14) 푝

At initial condition,

푏 푦 = − +푑 푒푝푡0……………………………………………………………(3.15) 0 푝

Similarly, the coefficient calculation from above expressions would show the trends of an uncharged droplet.

3.4 Results and Discussions

3.4.1 Generation of Non-Uniform Electric field and effect of electrical parameters: Corona induced electrical parameters are shown in (Table 3.3) Ions generation and its physical application can be understood by invoking the

Electrohydrodynamic concepts and the effect depends on the width of air that is being ionized Consequently, we did an optimization study keeping the air width as variable to find the most efficient one that caused maximum ionization efficiency. Above certain

Electric field, electron will ionize the gas and charged particles will accelerate. This extra kinetic energy helps ionizing other molecules according to Townsend effect. The needle being a part of non-uniform E, will create a curvature through which ions will be drifted.

The drifted ions will create a space charge density which is asymptote in nature67 and with increasing voltage, the charge induced current will show non-linearity .Warburg’s radial distribution is maximum to a point just underneath of the source. Initial charge densities from the inception does not greatly affect the charge densities of the plane. In other ways,

50

we can say that spread of charges on plane does not depend on a variable source but constant. So, J should be proportional to voltage applied and corona inception voltage for a given medium. Also, J is a product of charge density and ion carrier velocity. In a place away from center, not only ion number density decreases but also, they drift with a slower velocity under weak E. Result is an abrupt change of J towards edge. The response of this incoming current to the medium liquid is our subject of interest to establish the fact that there is no corona induced instability in the liquid and the transport of droplet is not due to strong electro convective motion but solely because of dielectrophoresis. The electrical parameters distribution is understood by simulating the medium fluid without the droplet, using a point as source at different thickness level of medium. We reason with the fact that the charge distribution within the medium fluid is space charge limited (SCL)68 and the distribution of property would confront to a point source .(Figure 3-2.a-d) displays the surface potential, Vs and electric field at certain plane height (here topmost layer of liquid medium). Surface potential is the integral of the fields created by ions and the concentrations of ions would decrease, the more we approach to edge of container. It speaks one advantages of the current methodology where we can safely ignore the wall effects69 as ionization region is very confined at the center. The distributed field lines, narrowly spaced towards the center, establishes the fact of non-uniformity inside the bulk. More

2 important is the variation of grad.E in space (Figure 3-2.e), a parameter of DEP force (FDEP

훼 grad.E2) that drives the droplet here under realm of positive DEP. Their quick decreasing

51

magnitudes to zero, along y, tells why the vertical motion dictates over translation of droplet.

52

Figure 3-2: Numeric simulation displaying the electric parameters created by ions. An ion is modeled as a point charge and the strength of whose is found analytically. The value is given as boundary condition in Poisson equation. (a)-(d) Contour of potential and electric field. The distributed lines display the degree of non-uniformity inside the bulk liquid and support claim to dielectrophoresis as reason of motion. (e)-(f) Contour of ∇(E.E) and lines of them by Lambda (Lambda=0.5*∇(E.E). The distribution shows that there is a very strong non- uniformity within the very close bounds in center region along line of corona electrode) and dielectrophoretic effect consequently dies out abruptly as we move toward the wall.

3.4.2 Electroquasistatics of a sessile droplet and pattern of deformation: First we tried to see how a droplet responds to the incoming ions. We let the droplets settle for such a time that they wetted the bottom metal electrode with certain contact angles and their electrowetting nature was studied for a variable source voltage of about 4.5-7 kV.

Eventually, the shape evolution of the droplets suspended in another medium were found dependent on state of electric filed, static contact angle and property of droplet and medium as defined by non-dimensional numbers S, R, M in Table 3.3. While droplets made prolate

(vertical axis longer than horizontal) deformations for R>1, they were found to deform in oblate (horizontal axis greater than vertical) shape at R<1 as shown in Figure 3-3. When conductivity of the medium is higher than that of droplet, there develops a electric pressure in medium that imparts force against the contact line and droplets acts like an object squeezed between two parallel disc with force applied on wall. The dynamics of droplet break up could be co-related to their static contact angle (θ) and vertical semi-angle (β).

From Figure 3-4, we observe that at relatively lower viscous medium, the prolate droplets

o o were stretched and balanced by surface tension. The contact angle varied from 80 to 130 semi -vertex angle lower than 50o. The same kind of droplet under higher voltage of about

10 kV were found to create jets from the tips where β reduced here to less than 300. When same same kind of droplet were in relative higher value of M, they stretched, and their 53

growth formed a thin neck like structure from where they detached. This deformed shaped could never attain the criteria of β and there was found no jetting at any conditions.

Water droplet in matrix of castor

Silicone droplet in matrix of castor

Figure 3-3: Prolate and Oblate deformation of droplets under different voltages applied

54

(a) • Stretched and balanced by tension • No jetting 2β • 800 < 휃 < 1300 • 400 < 500 β < 5.2 kV

휃

(b) • Jetting • 휃< 1250 10 kV neck

• β < 300 length

(c) • Almost whole droplet jumps off • No jetting • 1300 < 휃 < 1800

• β > 350 6.2 kV

Figure 3-4: Relation of contact angle and vertex angle to droplet deformation. (a)-(b) Water- Silicone 100 cst. (c) Water-Castor

55

3.4.3 Electroquasistatics of a moving droplet and effect of deformation:(Figure 3-5) stands for how droplet responds to this space charge limited current while they move. With initiation of J, liquid experiences a charge build up within itself and depending upon the magnitude of J corresponding to 5.2-5.4 kV for 1 cm thicker liquid medium, we ensure a steady state space charge limited conductance (SCLC). We see different deformation rate for each of systems A, B, C, D in the regions categorized as region1(within 5 % of top), region3 (within 5 % of bottom), region2 (rest 90 %). Arguably the metal has higher contact charging effect on droplet (region3) in comparison to the top liquid layer when droplet touches them, while the droplet maintains a steady state deformation rate in region2 for each of the systems. We have followed the Extended Leaky Dielectric Model70 to track the dynamic droplet deformation under Dc Electric Field and calculated the Electric

휀 푎퐸2 capillary number, Ce (퐶푒 = 푑 ) at different regions during their flight, 훶 being surface 훶 tension of system (훶 = 훶푑+훶푚-2√훶푑훶푚). A deformed droplet condition is an output of competition of electric stress provided by E to the tensile stress provided by 훶 and the drop can achieve large deformation when one is dominant over other. We advocate for this method of calculating Ce that takes morphology change as inputs since it is very difficult to account the space varying E. The values of Ce, corresponding to red line (Figure 3.b-e), in region 2 are on increasing order of A, C, D, B where system A has the larger droplet radius and larger viscosity ratio. The results comply with the Feng’s analytic model of degree of deformation DD, described as direct function of a and a3. It is also evident from the result that the viscous stress induced by fluid motion has not that effect on droplet stability as they show a constant rate of deformation in this region. Also, the viscosity of

56

the medium affects the mobility of ions. System B, having the lowest viscosity, shows lowest Ce which we can correspond to their lowest E distribution owing to mobility. The findings, hence, safely negate the effect of M on droplet deformation. In region1 and region3 where contact charging happens, we see almost same spectrum of Ce (dot line for region3 and dash dot for region 2) for all the systems. The conclusions are defiant of earlier researchers work in metal electrode contact charging process71 who have shown that contact charging increases with droplet radius, hence deformation. To explain this behavior, we seek to transit time Tr. Due to their lower values of N in system B, D, they will have a faster Tr. than the system A, C. As ions will move faster, there will be less surface charge density qs that will yield a less electric stress. So the expected larger deformation due to larger a is negated by lower contact charge induced deformation while

Si450 cst is used as medium. Contrary for Si3000 cst being used as medium, lower ion movement will help accumulation of larger qs. Consequently, the expected lower deformation would be supplemented by larger contact charge induce deformation.

Eventually we see almost equal band width of Ce irrespective of the systems in region1 and region3 respectively. Our final remark is on narrower width of Ce in region1 than region 3 which indicate that the droplet shows more abrupt deformation rate when they touch the bottom copper electrode. This raises the probability of their break-ups if they continue to travel with this deformed rate. Our method restricts this probability when liquid is being used as other electrode from where they bounce off in region1. We like to call this liquid layer as pseudo-liquid electrode.

One distinct behavior of this air ion-injected method is on how the process polarizes the droplet in dielectrics. The electroquasistatics of the moving droplet can be interpreted by 57

(a)

(b) (c)

Figure 3-5: (a)Medium property effect on deformation. (b)-(e)Band width of electric capillary number for all the systems studied. The result shows the contribution of electric stress over surface tension.

58

comparing the characteristic time ힽ, time associated with electrical or mechanical process, to the time constant of the system,τ푒푚. By considering ힽ as time period of droplet motion

-2 (10-15 sec) and τ푒푚 as Tr (order of 10 ), we can clearly see the system in realm of EHD since τ푒푚 ≪ ힽ. Again, charge relaxation on time, τ푒푚 being lower, there would be no liquid breakdown and the experiments are completely subjected to simple mechanism of injection to non-polar liquid (medium) and polar liquid (droplet), discarding any chance of field ionization or field emission. Needle electrode being cathode, positive ions are expected to accumulate on liquid surface and direction of global Electric field would be downwards and water droplet would polarize accordingly. It is clear that Polarization, even with

2 general definition of P=(1-εr)E, would happen on scale of order 10 inside droplet with respect to liquid medium due to large difference of dielectric constant. It is an interesting case of uniform polarization of droplet in non-uniform field distribution thence introducing only surface bound charges qsb for the droplet, unlike non-uniform polarization where both surface bound charge and volume bound charge exists. Experimental measurement of these values are out of scope of this work, whereas we have simulated the droplet of different radius with known strength of E as portrayed in Figure 3-6.a-b. Four different E values are taken at certain height levels of their path line and point 1 falls in region1 while region2 holds the point 2,3and 4. Polarization density, P and values of qsb decreases with smaller volume droplet (System B, C). The direct relation of P to E is evident from the table as well. The droplet experiences a drastic change of E when it enters from region2 to region1 and here lies the highest value of qsb. An order of 1-degree change in E causes about 10- degree change in qsb. Such rapid change, surprisingly, seems to induce minor effect on DEP motion. Local E. field induced by polarization in droplet, being spherical, is zero. 59

(a) region1

region 2 (b)

Figure 3-6: (a)-(b)Interfacial polarization effect on droplet at two different locations.

60

The conclusions is established by plotting the radial E field distribution Figure 3-7.a. using

Popinnet and E=0 up to droplet radius.72 Outside the droplet, the field lines appear to maintain equipotential symmetry distribution. These distributions are complete identical to the contour plot of Figure 4.a-b. The results help us to conclude that the order DEP motion in region2 and region3 is more because of the global non-uniformity of E, and surface charge distribution caused columbic attraction/repulsion has least role to play with it even in the vicinity of high injection area.

region1

region2

Table 3.4: Relative variation of polarization strength in different location

3.4.4 Analogy of contact charging effect from spring-damper model: First we will try to establish the fact by formulating the source and nature of all forces, the droplet experince while it moves. A droplet behaves different during their flight depending on wheteher they are charged (region1 and region3) or uncharged.

Corona electrode would let accumulate positive charge on the liquid surafce and the uncharged droplet will be charged positive when they touch the surface. Same analogy

61

(a)

Er E a

θ

(b)

Figure 3-7: (a)-(b)Electric field distribution and velocity distribution inside and outside of the moving droplet.

62

goes for when they touch the bottom electrode. Considering the initial position of the droplet in region3, they are uncharged and levitated till the initiation of J, due to space charge, creates Electric field gradient in upward direction. A levitated droplet in this region would feel a competition to respond beetween positive dielectrophoresis and coloumbic attraction. The droplet surface facing ground electrode would grow negative qsb and would approcah towards the ground electrode if it is very closed to it (To our findings, if distance between center of droplet and ground electrode is less than 2a). For rest all cases, either leviated or just sitting, it would move in high field gradient (towards liquid surface) and it would experience a dielectrophoretic force 퐹푑푒푝, drag force 퐹푑, gravitational force 퐹푔, inertia force 퐹𝑖 while it moves. Another force, electric 퐹푒, would add these foces only when the droplet touces the electrodes. For brevity, we would mean both the ground electrodes and psuedo-liquid electrode by term “electrodes”. When the droplet is entering into the region1 from region2, the electric field between the electrode surface and the drops preceding region rises. Within SCL regime of EHD, the electric field is not strong enough to overcome the critical value of resulting the dielectric breakdown, therefore, denying the possibility of charge transfer through a conduction path in our case. We , instead, rely on the contact charging of the droplet with significant elongation of leading edge to touch the nearest electrode.71, 73 The reversal of motion depends on strength of resultant of all forces mentioned above, the amount of charge it aquires and charge leakage in the medium. Since

휀푚 the charge relaxation time of the medium,(휏푚 = ≈ 240 푠) is much longer than ힽ (15- 휎푚

20 sec) of the system, we can safely assume zero charge leakage. We can see droplet motion behavior depending upon the position (different E), droplet size, electrical and

63

physical properties of the droplet-medium system in Figure 3-9.a. Initially, there would be non linear increase of velocity for all the cases due to sudden impart of 퐹푑푒푝, and conditionally with 퐹푒. For 퐹푑푒푝 being proportional to droplet size, an uncharged droplet with larger “a” would undergo through larger dominance of dielectrophoretic force that drive them with larger scale motion while it passes in region3 and region2. Also lower viscosity ratio imparts lowest drug on droplet and it is quite reasonable why the System A shows higher order motion. If droplet gets charged from region3 (condition described above), the deformed droplet would relax to spherical shape again at a distance far from ground electrode (mostly in region2) since time scale of retreat of droplet (≈ 1 − 3 푠푒푐) is

휇 푎 much higher than that of shape relaxation (퐷퐷 푚 ≈ 0.02) Figure 3-9.a-region 2. With 훶 continued 퐹푑푒푝, droplet would enter in region1 with higher velocity and would touch liquid surface, hence, gain positive charges.

Figure 3-8: Schematic of spring damper analogy for droplet deformation

64

These is where 퐹푒 comes into play. Consequence is the sudden appearance of electric force in opposite direction (direction of E is outward from positive) that repulse the droplet towards ground electrode. On rebounding drop, the electrophoretic force pushes the drop to the ground while the 퐹푑푒푝 tends to pull up and the resultant is a weaker force. The changes are clear from low order motion of the droplets in their second cycle of motion

Figure 3-9.a. In our whole analogy, we have emphasized on rate of deformation as an significant cause of change of velocity. The conclusion is supported by the constant α

Figure 3-5.a. and their constant corresponding velocity Figure 3-9.a in region2 So we see that Fe comes into action after every T/2, T being time period of each cycle of motion. This periodical action to the moving droplet can be modeled as a time varying impulse/time response, Fe(T) and the motion can be interpreted as a dynamic system of moving object with spring-damper. In downward displacement, Fdep is resembled with a damper, when dielectrophoresis opposes electrophoresis. Similarly in forward motion, when DEP and EP acts in same direction, Fdep can be apprenhented as a negative damper.We see that both the system, system A with smaller droplet in 3000 cst medium and system B with comparatively larger droplet in 450 cst medium, show a sudden rise of velocities in the same ranges in region3. We must notice again that it is the region where EP dominates over

DEP and radius effect is negligible. Region 2 is the area where the droplet experiences the strongest magnitude of DEP over EP, consequntly making the motion size dependent in this region. Figure 3- 9.b shows the simulated behavior when the droplet moves upward.

There will be much electric stress in 450 cst than 3000 cst and the velocity profile would continue to grow unlike system A.The constant velocity nature of system A is hold good

The observation holds right DEP being more dependent on radius (Eq. 3.7). When the 65

droplet reverses its direction, we observe a behavioral pattern of a second order dynamic system, arising from the fact that, Fdep will continue to oppose the motion untill droplet touches. A larger drop is prone to oscillate not just because of its deformation disturbance, but also for their tendency to selfpropagte with deformed shapes.

(a)

t/2T

(b) System A- position (mm)

System A- velocity (mm/s) First cycle motion: DEP+EP

(secs) 66

(c) System B- position (mm) System B- velocity(mm/s) First cycle motion: DEP+EP

(secs)

(d) Second cycle motion: DEP-EP System B- position (mm)

System B- velocity (mm/s) System A- position (mm) System A- velocity (mm/s)

(secs)

Figure3-9: (a)Conjugate effect of radius and viscosity on motion of droplet. (b)-(d) Results of dynamic system consideration incorporating the radius and medium viscosity to describe the trend of displacement and velocity.

67

From a dynamic response point of view, coefficinet K2 and m have higher values for system B. Consequently the damped contribution by Fdep is going go be lower due to lower damping ratio and we would see a faster process for larger droplet in relatively lower viscous medium. The displacement curve tells that the system behaves like a first order system with second order system equation, with no overshoot in displacement, which only speaks for overdamped case.

One of the observations to make in such DEP assisted manipulation is to characterize the platform. The mobility coefficient in Figure 3-10.a shows that there are two range of mobility coefficient. The coefficients, which can be used to measure the permitivity and electrical conductivity of particles, here indicate the relative variation of electrical property change for the droplet while they undergo movement and contact charging. The discrepancy Figure 3-10.b is most likely to occure from quadrople fileld assumption in

DEP expressions.

(a) 0.8

DEP+EPDEP DEPDEP+-EP EP

0.6

0.4

Mobility coefficient Mobility 0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 Time period constant

68

(b) 1.0 Experimental Theoretical 0.8

0.6

0.4

DEP (mm/s) velocity 0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0

Non-dimensional z-position

Figure3-10: (a)Mobility coefficient as DEP platform characteristics. (b) Analytic model can predict the experimental behavior on same order.

3.4.5 Statistical analysis of random motion when the medium experiences strong electroconvection: Most of the theoretical study on the electrical charging of droplet holds good only when the medium is stationary and carrier moves through it. The study of non uniform field brings variation of more functionality that control the system due to breakage of similarity. It becomes more difficult if the liquid medium carrying this droplet like particle undergoes through motion and the particle, hence,would display random behavior of motion. If there are n number of droplets ,the possible outcome of these droplets during their flight of motion: their change of position, their probability of colliding among one another or merging to other thus reducing the number of species is predicted with probabilistic distribution based on initial observation. If we know the location of a droplet 69

at (x,y=0) at time t=0, we continue to seek a way to find its location at time t=t. The droplet, for single ground electrode, periodically bounces up and down . So it changes its position with a probability of changing direction of 0.5. On the other hand, the translation along with lifting can be interpreted as a drift addition to the probability. For a uniformly distributed ground electrode, the ratio of drifted distance to the lifted distance appears to be 0.5. If we add this to the directional probility, the resultant comes out as 0.5*0.5=0.25.

Now this observation is feed to the computer to randomly predict about 100 droplet motion each making 20 steps. Outcome are presented in Figure 3-11.a-b .

(a) (b)

Figure 3-11: (a) Probabilistic distribution of path- line of 100 droplets under high medium motion without translation. (b) Probabilistic distribution of path- line of 100 droplets under high medium motion with translation when multiple electrode are used

We see that the droplet has a tendency to travel 20 unit in upward direction against 2 unit in sideways for single electrode. While drifting, they make about 7 unit sideways against

20 unit vertical movement. Spatial distribution density for 100 droplets are found using the

70

same analogy and we see a close resemblance with previous conclusions and experimental findings The concept is extended to understand what would be the fate of 100 randomly distributed droplet if they randomly collide and merge. We construed the proposition by setting a droplet as trap and letting another droplet move in the domian. When the droplet should find the trap, it would merge and consequently generating another trap for other droplets and thus continusly decreasing the concentration of the droplet Figure 3-12.b.

Initialy when there is higher density of droplet, the probability of finding the trap is higher making a higher decrease rate ( 70 % reduction within first 33 % time ). The reduced number of droplet, a subsequent aftermath of merging, would take longer time to find the nearest trap and thus yielding lesser rate of decrease.

(a)

71

(b)

Figure 3-12: (a)Spatial distribution of 100 droplets each moving 20 steps at t=0, dt=1, dx=1. (b) Number of reduction of droplet if 100 randomly distributed droplet collide and merge.

3.4.6 Rayleigh-Plateau instability of dielectric-dielectric system: To understand the effect of conductivity, a more heterogenous system was made by inserting both a conducting droplet (water) and a dielectric droplet (castor oil) inside another dielectric medium (silicone oil). Due to non-uniformity of the field, both the droplet show prolate deformation but liquid behavior in castor arises from existence of small perturbations developed inside (Figure 3-13). As castor droplet co-exists with water droplet, the maximum contact charging happens to water droplet due to its higher conductivity upon contacting the electrodes and consequently castor droplet shows straddling nature in close proximity of the electrode. This is most likely because there is not enough EP repulsion as they can not acquire enough charge. The deformation in the form of long cylindrical 72

coloumn can be represented by a series of periodic displacement sinusoids and is dependent on wavelengths. The growth of instability is found to depend on mode number and reducing the mode number can be a trick to resist the droplet break up (Figure 3-14).

Castor t=0 sec

Water

t=10 secs

3 modes of perturbation 푘푅표 ≅0.75

Figure 3-13: Rayleigh-Plateu instability developed for castor-water inside silicone 3000 cst.

t=0 sec t=10 secs

Castor

2 modes of perturbation 푘푅표 ≅0.85

Figure 3-14: Rayleigh-Plateu instability developed for castor-castor inside silicone 3000 cst.

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3.4.7 Translation of droplet in multiple electrode: Along with vertical motion, droplets were found to translate in the direction of switched on electrode when multiple ground electrodes were used using the same corona ion injection. The findings speak for the methodology to be used for potential applications like electrocoalescence where we need to not only increase the length scale, but also increase the speed thus enabling them at higher collission rates. The multiple electrode reduces the contact area and drolets can also take the benefit of edge effects which should raise their DEP mobility coefficient.

t=0 secs

t=4 secs

t=7 secs

t=9 secs

74

t=11 secs

t=12 secs

Figure 3-15: Successive position of single droplet showing both vertical and translatory motion. The box on upper right position shows the electrodes those are operated (green and red).

t=0 secs

t=3 secs

t=6 secs

t=9 secs

Figure 3-16: Successive position of multiple droplet showing coalescence.

75

3.5 Repeatability of experiment data

The experiments are done by applying an ionisation technique which is one of the special categories of gas discharges. Like other gas discharge process, it depends on the environment factors like temperature, pressure and humidity. The reported voltages were found to vary as V ∓0. 2 kV depneding on situations. Also the behavior of liquid and droplet highly depends on initiation time and time elapsed for liquid to respond.

The corona unit is a closed chamber and experiments were done maintaining distant positions. Making a samples of discontinuous phase (droplet) inside the continuous phase is time consuming and a lot of attnetions and precautions needed to be followed. It has to be carefully observed that the droplet does not get enough time to settle at the ground electrode. A time elapse of about 10-15 seconds altered the experimental obervations in significant ways. In addition, maintaining the purity of the sample is a must. If there are other dispersed objects, they will act to ion injection bringing variations in EP response of droplets.

3.6 Conclusions

We asses the plausibility of manipulating conducting droplet with the help of atmospheric corona induced ions. We advocate for this type of non uniform electric field generation with DC source against AC for bulk cm level viscous liquid. We conclude on:

• The extended leaky dielectric model applied for dynamic shape deformation can be

essentially very handful to understand the electric stress developed at different time

and space locations.

76

• Dielectrophoresis is understood by motion of droplet, analysing the effect of radius

of droplet and properties of fluid medium.

• We showed that how liquid surface can act as a pseudo electrode and can be very

helpful in restoring shape in comparasion to metal electrode which are identified as

area of highest possibility of droplet breakup.

• We show a new method of analysing the competing nature of dielectrophoresis over

electrophoresis when both work simultaneously, by dynamic system modeling of

spring-damper. We also represent a mathematical frame of capturing the random

behavior of n number droplets subjected to heavy motion.

77

Chapter 4

Instability of bulk dielectric liquid under Atmospheric Air Corona

Liquid deformation is a quite interesting and significant phenomenon noticed when it experiences ion movement through it. The electrohydrodynamic nature of this motion is largely dictated by the conductivity of liquid, ion injection process and geometry of the electrode demanding an area of extensive studies. A unipolar case with atmospheric air corona applied to dielectric liquid of different thickness and viscosity is investigated in quest of understanding the instability and electroconvection. The order of magnitude analysis is carried in both air and liquid in terms of induced voltage, corona current, instability parameters and criterion. Interfacial dynamics of liquid is explained with proposed capacitive model where bulk dynamic is enquired in light of convection motion analogy. Electroconvection is initiated with the non-linearity of current-voltage (I-V) relationship and threshold is determined with conjunction of hydraulic model and capacitive model. It has been found that the vertical rise of electro-convective cells is a resultant of inward acting electrostatic force at edge of each cell and upward acting volume forces due to non-uniform electric field. For very low conductive liquid (order of

78

10−13 푆/푚), both volume and surface instability have been observed. At higher current, the cells are found oscillating, predicted due to polarity/partial charges and their pattern is found dependent on the liquid thickness and the time ions take to travel across and getting relaxed. The current density calculated hold a good agreement with the measured current spectra qualitatively and quantitively.

4.1 Introduction

Any low conducting liquid subjected to an ion injection experiences instability popularly known as Electrohydrodynamic instability. These interfacial instabilities have been the subject of extensive studies since the very classical work of Taylor and McEwan 74. With an overgrowing importance of dielectric in industries, its behavior has been scrutinized under various conditions. The unstable nature of liquid surface was noticed for the conducting liquid between two plane electrodes for a critical Electric field. Watson and

Schneider highlighted space charge effect when they made a experimental75 and theoretical76 investigation on dielectric liquid. Convection assisted conduction in Dow corning 703 was brought in picture and the onset criteria of electroconvection was set for a particular shape of surface.

Koulova77 while studying air/liquid two layer system explained the same kind of criteria on different air-liquid thickness ratio and concluded that a deformed surface with lower surface tension would have a lower criteria value.

There are different regimes i.e. ohmic, unipolar; which monitor the EHD effect in liquid in different ways. Under unipolar injection, ions will be drifted to the opposite electrode and 79

create space charge decreasing the Electric field. This injection can set the liquid in motion depending on if they can traverse the liquid layer before being neutralized. Numerous effort have been put to examine the liquid behavior formed as such 78-83 including Watson

Schneider work. The work of Zahn, Melcher,Sojka82-83 described the wave dispersion & instability of space charge in perfectly conducting liquid.

A unipolar charged injected unstable nature of liquid layer is well studied by Atten et al80-

81, 84-85 .Within a band of injection levels, the studies reveal the threshold criteria ignoring the effect of surface tensions and interfacial stresses. Charge can be injected to liquid by various means. Injection with corona in different configuration like point-plane, wire- cylinder, wire-plate have been a wide subjective study.86-89A perpendicular field with ion injection generate electric forces. The forces can create surface instability or volume instability depending on the ratio of relaxation time and transit time. Both the conductivity dependent parameters suffice that even a single fluid undergoing change of conductivities might experience both surface and volume instabilities.

For a relatively less conductive liquid like silicone (order of 10−13푆/푚), certain value of corona current (I) and liquid thickness (T) initiate a convective pattern of cells. The cell sizes are small in the order of liquid layer thickness and the pattern holds good for 퐼푇3.

Current I will cause a voltage drop across liquid equaling the same effect of space charge resembling an unipolar(volume) induced one. The liquid also shows another pattern where cells appear to be much larger than thickness T and can be related to surface electric pressure.

Perez87 introduced a new kind of surface instability named Rose-window while studying the effect of corona discharge from needle-plane on low conducting liquid. The electric 80

pressure on surface is thought to be driving the instability. The cell sizes are identified as much larger than the liquid layer thickness which decreases with increasing electric field.

Some theoretical and experimental works of surface instability by Koulova et al.77, 90 speaks of the same trends of Rose-windows. The electric pressure is found to have a maximum when plotted against liquid thickness indicating that instability sets in when liquid is enough thick and electric pressure decreases with thickness. Gravity being included, the work is extended to find threshold voltage as a function of liquid layer thickness making a large wavelength assumption.

For dielectric like castor, corn with conductivity (order of 10−11푆/푚) less than silicone, the visible pattern of cells is only in the order of size of cells indicating the existence of

EHD volume instability only. Here the critical voltages are found to decrease with decreasing T unlike the case of silicone where it shows a larger threshold voltage for very thin layers.

So the kind of instability is dictated by both conductivity and liquid layer thickness, hence

푇2휎 a non-dimensional parameter so defined as 푆 = 푟푒푙푎푥푎푡푖표푛 푡푖푚푒⁄ = 푡푟푎푛푠푖푡 푡푖푚푒 ∈휇푉 can describe the system , where ∈, 휇, 푉 stands for permittivity, mobility of ions, Voltage drop across liquid layer respectively where 휎 represents conductivity.

The effect of S on EHD instability is well understood from works of Chicon, Vega, Perez91-

94. Perez and Vega93 showed that the surface charge can be both positive and negative in direction which can be related to S. For large S, the liquid surface charge is of the same sign than the injected charge and the liquid can be treated as an electrode and vice-versa.

Liquid being treated as Ohmic in an air-liquid interface, the instability resulted into a

81

surface case as liquid velocity was neglected. The convective cell size was interpreted with wave number mode and the most unstable mode was found to be zero meaning a very larger convective cell. The role of surface tension accounted in terms of Bond number showed a very little effect on critical value and the whole analogy picturize the surface instability.

Chicon et al.91-92 included liquid velocity which resulted a different outcome of wavenumber of Vega93.The previous zero value of unstable wave number mode shifts to a finite value now but convective cell size still showed a larger size than thickness T.

Threshold voltage, being studied as function of conductivity, showed a fast increasing values with higher conductivities. At higher conductivity, ions travel faster and there is less surface charge 휎푠. At a critical lower value of 휎푠, the surface will be charged with opposite kind to that of injecting electrode and liquid can act as an electrode ,same analogy put by

Vega93.

Recently, some works have been carried with corona discharge injection in a needle-plane configuration.3, 89, 95-96 Studying the EHD effect of corona in compressed air, Zhao and

Adamiak89, 96 have described parameters like voltage , current and inception voltage for different tip radius and tip-plane distances. Adamaik et al.89 have extended the studies in point-plate , wire-plane and wire-cylinder configuration but each of the studies are yet to successfully depict how different dielectric respond to these dynamics controlling parameters.

Besides there are a lot of scope of revisions for their theoretical and experimental conclusions in different perspective considering the difficulty arising due to coupling of Electro-Hydrodynamics.

So this work aims -(1) to imply EHD phenomena in understanding the effect of injected ions on dielectric liquid. (2) An order of magnitude analysis of the flow controlling parameters. (3) Electro- convection investigation as a part of liquid layer instability and (4) Exploring the potential

82

effectiveness of this ionization technique on low conducting liquid in scopes of coalescence formation, pumping etc.

4.2 Bulk instability:

4.2.1 Experimental design and methodology:

Both experimental and analytic studies is carried to understand ion induced effects on low conducting liquids. A classical needle-plane configuration is used to ionize the air by applying high voltage at the sharp edge of an emitting electrode. Ions of positive polarity generated from the air was thus directed to a copper ground electrode of 2.5 cm diameter.

The underlying mechanism of generating these ions in a plane is explained by 97 and is popularly used to investigate the EHD studies. The experimental set up is Fig1. A voltage in the range of 2-10 kV was applied by a DC power supply with the help of a ± 10 kV

TREK Model 10/10B-HS high -voltage amplifier. Injected ions create a variable corona current which is computed under scheme A.

The parameterization of flow controlling variables has been done with the steps of

Flowchart 1.

83

The phenomena in gas(air) at SATP including corona initiation is addressed by Scheme1.

At any point, say the center of the liquid surface, current 퐽0 is computed with Sigmond’s formula

퐽0 = 푎퐾휀V (V-푉0)/푑 (4.1)

Where a=constant, K=mobility of ions, 휀=permittivity of the medium, V=applied voltage and d be the distance from tip of the needle electrode to any point between the electrodes.

84

This point current can be distributed across any plane under condition d≤ 3 cm between the electrodes in point-plane configuration using Warburg law represented by Eq. 4.2 as follows:

푚 0 퐽(푟) = 퐽(휃) = 퐽0푐표푠 (휃) , 휃 ≤ 60 (4.2)

Where 퐽(푟)= distributed current on the plane, r=radial distance on plane from center, 휃 =

푟 푡푎푛−1( ). m takes the value of 4.82 for positive ions. 푑

Scheme: 1

85

푊ℎ푒푟푒 ∝푇, γ, A , 푟푐 are the ionization coefficient, electron emission coefficient, environment constant, electrode tip radius respectively and 퐸0 is the Peeks Electric field for a cylinder geometry at corona voltage 푉0.

The response of ion injection on silicone and castor in terms of cell deformation is investigated by a proposed capacitive model. The idea is very simple. If two parallel plates of capacitors are inserted into a dielectric, the liquid rises between capacitors. Reversely any risen charged layer with distinct edges can be treated as a layer bounded by two imaginary infinite lines of capacitors along the edges.

The experimental evidences are strongly supported by mathematical formulation of capacitive laws acting on a liquid. We strongly believe that the liquid obeys Clausius-

Mossotti relation. Then pressure differences between any two points within Electric field

E is given by

2 2 휀0퐸 (휀−1)(휀+2) 푝2 − 푝1 = [ ] (4.3) 6 1 where 휀0=permitivity of vacuum and 휀 =dielectric constant of the liquid used.

At this point our propsed model simplifies the each cell between two edged lines Figure 4-

4.a as a sphere.

The assumption put us directly in a position to measure the pressure inside the liquid as follows : 86

3 휀−2 푝 = 휀 퐸2 (4.4) 2 0 휀+2

The electrostatic force acting on dielectric are concentrated at edge of sphere/cell and Eq.

4.4 tells that , for a vertically downward E ,the force acting should be radially inward.The analogy is complete opposite to rigid conducting sphere for which ε=0 and which can be verified by Eq. 4.4 as well .

Now lets consider a point A lying just above surface of liquid in between lines and a point

B above surface well away from lines (E=0). The existance of point B is proven by the fact that for a needle-palne configuration , the field lines are a limited region streamed lines. The pressure difference can be formulated as :

휖 (휀−1) 퐸2 푃 − 푃 = 0 ⌈퐸2 + ┴⌉ (4.5) 퐴 퐵 2 ║ 휀

Where 퐸║, 퐸┴ are tangential and normal component to the surface. For a vertical field acting in -z direction, the tangential component are ignored.This electrostatic pressure difference can be equated with hydrostatic pressure difference ρgh to measure the rise of liquid of density ρ between the lines.The resultas are shown in Figure 4-2.

The behavior of each cell between two edges of capacitive model is driven by the kind of forces acting. At this point , the authors carefully rule out the effect of surface forces when it comes which one push the liquid upward.The conclusion is supported by Eq. (4).The force density inside dielectric under an electric filed is given by:

87

휖 휖 푑휀 푓 = 휌퐸 − 0 퐸2∆휖 + 0 ∇(퐸2 휌) (4.6) 2 2 푑휌

Further modification of (6) shows that the last two terms of (6) can be explicitly expressed in (5). Hence , the first term i.e volime force due to non-uniform electric field can be treated as responsible for liquid movement inside the bulk of liquid. 휌 being liquid property, it is safe to say that E itself can depict the nature of instability inside the volume.

A criteria for this volume instability is set to

푉푠 = 푅휇휂/휀 (4.7)

Where electric Rayleigh number, 푅 = 푓(휀, 휂, 푡, 휏) and t, 휏 are thickness of DL,time scale respectively.The surface potential 푉푠 of dielectric is the integral of the field created by ions and is given by

퐽휏푡 퐽휇휏2 푉 (푡) = (1 − ) (4.8) 푠 휀 6휀푡

Schneider et al76 found minimum R=99 for a space charge limited layer to be unstable, and this motion delay which is assumed due to convection is predicted by

300휀휂 휏3 = (4.9) 푐 퐽2

Where 휏푐 is the time to start the volume instability.

A solution of Eq.8 for time dependent 푉푠 to reach the steady state 푉푠 is

2휀푡 휏 = ( )1/2 (4.10) 휇퐽

8퐽푡3 And by this time 푉 = ( )0.5 (4.11) 푠 9휇휀

Under the condition 푉푠=E(air)*air gap=E(DL)*DL thickness ,E is calculted as

퐸 = ∇푉푠 (4.12)

88

Non uniform E results to a unstable space charge distribution which is explained in terms of surface decay and bulk decay. The charge is expected to decay in follwing ways.98

푡 푞 = 푞 (1 + ) (4.13a) 0 휀(ℎ−푡)

휏휎 − 푞 = 푞0푒 휀 (4.13b)

Where q is charge density and Eq. 4.13a ,Eq. 4.13b are for primary injector and secondary injector (Figure 4-5) respectively. ∆푞 thus formed will create a path of channels through which the spherical convective cell will travel driven by pressure differences.This pressure differences can be computed by capacitive model of Eq.5 and should satisfy Hydraulic model99 expression in the form of :

2푞퐸푡 푃 − 푃 = (4.14) 퐴 퐵 1+훬

푤 훬 = , w is the induced vertical velocity component of cell as a resultant of Eq.13. 훬 is 휇퐸 a measure of liquid velocity and drift velocity 휇퐸.

When kinetic energy of the fluid (1/2)휌푤2 is equated with electrostatic energy (1/2)휌퐸2

, it gives an order of magnitude of fluid velocity w as:

1 휀 푤 = ( )2 퐸 휌

1 푤 1 휀 = ( )2 (4.15) 휇퐸 휇 휌

89

The right hand side of Eq.4.15 is represented by a non-dimensional number M , which is a

1 휀 ratio of hydrodynamic mobility ( )2 , to ionic mobility 휇 . 휌

The effect of w on instability and convection is understood from Reynolds number ,Re as:

푤푡 푅푒 = 휈

훬휇퐸푡 = 휈

훬휇퐸푡 휌휇2 = 휇휂 휀

푇 = (4.16) 푀2

T is an instability parameter showing the effect of Coloumb force to viscous damping force.Instability also depends on the level of strength of injection denoted by :

휇푞2푡 퐶 = ( )0.5 (4.17) 휀퐽

Depending on value of C , there are there can be finite amplitude electroconvection(C<<1), and strong injection electroconvection(C>>1). With our set up and specification, our study focuses on finite amplitude case.Moreover,the later one is very unsteady in nature and their lifetime is so short that they no longer can be considered as a well defined cell.Contrary to it , the convection for weak injection is steady which in this study is investigated with

Hydraulic model.

At C<1, liquid motion steadily affect the enhancement of current and surface B (Figure 4-

3.b) is designed to be autonomous injection which is charge density is not affected by liquid convection and its subsequent purturbations. We can safely assume that q remain constant

90

along the trajectories of charge carriers i.e 푞 = 푞0(푡 = 0).The convection is steady and a solution exists which relates 힚 with instability parameter T in the form of:

훬 = 0.2(푇퐶)1/2 (4.18)

Eq. 4.18 puts us in a state to calculate T for known 훬, 퐶 for different conditions.

Current I is caluculated both by experimentally and by left coloumn of Flowchart.1, hence

Eq.8-11 are dealt accordingly.The authors like to point out again that all the expressions of

Eq. 4.15 and Eq. 4.16 have the variables of only fluid properties other than E which re- establishes the idea of EHD effect of first term of Eq. 4.6 with these expressions of Eq.

4.15 and Eq. 4.16. Finally the mathematical analogy is compared with the experimental results of silicone oil for different viscosities and thickness.

4.2.2 Results and discussions

Corona induced electrical parameters are shown in Figure 4-1.a. Ions generation and its physical application can be understood by invoking the EHD concepts. Above certain E , electron will ionize the gas and charged particles will accelerate. This extra kinetic energy helps ionizing other molecules according to Townsend effect of scheme1.The needle being a part of non-uniform E, will create a curvature through which ions will be drifted. The drifted ions will create a space charge density which is asymptote in nature67 and with increasing voltage, the charge induced current will show non-linearity Figure 4-

1.a.Warburg’s radial distribution is maximum to a point just underneath of the source.

Initial charge densities from the inception does not greatly affect the charge densities of 91

(a)

Figure 4-1: (a) Schematic diagram of the experiment to create ionic wind

the plane. In other ways, we can say that spread of charges on plane does not depend on a variable source but constant. So, J should be proportional to voltage applied and corona inception voltage for a given medium. Also, J is a product of charge density and carrier velocity.

(a)

92

(b)

(c)

Figure 4-2: Current distribution in realm of Electro-hydrostatics in a positive point-plane configuration for V=2-10 kV. (a)Ionic current against applied voltage at a distance (h-t=15cm).(b)The distributed current for corona onset voltage along length of liquid surface.(c)Second order behavior of Vs and E to at higher J. Ignoring polarization, displacement current is unlikely and J is solely a part of conduction current. The needle creates a limited ionization curvature which will cause an abrupt change of ionic density followed by J towards the edge of the test cell

93

In a place away from center, not only ion number density decreases but also they drift with a slower velocity under weak E. Resultant is an abrupt change of J towards edge Figure 4-

2.b. Figure 4-2.c stands for how liquid of different thickness start responding to this space charge limited current. With initiation of J, liquid experiences a charge build up within itself and depending on the magnitude of J it directs either to steady state Eq. 4.11 or to the onset of convection. The trends of both Vs and E progresses to quadratic from linear at higher J which speaks for a convection enhanced conduction. The linear part can be termed as space charge limited conductance where J푡3/푉2 remains constant and this seems to deviate at the proximity of 1.5E-08 A/푐푚2 setting a zone of J α 푉2.

As the method is an ion injection, we experimentally investigated ionization of air band

(thickness of air) against the thickness of the oil. The purpose was to find an optimized state of generating corona wind so that we can conclude on impulse of liquid according to the effect. Figure 4-3: (A) and (B) show the current/voltage characteristics measured for variations in the needle height. Best-fit lines are shown as the expected relationship is linear for Townsend Discharge. (A) Does not include a liquid layer between the needle and ground and confirms that the discharge is comparable to that of Townsend Discharge until the needle is only 10 mm away at which point the discharge enters the glow-discharge regime. (B) repeated (A) but with a silicone oil layer with a thickness of t = 9.5 mm located between the needle and the ground electrode. The linearity seen in (A) is no longer present suggesting a transition from the Townsend Discharge Regime. However, no known law follows this discharge pattern, it is believed to be a result of the space charge build up at the air-liquid interface causing a significant reduction in current flow. The results at h =

15.5 and h = 20.5 mm suggest similar operating characteristics will occur occur for needle 94

heights within this range due to their closely matched curves. Also shown is that the closest needle is now producing the least current in contrast to the relationship seen in (A), likely as a result of the space .charge built up on the liquid layer only 0.5 mm away. (C) Shows the relationship between oil thickness, t, and the overall corona current for needle height changes. A sharp transition occurs from no liquid (t = 0) to t = 5.5 mm so that there seems to be little variation in current for large changes in needle height. Between a liquid thickness of t = 5.5 and t = 7 mm there is a clear transition in behavior as the lowest needle begins to produce the least current. Once again, this behavior can best be attributed to a greater space charge build-up near the electrode causing repulsion of additional charge carriers. It is not known why these transitions occurs at the given thicknesses. All measurements were taken for V=10kV.

Figure 4-3: Corona wind optimization study against different thickness of liquid.

95

In our experimental investigation with silicone oil, we have seen two kinds of cells when the liquid sets in motion under the condition that ions travel before they are being neutralized. First kind of cell are seen to appear on surface and cell diameter is a function of t and J. The earlier stage conical shape gradually increases with Voltage being increased.

Along the imaginary axis as described in methodology, liquid moves away from fluid interface in downward direction and penetrates about half of liquid thickness. The momentum carried with them supplies energy in surrounding and in return, liquid rises to create a concave surface contour (Figure 4-4.a).

On our proposed analogy, there develops opposite kind of polarity/partial charges along the two imaginary lines and any surface cell formed between them should be oscillating. It gives a rate of surface deformations. Transit time,푇푟 and viscous stress, both, have a significant effect on this mode of instability. With a faster 푇푟, there will be a less surface charge density 휎푠 which will yield a less electric stress. The viscous stress which equals the shear stress sets the liquid in surface motion which indicate that with higher viscosity, the rate of this deformation should decrease (Figure 4-4.c). We should notice that an increasing thickness yields to more 휎푠 for a reason that more ions get trapped within the liquid. This increased 휎푠 will account for a higher 푇푟 which reinforce the previous logic that ions will take longer time to traverse a longer distance.

An order of magnitude of vertical rise is estimated from the Electric pressure which is nothing but a qualitative electric stress, making a similar relation with viscosity and thickness. So, a thicker liquid should correspond to a larger E which contribute to larger pressure. The case will reasonably displace more liquid upward (Figure 4-4.d).

96

(a) (b)

(c)

(d)

97

Figure 4-4: capacitive model for developed cell and hence their idea of being pumped up in upward direction.(a-b) Array of cell developed on silicone oil (t=3.5 mm, 휈= 350 cst) .(c)Oscillatory motion of deformed surface on order of 퐶푠=.5~.6mm. (d)Risen up value across the surface due to volume force. The pattern of cell depends on the ratio of the time they take to travel to the time required for relaxation. Lower conductivity will result to a lower ratio scale. The ratio scale is a function of conductivity and thickness. A thinner layer of silicone will take larger threshold voltage to display this kind of cells. Contrary a low conductive like corn is unlikely to form these larger kinds of cells. The degree of volume force appears to be dependent on non-uniformity of E which is more extent at the center of DL resulting a higher 퐶ℎ values.

The other kind of cell was found on the order of liquid thickness and their existence is identified due to the motion of bulk liquid. There will be both bulk decay when charges moves through silicone and surface decay when charges are entitled within the surfaces due to columbic repulsion. At steady state level, liquid surface B (Figure.4-5.b) will act as an injector and it’s a simplified version of charge injection into liquid between parallel electrode and consequently the problem converts into Eq . 4.13b form Eq. 4.13a.

On the condition of injection strength C<1, we are in a state of steady convection under weak injection. We have made an adjustment on q being treated as Eq. 4.13b not considering constant. The liquid motion will decrease the q from B and E will increase there making an increased J. We must note that both J and E remain on the order of C and both the quantities are safe to assume constant soon the steady state level arises. The convective roll motion in Figure 4-5.a is understood with help of Figure 4-5.c(right). S1 and S2 be the stagnation points with maximum pressure. Alternatively, there is zero liquid velocity which can be only possible if there is no ions. S1 and S2 form a singular circular trajectory with no ion entering zone due to coulomb repulsion and we can clearly see it from Figure 4-5.a. Any charged point in liquid will decay due to columbic repulsion. 98

(a)

(b) (c)

Figure 4-5: Qualitative idea of electro -convective motion in Dielectric (silicone 350 cst). (a)Time evolution of convective motion at 10kV for 9 mm thick liquid. (b) Surface and Bulk charge decay acting as an underlying cause of torque. (c)Cross section of a steady state convective 2-D roll. b is the width of roll at any height z. S1, S2, are position of separatrix and S0 be center of cell. Separatrix shows the boundary of two convective cells

With reference to any time of flight of ions (for liquid yet to set in motion, there will be a

reduced flight time caused by added velocity components along field lines (for liquid in

motion). On the other hand, some regions will have a higher flight time caused by

diminishing effect of liquid velocity. Result is a net torque acting as a source of

99

convection.Watson75 in his experimental study of space charge limited current in Dielectric mentioned both space -charge limited conduction and convection enhanced conduction.

The bulk liquid with enough thickness in our studies should have significant amount of space charged developed within the volume of liquid. The liquid movement, thus, between the edges of each cell described above is driven by convection, also clearly seen from

Figure 4-4.a. The time between when the current starts flowing, and initiation of convection is a good way of investigating this nature of convective cells which shows evolution of them in space and time. The low E values correspond to low J and at this condition, Tr of

Figure 4-4 should estimate the time required to reach the steady state level according to

Eq.10.Consequently it satisfies 퐽푇푟2 = 푐표푛푠푡푎푛푡 . Reversely we clearly see a breakpoint on Tc curve where E and Vs are supposed to show peak in Figure 4-6. From this E value, the corresponding threshold of J and V can be found for a given thickness.

Also, at any point afterwards, the trend would not follow 퐽푇푟2 ≠ 푐표푛푠푡푎푛푡 , but 퐽푛푇푐2 =

푐표푛푠푡푎푛푡 where n is reported as 3,no of times. Mobility might create a deceived perception that it should control the time delay which is not the case. It is a good assumption that the extra current of convection is supplied by the space charge layer of the surface which reasons for why Tc is independent of t.

Figure 4-7 suffices the nature of finite amplitude electroconvection for the condition that the motion develops with a circular cell as described before. Condition 힚>1(Figure 4-7.c) indicates that this finite amplitude convection is stable in nature and in this regime, the liquid velocity w is greater than the drift velocity με.

100

(a)

(b)

Figure 4-6: (a-b) Time Tc required from initiation of current to start convection. Tc are found to be independent of t and viscous effect affect electroconvection. The instantaneous position of particle has been traced. The idea is the increase of characteristic flux at the free boundary. From initial position, both the yellow & light blue particle accelerates along boundary of the cone. Due to excess flux, energy must be transported at the boundaries and convective cells likely to form to be a part of transport. There is a breakdown point in the trendline of Tc indicating the onset of fluid motion. 101

Now the convective cell proceeds to a more stable form where the injected charge carriers in region 2 (Figure 4-5.b-c) and cannot move towards the bottom electrode because of their slower motion than the fluid. It results the region 2 free of charge and this free region will gradually increase as we move away from center towards the edge of the container. The trends of instability parameter T in Figure 4-8.a shows how this nature of motion is going to persist and hence accordingly affect the field and current flow. The critical value for silicone of 2mm,3.5mm, and 5.5 mm thicker liquid is found to be on the order of 200,350 and 400 which are computed with the assist of critical condition used in Figure 4-6.b.

a b

(c)

Figure 4-7: Nonlinear instability analysis from an extension of steady state convection. (a)Transient state of electroconvection. (b)Unsteady convection due to chaotic movement in the region of viscous dominated region. (c) Non-dimensional value on 102

the degree of liquid velocity in comparison of ionic movement. It is a good way of approximating convection strength subjected to fluid motion under effect of E and J gradient.

It is the onset afterwards the liquid velocity dominates over the mean ionic velocity and the cell sizes Cs tends to decrease and we can assume that surface instability enters into the volume instability with smaller cells than before. The values of T decreases for all thicker liquid after the critical point which supports one of the findings of koulova 77 who concluded that with surface deformation, the instability criterion should be lower than for a non deformable surface. The increased values of T against higher thickness accounts for higher corresponding critical 힚 to set the onset of convection. The analogy becomes clearer when we can relate the mobility parameter M to 힚 (Eq. 4.15). More thicker liquid will induce more hydrodynamic mobility which will take higher values T to set the liquid in motion.

Finally Figure 4-8.b in brief validates and strengthens all the claims in this study. The measured current spectra show discrete peaks at a well-defined time interval. At a voltage

6 kV which is above the critical one, the spectra show periodic fluctuation which can only stand for the velocity field undergoing movement with periodic nature. At higher voltage, the spectra become continuous and we can conclude that liquid motion is chaotic passing from periodicity. This spectral behavior hints also on how cell undergoes changes with

푡 change of applied voltages and thickness. At higher voltages, the ratio tends to increase 퐶푠

푡 indicating EHD volume instability from comparatively lower values of of surface 퐶푠 instability described in the previous sections.

103

(a)

(b)

Figure 4-8: (a)Instability parameter T as a function of Electric field. The vertical line shows the point of threshold where non-linear instability starts. (b)Spectra of fluctuation of current through a domain of cell size Cs for different thickness. Evolution of velocity amplitude 힚 shows that 힚 moves to a steady value at larger time. Though it is very irregular, but it shows a very well -defined frequency.

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4.3 EHD pump

The techniques employed to drive liquids on small length scales falls under to either displacement pumps : that exert pressure on working fluid by moving parts (like piston or cylinder that displaces volume), or dynamic pumps: that imparts forces directly on liquids without the help of any moving parts. For dynamic pupms, methodology involved are mostly of following types :

• Electric forces generated in liquid pump : Conduction, induction , EHD injection.32,

98, 100

• Electric forces generated in diffuse double layer: Electroosmotic, AC induced

electroosmotic.101-102

• Magnetic forces generated in liquid pump : DC MHD, AC MHD.103

The bulk instability studied in previous sections of this chapter is of EHD injection types and we have extended the study if this volume instability can be an assited in pursue to drive the liquid in an open path modifying the electrode configurations.

4.3.1 Experiment set up

The schematic of EHD pump is shown in Figure 4-X. This is a two phase scenario where corona discharge is created at air above the liquid surface and and upon injection on liquid, they drag liquid along with the direction they are configured. It is a 3 electrode configuration types : one is corona source, two is ground. Now of corona type, we have investigated single needle electrode, single wire electrode and double wire electrode. The

105

ground electrodesused are copper and steel plate where aluminum wire is used as corona wire. The liquids investigated are silicone 50 cst and silicone 150 cst.

Figure 4-4: Schematic of two phase (Air-Liquid) type EHD pump

4.3.2 Theory and characterization

Considering the operations and systems, this is the interactions of electric field and the charges injected into dielectric liquid. It is also known as ion drug pump whose theory is known for some time.104-105

If we simplify the problem in one dimension to formulate the flow parameters

• Force per unit area from E. field as

퐿 ∆푃 = 퐸푑푥 (4.19) ∫0

• E is a variable of any distance x, then

2퐽푥 퐸(푥) = ( )1/2 (4.20) 휇휀 106

• If we integrate this field, we can get potential, from which Current density can be

found as:

2 9휇휀푉 ⁄ 퐽 = 8퐿3 (4.21)

L is the length scale of liquid which experience the ion injection. We can assume this as liquid thickness.

• If we apply boundary condition (emitter is much smaller than average E. field and

charge density approaches infinity). We can deduce maximum pressure

2 9휀푉 ⁄ ∆푃푚푎푥 = 8퐿2 (4.22)

• Consequently, average fluid velocity and flow rate would be as

9휀푉2퐷2 푢푚푎푥 = ⁄8퐿332휂

9휀푉2휋퐷4 푄푚푎푥 = ⁄8퐿3128휂 (4.23)

Where D is the equivalent diameter of a pipe if the disturbed liquid was flowing through.

• Pump efficiency

푃𝑖푛 = 퐽𝑖푛푆푉 = 휌(휇퐸 + 푢)퐴푉

푃표푢푡 = 퐽표푢푡푆푉 = 휌(0 + 푢)퐴푉 (4.24)

Where A is the cross-sectional area.

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4.3.3 Results and discussions

EHD ion drag pumped liquid movement was observed for each of the configuration studied as shown by Figure 4-5. The liquid layer creates different kind of surface waves while they were flowing toward the inclined plane electrode from reservoir.

Figure 4-5: Driven state of silicone 100 cst at wire and needle electrode

Now there are liquids that are suitable to be pumped by this method and there is an upper

휀 bound in terms of conductivity. If the charge relaxation time ( ) is too short in comparasion 휎 to time taken for an ion to go from emitter to collector, charge is screened before they can impart enough force to liquid. In theory this method would fail to actuate liquid with

휀휗 conductivity higher than ⁄퐿 where 휗 is the ionic velocity. From experimental observations, for silicone with 50 cst, higher velocity order was found in comparison to 108

silicone 100 cst. The trends of liquid layer rising was gentle and an established layer of flow was found to happen at around 7.5-8.2 kV for 10 mm thicker oil. The waves are triangular in shape and at around 9-9.5 kV, liquid was found to be completely overflowing across the inclined electrode. On the other hand, for 100 cst silicone oil, the movement was found to happen around 6-6.5 kV for same thicker liquid. The higher viscosity comes with lower ion mobility. The transit time would decrease that will result to lower transit time/relaxation time ratio and consequently increase the efficiency in terms of creation of liquid disturbances. When wire electrode was replaced by needle electrode, a corona voltage of about 4.2-4.6 kV was noticed to initiate the movement. There was more volume instability with respect to surface instability and the bulk stability were completely broken by electroconvection. The fully developed streamline was created at around 7.5-8 kV. To understand the area effect of injecting electrode, we also employed 2 parallel wire electrode and observations were made in reference to single wire. There was found relatively more uniform climbing of liquid over the inclined electrode. It may be reasoned to the fact of increasing A in Eq. 4.24.

The experimental velocity was calculated by inserting the aluminum micron level particle and the motion was tracked down by a velocity calculating tracer module. Also the current was measured by a digital electrometer. The results of velocity are on the same order with the velocity calculated by Ohyama et al.100

109

D

T= 0 sec T= 8 sec

Figure 4-6: Driven state of silicone 100 cst at double wire

Figure 4-7: (a) Average velocity of the liquid along direction of flow. (b) Current measured in EHD flow for different corona set up.

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Chapter 5

Conclusions and guidelines for future work

Here we would like to summarize the outputs of this thesis with a potential effect in terms of applications. Also, we portray directions along the future work to be carried forward.

5.1 Summary of Thesis

In this work, we tried to investigate property and behavior of liquids and droplets when they are subjected to any ionization technique like corona discharge. In the process, we have addressed number of fundaments we have encountered related to motion of low conducting viscous liquids and conducting droplets.

Chapter 1 highlights different branches of EHD and concludes on Electro-quasistatics of moving fluids. In the process, Maxwell’s equations have been discussed from perspectives of the context. A brief summary of the chronology of development links the dots of EHD and gives an insightful idea on fields and sectors where the researches can be conducted and extended.

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Chapter 2 is entirely on Corona discharge. It is a good art of ionization of air holding immense prospects. Corona discharge is not new with a heavy historical background in gas pump technology until recently where the attention has shifted towards liquids, and hence, constitutes the main theme of this research. It has several advantages with distinct features which have been discussed along with its mechanism.

A major part of this thesis work, the behavior of conducting droplet dispersed in non - conducting medium, is included in Chapter 3. The effect of various parameters like radius, source, medium etc. are discussed in terms of deformation, polarization. The ICEP flow studied around the droplet helps visualize the combined effect of DEP and EP.

In chapter 4, we have conducted the research on bulk cm level viscous liquids. Low conducting liquids has emerged as new subject of interest when they are part of any electrical systems. We have reported different types of volume and surface instability and classified them on basis of their intrinsic property and scale of physiological systems. The success of EHD gas pump is very promising and we have applied the same technique to viscous liquid to drive them in a configured direction.

5.2 Directions of future work

• This manipulation techniques would be investigated to other kind of particles i.e

colloids and their response would further conclude on wide range of applicability

of such method. The drop-drop interaction would be another aspect to look at as

electrohydrodynamics of pair interactions is still an incomplete study.

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• The volume instability created can be controlled by operating on an automated

source input. As previous studies have shown the prospect of oil bath cooling over

liquid cooling, the electroconvection produced would be assessed for heat transfer

purposes to see its applicability for cryogenic cooling.

• Numerical studies are a good tool to clarify a lot of underlying fundaments.

Consequently, an extension of this work is to apply any method like boundary

element (BEM) to incorporate the computational results.

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