Impact Dynamics of Newtonian and Non-Newtonian Fluid Droplets on Super Hydrophobic Substrate

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IMPACT DYNAMICS OF NEWTONIAN AND NON-NEWTONIAN FLUID DROPLETS ON SUPER HYDROPHOBIC SUBSTRATE

A Thesis Presented

Yingjie Li

The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements for the degree of

Master of Science

in the field of

Mechanical Engineering

Northeastern University Boston, Massachusetts

December 2016

ACKNOWLEDGEMENTS

I hereby would like to appreciate my advisors Professors Kai-tak Wan and

Mohammad E. Taslim for their support, guidance and encouragement throughout the process of the research. In addition, I want to thank Mr. Xiao Huang for his generous help and continued advices for my thesis and experiments. Thanks also go to Mr. Scott Julien and Mr, Kaizhen Zhang for their invaluable discussions and suggestions for this work.

Last but not least, I want to thank my parents for supporting my life from China. Without their love, I am not able to complete my thesis.

TABLE OF CONTENTS

DROPLETS OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IMPACTING SUPER HYDROPHBIC SURFACE ...... i ACKNOWLEDGEMENTS ...... iii 1. INTRODUCTION ...... 9 1.1 Motivation ...... 10 1.2 Characteristic outcomes from a droplet impact on solid surface ...... 11 1.3 Super hydrophobic surface ...... 12 1.4 Related theories ...... 14 2. Experiments ...... 19 2.1 Experimental apparatus ...... 19 2.2 Preparation of super hydrophobic surface ...... 27 2.3 Droplet generation ...... 29 2.4 Experimental procedures ...... 31 2.5 Surface tension measurement ...... 37 3. Results and discussion ...... 38 3.1 Definition ...... 38 3.2 Droplet impact behaviors ...... 45 3.3 Weber number and impact behavior ...... 61 3.4 Viscosity and Spreading ...... 67 4. Conclusion ...... 73 5. Suggestions and Future work ...... 73 REFERENCES ...... 74 Appendix ...... 78

LIST OF FIGURES

Figure 1 : Examples of characteristic outcomes from a water droplet impact on solid surface ...... 12 Figure 2: Sketch of a hydrophobic surface and hydrophilic surface ...... 13 Figure 3: Water droplet with 150° contact angle ...... 13 Figure 4: Viscosity of Newtonian, Shear Thinning and Shear Thickening fluids as a function of shear rate ...... 14 Figure 5: Experimental apparatus schematic illustration ...... 21 Figure 5a: High speed camera ...... 22 Figure 5b: Light source, RPS CoolLED 100 Studio Light RS-5610 ...... 23 Figure 5c: Rainin pipette ...... 24 Figure 5d: Conduct chamber...... 25 Figure 5e: Tokina optical lens...... 26 Figure 6: : Self assembled monolayer made of HDFT molecules ...... 27 Figure 7: Illustration of droplet generation ...... 30 Figure 8: Illustration of a micropipette positioning ...... 33 Figure 9: Camera setting at pre-focusing stage ...... 34 Figure 10: Camera setting at experiment stage ...... 35 Figure 11: Illustration of record button ...... 36 Figure 12: Sketch of experiment camera locations ...... 36 Figure 13: Pendant drop schematic ...... 37 Figure 14: Illustration of pendant droplet method measurement ...... 38 Figure 15: Spreading stage of a water droplet impact on a solid surface ...... 39 Figure 16: Recoiling stage of a water droplet impact on a solid surface ...... 40 Figure 17: Rebound stage of a water droplet impact on a solid surface ...... 40 Figure 18: Illustration of contact diameter ...... 41 Figure 19: Illustration of rim, spire, film and capillary waves ...... 42 Figure 20: Illustration of jet ...... 43 Figure 21: Illustration of smooth rim ...... 43 Figure 22: Illustration of fragmentation ...... 44 Figure 23: A water droplet with D =2.6mm and v =1.45 m/s impacted on a super hydrophobic surface ...... 46 Figure 24: A milk droplet with D =2.75mm and v =1.91 m/s impacted on a super hydrophobic surface ...... 49 Figure 25: A 5% corn starch droplet with D =3.41mm and v =1.72 m/s impacted on a super hydrophobic surface ...... 52 Figure 26: A 5% corn starch droplet with D =3.40mm and v =1.71 m/s impacted on a super hydrophobic surface ...... 55 Figure 27: A blood droplet with D =2.93mm and v =1.81m/s impacted on a super hydrophobic surface ...... 57 Figure 28: A blood droplet with D =3.28m and v =1.72m/s impacted on a super hydrophobic surface ...... 59 Figure 29: Spires number K vs impact velocity v of water droplet with volume 1(3.6mm±0.1mm) and volume 2(2.6mm±0.2mm) ...... 62 Figure 30: Spires number K vs impact velocity of milk droplet with volume 1(3.4±0.16mm) and volume 2(2.5±0.15mm) ...... 62 Figure 31: Spires number K vs impact velocity of 5% corn starch solution droplet with volume 1(3.4±0.13mm) and volume 2(2.5±0.22mm) ...... 63 Figure 32: Spire number K vs velocity of 15% corn starch solution with volume 1(3.3±0.18mm) and volume 2(2.4±0.18mm) ...... 63 Figure 33: Spire number K vs velocity of rabbit blood with volume 1(3.3±0.2mm) and volume 2(2.97±0.13mm) ...... 64 Figure 34: Spire number K vs velocity of 1:1 diluted blood with volume 1(3.25±0.1mm) and volume2 (2.78±0.2mm) ...... 64 Figure 35: K vs Weber number of all experimental fluids ...... 66 Figure 36: Illustration of pinched section and bulging section ...... 67 Figure 37: Schematic of hypothetical droplet evolution with time variation ...... 69 Figure 38: Time variation of spread factor ...... 69 Figure 39: Impact of water droplet, milk droplet and blood droplet from t0 to t8 ...... 71

ABSTRACT

Conventional rheological methods such as viscometry to characterize linear and nonlinear viscosity behavior requires an excessive amount of sample liquid, which is practically impractical due to the time and cost constraints, for instances, in blood, and other scarce and expensive bio-fluids. There is an urge for a handy tool to quickly evaluate the intrinsic properties of a liquid.

In this thesis, droplet of Newtonian (e.g. water) and non-Newtonian liquids

(e.g. shear thinning blood, shear thickening starch solution) with a desired dimension is released by a pipette from a vertical distance. Gravitational attraction gives rise to an impact velocity, and the droplet hits a rigid hydrophobic surface with a liquid-substrate contact angle of 150o. An experimental set up equipped with a manual pipette, high speed camera, and substrate holder etc. is constructed to capture the geometrical change over the sequential the impact-spread-recoil- rebound process. Upon impact, the droplet turns into an expanding pancake geometry with coronal spires developing over time. In extreme conditions of high impact velocity, splashing or fragmentation is observed. The video records are analyzed in terms of the classical dimensionless Weber number (We) which comprises impact velocity and surface tension. Other measurements are made:

(i) duration of droplet on the substrate, and the change in contact area at droplet- substrate interface, prior to rebounce, (ii) critical droplet dimension and impact velocity leading to fragmentation, (iii) jet formation at rebounce, (iv) maximum number of spires, and (v) wavelength of radial Rayleigh wave. Comparison between Newtonian and non-Newtonian liquids are made, and non-linear behaviors are observed. Weber number is shown to be insufficient in describing spire formations. Non-linear viscosity, playing an indispensable role in droplet geometric deformation, must be incorporated in droplet dynamics.

Keywords: Droplet, Spires, Non-Newtonian fluids, Shear thinning, Shear thickening, Blood, Viscosity, Surface tension 1. INTRODUCTION

The phenomenon of liquid droplets impacting and spreading on a solid surface — such as rain drops falling on a windshield — is ubiquitous in daily life. The underlying mechanics has been historically appealing to many great scientists, including the Nobel laureate Pierre-Gilles de Gennes [1]. Many excellent works

[2-7] of water droplet impacting solid surface have been documented in the literature. Recently, how the wettability of the solid and the viscosity [8-13] of the fluid affecting the instability [14-16] of droplet impact and heat transfer [17-21] have drawn extensive attention from around the globe. Numerous industrial applications have been established, based on the fundamental understanding of the physical processes of droplet impact. Examples include cooling of hot surfaces [18, 22, 23], injection printing [24, 25], microfabrication [26] and laser induced transfer (LIT) [27-

29]. So far most studies have focused on Newtonian, rather than non-Newtonian, liquids. However, a wide variety of fluids encountered in science and technology— such as biological fluids (e.g. blood, synovial fluid, saliva), adhesives, dairy products and polymeric fluids — do not exercise classical Newtonian fluid behavior. A Newtonian liquid is one in which the viscosity is independent of shear strain rate  at constant pressure and temperature [30]. Non-Newtonian fluids, on the contrary, are characterized by their non-linear and time-dependent viscosity, which is a function of  [31]

1.1 Motivation

Recently, non-Newtonian bio-fluids have attracted much interest in the scientific community, due to their wide applications in life sciences [32, 33]. For instance, a comprehensive understanding of the rheology of non-Newtonian fluids will facilitate the study of pathophysiology. It is logical to presume that the viscosity of blood, for example, changes with pathologic conditions because the apparent viscosity is determined by hematocrit, red blood cell (RBC) aggregation and plasma viscosity, which are influenced by such factors as infections, hypertension and diabetes [34-36]. The pathologic conditions of blood samples from virus- or bacteria-infected patients change rapidly with time. For example, in malaria- infected patients, the multiplication of the plasmodium parasite and its life cycle causes a large quantity of red blood cells (RBC) burst quickly and periodically [37].

Conventionally, in order to monitor a patient’s pathologic conditions, blood samples are taken and prepared for cytometry and observation under optical microscope, which are time-consuming and incapable to track the transient behavior of RBC, that is known to change rapidly within 1-2 minutes [35, 36, 38-40]. It is highly desirable if the transient changes in blood viscosity can be empirically quantified to identify infection and associated pathologic conditions.

In classical fluid mechanics and droplet dynamics, Weber number and

Reynolds number play an essential role in geometric changes of droplet impact on a surface. The sequential droplet deformation during impact, spreading, recoil and rebound can serve as indicators of surface tension, viscosity, advancing and receding contact angles, and, albeit, the rheological properties of fluid. Conventional methods such as viscometry require an excessive amount of sample liquid [34, 41], which is impractical for blood and other scarce and expensive bio- fluids. A rigorous but quick quantification of hematology and pathophysiology is most welcome for research in biology and medical science in general.

1.2 Droplet impact on solid surface

Six characteristic morphological stages are involved when Newtonian droplets impact a solid surface, and are discussed by R. Rioboo [42], as shown in Fig. 1.

“Deposition” on hydrophilic surfaces and “receding break-up” are related to wettability and lie beyond the scope of this thesis. “Prompt splash”, “corona splash”, and “partial / complete rebounce” are expected in non-Newtonian fluid impacting on a super hydrophobic substrate with an advancing contact angle of

150o. During “corona splash”, an impacting droplet turns into a “pancake” with uniform thickness, followed by “spires” developing at the rim, and might ultimately fragment or splash under special circumstances. This thesis focuses on the experimental investigation. A high-speed camera is used to perform in-situ observation over a range of droplet dimension and impact velocity.

Figure 1: Water droplet impacts a solid surface according to Rioboo.

1.3 Super hydrophobic surface

The natural self-cleaning ability of lotus leaves is appealing to the scientific community. The fascinating phenomenon is strongly related to micro-/nano-scale surface roughness and hydrophobicity, and has wide industrial applications.

Related papers are voluminous in the literature. Smooth and super-hydrophobic surfaces are used in the present study. Contact angle is determined by the wettability of the solid surface. A hydrophobic surface has a contact angle  exceeding 90o is hydrophobic, and becomes super-hydrophobic  > 130o. In contrary, a surface with  < 90o is hydrophilic as illustrated in Figure 2. . Figure 3 shows a water droplet standing on a super hydrophobic surface with  ≈150o.

Figure 2: Sketch of a hydrophobic surface and hydrophilic surface[43]

Figure 3: Water droplet with with  ≈150o 1.4 Existing models

1.4.1 Newtonian and non-Newtonian behavior

In fluid mechanics, the viscosity of a Newtonian liquid is a constant independent of the rate of change of shearing strain over time,  , but depends only on temperature and pressure [44]. Conversely, a non-Newtonian fluid exercises nonlinear viscous behavior, as its viscosity changes as a function of ,

휇 = 푓(훾̇) (1) as illustrated in Figure 4.

Figure 4: Viscosity of Newtonian, Shear Thinning and Shear Thickening fluids as a function of shear rate[45].

Non-Newtonian Fluids are in general categorized into four types based on the change of viscosity: thixotropic, rheopectic, shear thinning and shear thickening. Shear thickening liquid has its 휇 increasing with 훾̇, while shear thinning fluids has a monotonic decreasing 휇(훾̇). Should 휇 changes with time, the fluid is either thixotropic or rheopectic. Table 1 summarizes the four non-Newtonian types.

Type of Description Example behavior

Viscosity decreases Honey – keep stirring, and Thixotropic with stress over time solid honey becomes liquid

Viscosity increases with Cream – the longer you whip it Rheopectic stress over time the thicker it gets

Shear thinning Viscosity decreases Blood, tomato sauce or pseudoplastic with increased stress

Shear thickening Viscosity increases with Corn starch solutions or dilatant increased stress

Table 1: Summary of four types of non-Newtonian liquids

This study investigates a range of Newtonian and non-Newtonian fluids.

Water is the classic representative of Newtonian liquid. Milk only simulates

Newtonian, as its viscosity is fairly constant over strain rate at room temperature.

Corn starch solution is non-Newtonian shearing thickening. Here, it comprises

100% pure corn starch from local supermarket with a concentrations of 5% and

15% by mass. Rabbit blood purchased from Innovative Research serves as shear thinning liquid. In our droplet experiments, blood samples are either as-received or diluted with distilled water at 1:1 volume ratio. Table 2 summarizes properties of the liquid in this study. Droplet Liquid Surface Weber number Liquid diameter density tension We D(mm) ρ(kg/m3) σ(mN/m)

Distilled water 30.82~235.38 2.4~3.7 1000 72

Whole Milk 34.83~218.95 2.35~3.56 1035 60.05

5%Corn starch 33.46~215.23 2.28~3.53 1052.63 67.65 solution

15% Corn starch 49.75~253.27 2.22~3.48 1176.47 62.34 solution

Blood 120.48~242.01 2.84~3.50 1082.15 56.30

Diluted blood at 58.54~211.68 2.58~3.35 1042.7 68.05 1:1 volume ratio

Table 2: Weber number and droplet initial diameter are measured from experiments. Surface tension is measured by Fordham’s pendant drop method [46].

1.4.2 Non-dimensional parameters

The dimensionless Weber and Reynolds number play important roles in droplet dynamics. Weber number is a dimensionless number useful in analyzing fluid flows where there is an interface between two different fluids, or, in the present context, the droplet-substrate interface. They are defined by

𝜌푣2퐷 푊푒 = (2) 𝜎 𝜌푣퐷 푅푒 = (3) µ where ρ, σ, µ are denoted as the density, surface tension, and viscosity of the liquid, respectively, and D and the v are denoted as droplet diameter before impact, and impact velocity, respectively. We is a measure of the relative importance of the fluid's inertia compared to its surface tension [49], and indicates whether the kinetics or the surface tension energy is dominant. According to the literature, water droplet impacting on a super hydrophobic surface with We << 1, surface tension dominates and droplet remains roughly spherical. This study considers only We > 1. Re is the ratio of inertial forces to viscous forces within a fluid. Bhola and Chand [47] investigated spire formation at the rim of a molten wax droplet and asserted that the number of coronal spires given by

푊푒0.5푅푒0.25 푘 = (4) 4√3

Marmanis and Thoroddsen [48] investigated a variety of liquid droplets impacting a paper surface and found k to be a function of (We0.25Re 0.5)0.7. Such model is not not applicable to non-Newtonian fluids as expected.

1.4.3 Related models of characteristic behaviors

The dynamic behaviors of droplet impact can be described as three stages: spreading, recoiling and rebound, which are characterized by capillary waves, rim instability and jetting governed by different mechanisms. There are qualitative model discussing shock wave, moving contact line, capillary wave, Rayleigh-

Plateau instability, Rayleigh-Taylor instability, air cavity, and pinch-off dynamics.

The capillary waves observed at the early spreading stage is thought to be depending on generation of shock wave. The wavelength is a function of surface tension and viscosity as well as droplet kinematic input such as impact velocity.

The Rayleigh-Plateau instability is related to “break-up” of a liquid jet, while

Rayleigh-Taylor instability underlies the break up of an interface between two dissimilar fluids of different densities. The combined model is expected to be valid in the perturbation and fragmentation of the rim of a droplet upon impact. Jet was first observed by Worthington when he investigated a milk droplet impact in liquid pool, and was coined “Worthington Jet”. Similar jets are found in droplet impacting a solid surface. Air cavity dynamics and pinch-off dynamics closely related subjects.

In this thesis, the dynamics of droplet impact, specifically rim instability, is investigated experimentally. The results are compared with theoretical analysis based on Rayleigh-Plateau instability. Another graduate student in our research group, Xiao Huang, is currently building a theoretical model in this context. From

Huang’s unpublished work, the number of the spires during a water droplet impact is given by

푘 = 0.9421 ∗ [log(푊푒)]4 − 0.4122 (5)

Detailed comparison between this model and the experimental results will be discussed in Chapter 3

2. Experiments

The experimental setup and its components for this study are outlined below, and so are the step-by-step procedures.

2.1 Experimental apparatus

Figure 5 shows the assembled homemade apparatus and the components.

Specifications are given below:

 High speed camera, Edgertronic Monochrome: The high speed camera,

Edgertronic, whose exposures are able to be down to 1/200,000 seconds,

resolution settable from 192x96 to 1280x1024, ISO 400-6400 and frame

rates up to 17,791 fps (resolution dependent)

 Light source, RPS CoolLED 100 Studio Light RS-5610: The RPS Studio

LED Studio Light uses a single 100 watts (energy usage) LED that produces

light equal to 1000 watts when the 8” reflector is attached to it. The light

output is adjustable yet the color temperature of the light stays a constant

daylight (5200°K). Mounts to any standard 5/8” light stand spigot. The on/off

switch is in the 3-meter power cord. Complete with 8” Bowen’s mount style

reflector that will accept a standard umbrella, shower cap style diffuser, and

protective cap.

 Pipette, Rainin Classic PR-200: The volume range of PR-200 is from 20 µL

– 200 µL, and the manual increment is 0.2 µL. Accuracy of the pipette is ±

2.5 % per 0.5 µL and precision is ± 1 % per 0.2 µL.

 Aluminum experimental conduct chamber: The apparatus is designed and

assembled by an undergraduate capstone group, which is made of assembled aluminum rack and provides adjustable impact angle and impact

velocity.

 Optical lens, Tokina 100mm f/2.8: This lens is a macro lens for digital

camera, capable of life-sized (1:1) reproduction at 11.8 in. (30 cm). The

lens' multi-coating matches the highly reflective silicon based CCD and

CMOS sensors in digital SLR cameras, while the optics give full coverage

and excellent sharpness on 35mm film. The focal length is 28-70mm, close

focus up to 0.7 meter, working distance is 115mm.

Figure 5: Experimental setup comprising a frame (d) with the two platforms (A and B) and mounting fixtures for the micropipette (c), a light source (b), and the camera-lens assembly (a and e, respectively). The the camera-lens assembly is mounted on Platform A, and it is height and angle adjustable. The super hydrophobic surface is placed on Platform B. The vertical micropipette is mounted directly above the super hydrophobic surface and is used to dispense the sample droplet.

Figure 5a: High-speed camera. The camera has a computer interface to record the experiments at 6000 frame per second (fps). Recording is automatically triggered.

Figure 5b: RPS CoolLED 100 Studio Light RS-5610. The LED light is mounted on the conduct chamber (d) and provides light in case of recording video with high fps.

Figure 5c: Rainin pipette. Micropipette is used to dispense the sample droplets. During an experiment, the pipette tip was filled prior to adjust the volume adjustment knob (VAK). When it was time to dispense the droplet, the VAK was turned in the clockwise to decreasing volume. This gradually dispenses the fluid from the pipette tip, forming a gradually-growing droplet pendant at the end. When then pendant reached a critical volume, it broke free from the tip, and fell downward.

Figure 5d: Metal frame for assembly.

Figure 5e: Tokina optical lens

2.2 Preparation of super-hydrophobic surface

There are many standard ways to create super-hydrophobic surfaces made from polymers, metals or carbon nanotubes for different purposes. In the present work, a copper sheet is used as the substrate. All chemicals are purchased from

Sigma-Aldrich. The surface is prepared by two consecutive steps. Two main processes are composed to make the surfaces. First, we follow the instructions outlined in UVA super hydrophobicity manual [49] created by Backer et al. By silver coating with nano-scale surface roughness is produced by reacting the copper surface with silver nitrate. The silver cations (Ag+) are reduced by copper to metal silver. The coated copper sheet is then immersed in heptadecafluoro-1- decanethiol (HDFT) solution, resulting in a self-assembled monolayer with non- polar molecular segments as shown in Figure 6.

Figure 6: Self assembled monolayer made of HDFT molecules[50]

Step 1: Substrate preparation

Copper sheet (2cm x 5cm) is polished using a 500-grit pad under fingertip pressure. The residual copper and abrasive particles are wiped off using a tissue.

The plate is examined for surface roughness using an optical microscope.

Step 2: Fine polish

Polishing is repeated using grit pads of 800, 1200, 1500 and 2000 till a mirror surface is obtained. For the purpose of easily recognizing the polished side and facilitating capture by tweezers, pliers are used to bend up one corner of the copper toward polished face.

Step 3: Chemical solution preparation

Four beakers are prepared and labelled. Beaker 1 is filled with 40mL of silver nitrate (AgNO3), Beaker 2 with 40mL of De-ionized (DI) water, Beaker 3 with 40mL of dichloromethane (CH2CL2) and 11.5mL Heptadecafluoro-1-decanethiol

(HDFT), and Beaker 4 with 40mL of dichloromethane (CH2CL2). Gentle stirring is applied at each stage.

Step 4: Super hydrophobic surface creation

The polished Cu sheet is placed by using the tweezers in AgNO3 (Beaker 1) with the polished side facing up for 2 minutes. The Cu sheet is then transferred to DI water (Beaker 2) for 20 seconds and blown dry with a nitrogen gun. The Cu sheet is then placed in Beaker 3 for 5 minutes. The sheet is finally dropped in in dichloromethane (Beaker 4) for 20 seconds and blown dry.

2.3 Droplet generation

A micropipette is used to generate and dispense liquid droplets. The volume adjustment knob (VAK) is set to 20 µL before filling the disposable plastic tip with sample liquid. Two distinct methods are used to dispense a droplet. In method

(i), the plunger is depressed to eject the droplet. There is limited control over the velocity of the droplet. In method (ii), the pipette tip is filled prior to adjusting the

VAK. When it is time to dispense the droplet, the VAK is turned in the clockwise direction to decrease volume. This gradually dispenses the fluid from the pipette tip, forming a gradually-growing pendant drop at the tip. When the drop reaches a critical size, it breaks free from the tip, and falls downward. This method, illustrated in Fig. 7, is used to ensure a zero initial velocity.

Figure 7. Droplet generation

2.4 Experimental procedures

Step 1: Experimental apparatus assembly

The pipette (Fig. 5c) is held by a fixture vertically above the super-hydrophobic surface on platform B. The high speed camera-lens assembly is mounted on platform A to videotape the experiments. The light source (b) is mounted next to platform B in a direction pointing to the target plate.

Step 2: Camera and Micropipette

The height h between the micropipette tip and the super hydrophobic surface as shown in Fig. 8. Initially h is set to be 12.7 mm (0.5 inches) from platform B. Height of Platform B is adjustable to vary the flight distance. Height of Platform A is also adjustable to fine tune the camera position. Both platform A and B are kept horizontal. The working distance L between the camera and target substrate is set to be 600 mm.

Step 3: Camera setting

Camera is computer controlled and its setting includes two stages: pre-focusing and experiment. At pre-focusing setting stage, camera is set as shown in Fig. 9 and lens (e) is rotate to focus. The position of the camera is adjusted to make sure the surface is placed in the center on the screen. The setting is then switched to experiment stage as shown in Fig. 10 and lens (e) is rotate to focus again. The

ISO, light intensity and aperture ae modulated correspondingly to make sure the brightness is proper to see the details on the substrate.

Step 4: Experimental operations of taking horizontal view videos

Method (ii) mentioned in Chapter 2.3 is used to generation droplets. The record button as shown in Fig. 11, is trigger at the instant of droplet impact evolution completed. The height of h is increased by adjusting platform A with an increment of 6.35mm (0.25 in) and limited at the elevation of 140 mm (5.5 in). Experiments of each elevation repeat 5 times.

Step 5: Experimental operations of taking 45o view videos

The camera is regulated to the positon as shown in Fig. 12 by adjusting the height and angle of platform A. Then septs 3 and 4 are repeated.

Figure 8: Illustration of a micropipette positioning

Figure 9: Camera setting at pre-focusing stage

Figure 10: Camera setting at experiment stage

Figure 11: Illustration of record button

Fig. 12 Sketch of experiment camera locations

2.5 Surface tension measurement

Surface tension is measured by pendant drop method [46]. The shape of the drop a result of the relationship between the surface tension and gravity. The pendant drop geometry is presumably universal and is independent of liquid intrinsic properties such as surface tension. A snapshot is taken at the pipette tip and is analyzed according to the classical theory to deduce surface tension.

Fig 13: Pendant drop schematic [51]

푑 푆 = 푠 (6) 푑푒 where 푑푒 is the droplet diameter at its maximum width and 푑푠 is the width at the distance of 푑푒 from the bottom, and 푆 is the ratio of 푑푠 and 푑푒 ,as illustrated in

Fig.13. Then surface tension can be found by putting

∆𝜌푔푑2 𝜎 = 푒 (7) 퐻 where ∆𝜌 is the density difference between the interface, 1/H is a value dependent on S and the calculation tables from are given in Appendix.

Figure 14: Illustration of pendant droplet method measurement

3. Results and discussion

In this section, necessary terminological names are defined. Droplet impact behaviors of Newtonian and non-Newtonian fluids are discussed. The influence of impact velocity, droplet diameter and Weber number on the formation of spires on the rim are investigated. Experimental results are compared to Huang’s theoretical model. The effects of viscosity exerted on spreading are studied.

3.1 Definition

To better understand the droplet impact behaviors, necessary terminological terms are defined in this area section prior to discussion.

3.1.1 Stage, contact diameter and impact velocity

In droplet dynamics, three stages are observed during droplet impact evolution: spreading, recoiling and rebounce. The spreading stage, as shown in

Figure 15, begins at the instance of the droplet impacting on the target surface, and ends when the droplet reaches its maximum lateral spreading. At this stage the droplet spreads radially, and the contact diameter increases. The recoiling stage, as shown in Fig. 16, begins when the droplet contracts from its extent of maximum spread. When the contact diameter is equal to 0, the droplet lifts off the surface. This final stage of rebounce is shown in Fig. 17. The contact diameter (Dc) is illustrated in Fig. 18. Impact velocity is given as

푣 = √2푔ℎ (8) where ℎ is the released height denoted at Chapter 2.4.

Figure 15: Spreading stage of a water droplet impact on a solid surface. The spreading stage begins at the instance of the droplet impacting on the super hydrophobic surface and ends when droplet reaches its maximum spreading.

Figure 16: Recoiling stage of a water droplet impact on a solid surface. The recoiling stage begins when the droplet reaches its maximum spreading, and ends at the instance when the contact diameter is equal to 0.

Figure 17: Rebounce of a water droplet after impact. The contact diameter equals to 0.

Figure 18: illustration of contact diameter

3.1.2 Spires, film and jet

Corona splashing is one of the six types of droplet outcomes mentioned at

Chapter 1.2. During corona splashing, the spires are found and developed from the perturbations around the rim. The number of the spires at its maximum spreading is counted and denoted as k. The relation between the number of the spires k and the liquid properties is studied and discussed in subsequent sections.

The central area of the droplet where the capillary waves are found and observed is termed the “central film”. Illustration is shown in Fig. 19. At the recoiling stage, the droplet shoots back in the opposite direction of the droplet impact as a pillar and this behavior is defined as the “jet”, which is shown in Fig. 20.

Figure 19: Rim, spire, film and capillary waves

Figure 20: Jet

Figure 21: Smooth rim without spires

Figure22: Fragmentation

3.1.3 Smooth rim and fragmentation

Figure 21 shows a typical droplet with small We, the rim is smoother and no spire is observed. with smooth rim. Figure 22 shows another droplet with high We, fragmentation with splashing is observed.

3.2 Droplet impact behaviors

3.2.1 Droplet impact behaviors of Newtonian fluids

Most research works in the literature are based upon Newtonian water. The present study exploits water droplet impact on super hydrophobic surface. Fig. 7 consists of an image sequence of water droplet with D = 2.6mm and 푣 =1.45m/s impacting on a super hydrophobic surface. It showed the successive stages of droplet impact evolution, with time from initial impact indicated. The water droplet was recorded from t=0 at which right before the droplet landing on the super hydrophobic surface. The rim of the droplet was unstable, since spires were generated around the edge. As time went on, it continued to spread and reached its maximum spread at t =2.33ms. At the same time, the number of spires also reached its maximum. As the water of droplet continued flowing outward from the center film to the rim, the thickness of the central film and contact area decrease, while the size of the spires increased. At t=3.33ms and t=4.5ms, growth of spires resulted in spire merging and spire number decreased. During the entire process, surface tension acted against the increase in surface area. The spires were pulled back together by surface tension, and eventually the droplet lifted off the surface at t =12ms.

Figure 23: A water droplet with D =2.6mm and 푣 =1.45 m/s impacted on a super hydrophobic surface. Scale bar was shown at t=0. At t=1ms, the droplet was impacting on the substrate. At t=2.33ms, the droplet reached its maximum spreading and 16 spires were counted. From t=2ms to t=4.5ms, corona rim was presented. At t=12ms, the droplet was pulled together by surface tension.

Whole milk is usually taken to be a Newtonian fluid, even though it is not a pure substance like water. This is because it does not differ appreciably from

Newtonian behavior at room temperature during shelf life. Figure 8 shows a series of photos of a milk droplet with v =1.91 m/s and D =2.75mm impacting on a super hydrophobic surface. Spiky and sharp spires show up around the rim when the droplet hit the solid surface at t = 0.67ms. The number of spires is counted as 14 when the milk droplet reached its maximum spreading at t =2.5ms. It is evident that central fluid flows radially towards the rim, reducing the thickness and contact area. Spires merge at t = 4ms. When t = 5ms, the spires number reduces to 8. At t =7ms, the spires retreats towards the center, as surface tension tends to minimize the droplet surface area. At t = 9.83ms, fragmentation occurs. Milk droplet are observed to be more stable than water, as the rim is smoother and coronal spires are fewer.

Figure 24: A milk droplet with D =2.75mm and 푣 =1.91 m/s impacted on a super hydrophobic surface. Scale bar was shown at t=0. At t=0.67ms, the droplet was impacting on the substrate. At t=2.5ms, the droplet reached its maximum spreading and 14 spires were counted. From t=2ms to t=5ms, corona rim was presented. At t=7ms, the droplet was pulled back to the center by surface tension. At t=9.83ms, fragmentation was observed.

3.2.2 Shear thickening and shear thinning fluids

In shear thickening fluids, viscosity increases with strain rate. When shear is applied, the fluid thickens and its behavior becomes solid-like. Two different concentrations of corn starch solutions — sometimes called oobleck — are investigated in this research: 5% and 15% by mass.

Fig. 25 shows a droplet of 5% corn starch solution with v =1.72 m/s and D

= 3.41mm impacting on a super-hydrophobic surface. Spires begin to appear at t

= 0.83ms. Fluid then flows radially to the rim turning into flat pancake at t = 1.67ms.

Spires are were obtuse at the tip. At t = 3.83ms, the droplet spreads to its maximum diameter, and 16 spires are observed around the rim. Additional minor spires protrudes from the rim and merge with the adjacent spire from t = 5.7ms to

7.3ms. At t=15ms, the droplet pulls back together by surface tension, followed by jetting.

Figure 25: A 5% corn starch droplet with D =3.41mm and 푣 =1.72 m/s impacted on a super hydrophobic surface. Scale bar was shown at t=0. At t=0.83ms, the droplet was impacting on the substrate. At t=3.83ms, the droplet reached its maximum spreading and 16 spires were counted around the rim. From t=0.83ms to t=7.33ms, corona splash was presented. At t=9.5ms, the droplet was pulled back to the center by surface tension. At t=15ms, the droplet jetted.

Figure 26 shows the impact of a 15% corn starch droplet with 푣 =1.71 m/s and D =3.40mm. Unlike water, milk and the 5% corn starch solution, the highly concentrated corn starch droplet spreads on the solid substrate with a smooth round rim like a bowler hat at t = 0.33ms. Perturbation on the rim emerges as protrusions. The protrusions grow into spires since more and more fluid flows towards the rim. Spreading of the droplet on the solid surface is out of sync with the spire growth. When the droplet reaches its maximum spreading at t = 4ms, no new spire is generated, but the existing spires do not develop fully until t = 5.17ms.

The spires are obtuse and rounded. The droplet remains symmetric and is apparently more stable. After reaching the maximum contact area, the pancake recoils and the adjacent spires coalesce. The spires do not have sufficient inertia to detach or the ability to detach from the mother drop to form secondary droplets.

The droplet retreats due to surface tension, followed by jetting at t =13.5ms.

Figure 26: A 5% corn starch droplet with D =3.40mm and 푣 =1.71 m/s impacted on a super hydrophobic surface. Scale bar was shown at t=0. At t=0.33ms, the droplet was impacting on the substrate. At t=4ms, the droplet reached its maximum spreading and 14 spires were counted around the rim. At t=5.17ms, the spires were developed completely. From t=4ms to t=7.83ms, corona splash was presented. At t=9.67ms, the droplet was pulled back to the center by surface tension. At t=13.5ms, the droplet jetted.

3.2.3 Droplet impact behavior of shear thinning fluids

In shear thinning fluids (e.g. blood), viscosity decreases with strain rate. In this work, rabbit blood as received and diluted blood are investigated. Figure 27 shows impact of a blood droplet with v =1.81m/s and D =2.93mm. The droplet spreads with a rounded and smooth rim without perturbations at t = 1ms. At t =

2.67ms, the droplet reaches its maximum spreading, and 9 spires develop at the rim. Upon recoil at t=5.67ms and t=6.67ms, the droplet retracts radially and capillary waves are observed on the central film. At t=14.5ms, jetting occurs.

Figure 27: A blood droplet with D =2.93mm and v =1.81m/s impacted on a super hydrophobic surface. Scale bar was shown at t=0. At t=1ms, the droplet was impacting on the substrate and there was no perturbation observed on the rim. At t=2.67ms, the droplet reached its maximum spreading and 9 spires were counted around the rim. At t=4ms, the spires were developed completely. From t=2.67ms to t=4.67ms, corona splash was presented. The droplet was pulled back to the center by surface tension at t=9.67ms and jetted at t=14.5ms.

Figure 28 shows diluted blood droplet with D =3.28mm and v =1.72 m/s. At t = 1ms, perturbation around the rim is seen. The spires are obtuse and regular, which are quite different from the sharp and spiky spires in milk. These spires distribute at approximate equidistance on the rim with similar size and shape. Symmetry persists throughout the impact-recoil process, contrasting the irregular and asymmetric spires in water droplet. At t = 3.17ms, the droplet reaches its maximum contact diameter with 12. At t = 6.5ms, capillary waves are observed on the central film. At t = 19.67ms, jetting occurs. The jet is large in cross section and comprises most of the overall mass.

Figure 28: A blood droplet with D =3.28m and v =1.72m/s impacted on a super hydrophobic surface. Scale bar was shown at t=0. At t=1ms, the droplet was impacting on the substrate and there were perturbations observed on the rim. At t=3.17ms, the droplet reached its maximum spreading and 12 spires were counted around the rim. At t=4.17ms, the spires were developed completely. From t=1ms to t=6.5ms, corona splash was presented. The droplet was pulled back to the center by surface tension at t=10.67ms and jetted at t=19.67ms.

3.3 Weber number and impact behavior

3.3.1 Velocity and spire formation

Velocity and droplet diameter are two variables that can be varied as desired. Two different sizes of water droplets are created and released by different pipette tips with varying heights. Figs.29-34 show the relation of number of spires as a function of impact velocity for droplets of two different sizes. V1 and V2 represented the volume of larger and small droplets respectively. Regardless of the fluid nature, increase in impact velocity leads to more spires. With the same velocity, large droplets generate more spires. From Equation (2), the square of velocity and the diameter are directly proportional to We. Higher impact velocity and a large droplet volume trigger more perturbation and provide more kinetic energy to the liquid to generate more spires. The number of spires is directly proportional to We no matter the fluid involved is Newtonian or non-Newtonian.

15 V1 Water V2 Water 10 V1 V2

5 The number number The spires of k

0 0 0.5 1 1.5 2 2.5 Impact velocity v m/s

Fig. 29: Spires number K vs impact velocity v of water droplet with volume 1(3.6mm±0.1푚푚) and volume 2(2.6mm±0.2푚푚)

K 14

10 V1 Milk 8 V2 Milk

6 V1 V2 4

2 The number of spires spires of number The 0 0 0.5 1 1.5 2 2.5 Impact velocity v m/s

Figure 30: Spires number K vs impact velocity of milk droplet with volume 1(3.4±0.16푚푚) and volume 2(2.5±0.15푚푚)

15 V1 5% CS 10 V2 5% CS V1 5 V2

The number number The sipres of K 0 0 0.5 1 1.5 2 2.5 Impact velocity v m/s

Figure 31: Spires number K vs impact velocity of 5% corn starch solution droplet with volume 1(3.4 ±0.13푚푚 ) and volume 2(2.5±0.22푚푚)

18 16 14 12

10 V1 15% CS 8 V2 15% CS 6 V1 V2 4

2 The number of sipres sipres K number The of 0 0 0.5 1 1.5 2 2.5 Impact velocity v m/s

Figure 32: Spire number K vs velocity of 15% corn starch solution with volume 1(3.3±0.18푚푚) and volume 2(2.4±0.18푚푚)

10 V1 Blood 8 V2 Blood

6 V1 V2 4

2 The number of sipres sipres K number The of 0 0 0.5 1 1.5 2 2.5 Impact velocity v m/s

Figure 33: Spire number K vs velocity of rabbit blood with volume 1(3.3±0.2푚푚) and volume 2(2.97±0.13푚푚)

18 16 14 12 V1 1:1 Diluted 10 Blood V2 1:1 Diluted 8 Blood V1 6 V2 4

2 The number of sipres sipres K number The of 0 0 0.5 1 1.5 2 2.5 Impact velocity v m/s

Figure 34: Spire number K vs velocity of 1:1 diluted blood with volume 1(3.25±0.1푚푚) and volume2 (2.78±0.2푚푚)

3.3.2 Weber number and spire formation

A positive correlation of k(We) is expected in both Newtonian and non-

Newtonian fluids. Figure 35 shows k(We) for water, milk, blood, 1:1 diluted blood,

5% corn starch, and 15% corn starch, along with Huang’s theoretical perdition.

Curve fitting in Figure 35 shows monotonic increasing k(We) for all liquids. From his work, k is predictable and is a function of We. Huang’s model is capable of predicting the number of spires in water but not the non-Newtonian fluids. The phenomenological equations of each fluid are shown below. For

Water, 푘 = 6 × 10−6푊푒3 − 0.0029푊푒2 + 0.547푊푒 − 18.769

Milk, 푘 = −2 × 10−6푊푒3 + 0.0005푊푒2 + 0.0543푊푒 − 0.5028

5% corn starch, 푘 = 14.011 × 푙푛(푊푒) − 56.697

15% corn starch, 푘 = −3 × 10−6푊푒3 − 0.0013푊푒2 + 0.0549푊푒 − 0.5028

Blood, 푘 = 20.453 × 푙푛(푊푒) − 99.417

Diluted blood, 푘 = 6 × 10−7푊푒3 − 0.0008푊푒2 + 0.279푊푒 − 12.129

It is apparently that We alone is not sufficient to predict the impact behavior, especially the number of spires.

We Water 20 Weber Milk Weber Corn starch 5% Weber Corn starch 15% 15

Weber Blood K Weber 1:1 Diluted Blood Xiao' theoretical predition 10 Water(72,1000) Milk(60.05 1035)

5 Corn starch 5%(67.6,1052.63) Corn starch 15%(62.34 1176.47) Blood(56.30 1082.15) 0 0 50 100 150 200 250 300 We

Figure 35: K vs Weber number of all experimental fluids

Figure 35 shows the best fits of the liquid investigated. The higher the surface tension the more spires are generated at the same We (c.f. Table 2). It is worthwhile to remark that the dilute corn starch solution has roughly the same  as dilute blood, and their k(We) overlap. This is also true for the concentrated corn starch solution and milk. Such correlation is quite consistent with the Rayleigh-

Plateau instability. The surface tension–driven instability describes a stream of fluid that breaks into smaller droplets. When a drop impacts on a solid surface, perturbation around the rim appears as crest and valley of waves with positive and negative curvatures in regular intervals or wavelength [52]. Liquid with higher  tends to create more spires with the same We.

Figure 36: Illustration of pinched section and bulging section

3.4 Viscosity and Spreading

Toivakka [53] demonstrated that both  and  have negative influence on initial spreading. But how they affect the impact behavior remains unclear. The contact diameter Dc immediately after impact should be a function of time as shown schematically in Figure 37. If two different droplets (e.g. blood and water) with the same We impact a super-hydrophobic surface,  pushes Dc(t) to the right. Higher

 prolongs the contact interval. Increase in  shifts the curves up as surface tension constrains the spreading and minimizes the surface area. Figure 38 shows lateral spreading of water, milk and blood droplets. Since it is difficult to generate the droplets with identical initial diameter D by the pipette, instantaneous diameter

Dc is normalized with respect to D. Here D is defined to be the diameter just before impact at to = 0. Water, milk and blood spread from to to their maximum extent at t2 = 3.33ms, t4 = 4.17ms and t3=3.83ms. Recoil follows immediately. At t5=7.33ms, water droplet begins to jet and is lifted off the substrate at t8=12.5 ms. Surface flaws on the substrate cause some droplet to stick. Blood and milk droplets jetted at t6=9 ms and t7=10.17 ms respectively, but no complete lift-off is observed. Liquid

Table 3 summarizes the liquid properties and behavior. The measurements are qualitatively consistently with the hypothesis: (i)  maximizes spreading, and (ii)  delays spreading and prolongs contact. It is remarkable that water droplets lead to numerous coronal spires contrasting the fairly smooth rims in blood. Viscosity does not seem to control the spire formation directly, but apparently prolongs the contact time and the impact-spread-recoil process. Viscosity slows down the advancing and retreating fronts. Figure 39 shows the droplet geometry as function of time.

Figure 37: Schematic of hypothetical droplet evolution with time variation

Figure 38: Time variation of spread factor

Liquid Water Whole Milk Blood

Weber number 122.01 122.60 120.48

Reynolds number 4224.43 1691.44 1832.72

Spire number 14 10 0

Surface tension 72 60.05 56.30 (mN/m)

Viscosity (cp) 1 3[54] 2.6[55]

Initial diameter (mm) 2.75 3.38 2.67

Time of maximum 3.33 4.17 3.83 spreading (ms)

Time of jetting (ms) 7.33 10.17 9

Maximum dc/Do 6.79 7.29 7.62

Table 3: Droplets properties and behavior

Figure 39: Impact of water, milk and blood droplets from t0 to t8. At t=t1, three droplets was impacting on the super hydrophobic surface.

At t=t2, water droplet reached its maximum spreading. At t=t3, blood droplet reached its maximum spreading. At t=t4, milk droplet reached its maximum spreading. At t=t5, water droplet started to jet.

At t=t6, blood started to jet. At t=t7, milk started to jet. At t=t8, water droplet lifted off the surface.

4. Conclusion Spire generation by liquid droplet impact is investigated based on the classical model of Weber number. Our experimental data supports a positive correlation between Weber number and the number of spires, k, in both Newtonian and non-Newtonian fluids. A droplet impact with higher Weber number leads to more spires at the rim. It is also found that number of spires increases with surface tension. Comparison between theory and experiment shows that classical model for Newtonian liquids is inadequate to predict spire formation in non-Newtonian fluids. Viscosity affects the droplet geometric deformations during impact evolution, and must be incorporated into the model involving Weber number.

Nonlinear viscosity prolongs the contact time with the substrate and therefore modifies the impact-recoil process. Droplet impact provides a tool to gauge surface tension and nonlinear viscosity in short time.

5. Suggestions and Future work

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Appendix