J. Indian Inst. Sci. A Multidisciplinary Reviews Journal ISSN: 0970-4140 Coden-JIISAD © Indian Institute of Science 2018. Electrohydrodynamic Phenomena Aditya Bandopadhyay1* and Uddipta Ghosh2 REVIEW REVIEW ARTICLE Abstract | This work is a review article focused on exploring the interac- tions between external and induced electric felds and fuid motion, in the presence of embedded charges. Such interactions are generally termed electrohydrodynamics (EHD), which encompasses a vast range of fows stemming from multiscale physical effects. In this review article we shall mainly emphasize on two mechanisms of particular interest to fuid dyna- mists and engineers, namely electrokinetic fows and the leaky dielec- tric model. We shed light on the underlying physics behind the above mentioned phenomena and subsequently demonstrate the presence of a common underpinning pattern which governs any general electrohy- drodynamic motion. Hence we go on to show that the seemingly unre- lated felds of electrokinetics and the leaky dielectric models are indeed closely related to each other through the much celebrated Maxwell stresses, which have long been known as stresses caused in fuids in presence of electric and magnetic felds. Interactions between Maxwell Stresses and charges (for instance, in the form of ions) present in the fuid generates a body force on the same and eventually leads to fow actuation. We show that the manifestation of the Maxwell stresses itself depends on the charge densities, which in turn is dictated by the under- lying motion of the fuid. We demonstrate how such inter-related dynam- ics may give rise intricately coupled and non-linear system of equations governing the dynamical state of the system. This article is mainly divided into two parts. First, we explore the realms of electrokinetics, wherein the formation and the structure of the so-called electrical double layer (EDL) is delineated. Subsequently, we review EDL’s relevance to electroosmosis and streaming potential with the key being the presence and absence of an applied pressure gradient. We thereafter focus on the leaky dielectric model, wherein the fundamental governing equations and its main difference with electrokinetics are described. We limit our 1 Department attentions to the leaky dielectric motion around droplets and fat surfaces of Mechanical Engineering, Indian and subsequent interface deformation. To this end, through a rigorous Institute of Technology review of a number of previous articles, we establish that the interface Kharagpur, Kharagpur, West Bengal 721302, shapes can be fnely tailored to achieve the desired geometrical charac- India. 2 Discipline of Mechanical teristics by tuning the fuid properties. We further discuss previous stud- Engineering, Indian ies, which have shown migration of droplets in the presence of strong Institute of Technology Gandhinagar, Palaj, electric felds. Finally, we describe the effects of external agents such Gujrat 382355, India. *[email protected] J. Indian Inst. Sci. | VOL 98:2 | 201–225 June 2018 | journal.iisc.ernet.in 1 3 A. Bandopadhyay and U. Ghosh as surface impurities on leaky dielectric motion and attempt to establish a qualitative connection between the leaky dielectric model and EDLs. We fnish off with some pointers for further research activities and open questions in this feld. Keywords: Electrokinetics, Electrohydrodynamics, Leaky dielectric model, Electrical double layer, Droplet, Electroosmosis, Streaming potential, Thin flm, Interfacial phenomena 1 Introduction polymer transport, protein manipulation etc.26– Electrokinetic phenomena refers to those pro- 29. Streaming potential phenomenon has been cesses in which the fuid fow affects and is utilized to sense fows through porous media30–37 affected by the presence of electric felds. Reuss1 and for harvesting mechanical energy into electri- was the frst to investigate the phenomenon in cal energy18–20, 38–43. which the action of an electric feld led to the fow While the above development of EDL and of liquid and a potential difference at the end of electrokinetic phenomena took place for single two columns. Based on these ideas2 showed that phase fows there was a parallel development of the process of driving a fow across a charged the area of electrohydrodynamics (EHD) which membrane leads to the generation of a poten- refers to the study of fuid fow interacting with tial across the two ends. The former case where electric felds. Historically the studies of EHD the application of an electric feld leads to the have been to study two phase fows in the pres- generation of a fow is termed as electroosmosis ence of electric felds44–46. The developments of while the later phenomenon in which the fow of the last century can be traced back to47, 48 who a fuid in contact with a charged substrate in the studied the action of electric felds at liquid inter- absence of any electric feld leads to the genera- faces and their stability in particular. Much of the tion of a potential difference is known as stream- developments of the fows between conducting ing potential. The fundamental coupling between and insulating fuids was undertaken by Melcher the charged substrate and fuid fow is possible and coworkers49. The assumption of fuids being due to the generation of the electrical double completely conducting or completely insulating layer (EDL)3–14. The idea is that the preferrential however incorrectly predicted some of the obser- attraction of counterions towards a charged sur- vations of deformation of oil droplets suspended face leads to the formation of a region with net in other oils. The discrepancy was resolved by46 charges in the vicinity of the wall. This region who considered the fuids to be leaky dielectrics with a net charge is then able to interact with in which the small yet fnite conductivity of the applied electric felds. The fundamental concepts fuids is accounted for. In this way the net charge behind the EDL were introduced by13 and later accumulated at the interface between the two fu- improved by14, who incorporated the effects of ids leads to remarkably different behaviour than thermal energy due to Brownian motion, which the analysis in which the two fuids are consid- were previously neglected in the capacitor based ered to be either conducting or insulating. The model put forward by15. The developments in leaky dielectric model has found success in a wide the theory of the EDL led to developments in variety of situations involving commonly used the linear relationship between the net mass insulating oils such as silicone oil, castor oil, corn fux and the applied electric feld for the case of oil etc.50, 51. The leaky dielectric model was then electroosmosis8, 16. On similar lines, the linear utilized extensively by Melcher and coworkers to relationship between the applied pressure gradi- address a host of problems ranging from stability ent and induced electric feld was developed17–20. of fat interfaces44 to travelling waves with conju- The development of these theories was central to gated heat transfer45. the development of colloidal science. Manipula- The infuence of AC electric felds with high tion of micron and submicron sized particles frequencies on the interface between two fu- bearing a surface charge suspended in aqueous ids was studied by52. Later on53 demonstrated solutions by means of electric felds is termed as that the instability at the surfaces arises from the electrophoresis5, 21–25. Electrophoresis is a widely action of the Maxwell stress and not due to dielec- utilized phenomenon for many lab-on-a-chip tric breakdown. Later, the infuence of a thermal applications which deal with particle separation, gradient on bulk electroconvection was studied45, 202 1 3 J. Indian Inst. Sci.| VOL 98:2 | 201–225 June 2018 | journal.iisc.ernet.in Electrohydrodynamic Phenomena 54. The idea is that the presence of temperature link between the electrokinetic model and the gradients lead to the formation of permittiv- leaky dielectric model. Recently, efforts have been ity gradients. This allows for the electrostriction made to unveil the combined infuence of fuid term (see Appendix A) to yield a net volumetric rheology and applied electric felds in multiphase force. This mechanism acts in such a manner that systems78, 79. The fact that droplets can be coa- the temperature gradient is nullifed. The idea of lesced or sheared due to electric felds allows one utilizing electric felds to achieve an augmented to study emulsions in such systems80. We shall heat transfer has also been discussed by55. Later build upon the various aspects of this in the sub- on, there have been attempts to achieve enhanced sequent sections. rates of condensation by utilizing electric felds as At the heart of both the effects is the presence well56–58. On similar lines, there have been stud- of charges which are acted upon by electric felds. ies to understand the infuence of injected space The coupling of fuid fow and electric felds is charge on electrohydrodynamic instabilities aris- achieved through the Maxwell stress and ionic ing due to the EHD volumetric force described in advection5, 23, 24, 81–87. In this article we shall look the appendix A of59. On the basis of53, 60 analyzed into some of the fundamental aspects of electro- theoretically the problem of the action of an AC kinetic transport through narrow confnements. electric feld on a fat interface. Later61 studied Later on we shall dwell upon the leaky dielectric the effect on the similar fat interface between framework with an emphasis on the dynamics of two fuids due to the action of a transverse elec- droplets and fuid interfaces in the presence of tric feld. In an attempt to bridge the gap between high electric felds. The potential for further work electrokinetic phenomena and the electrical dou- is outlined as a conclusion. ble layer phenomena,62, 63 studied the infuence of electrical forces towards interfacial instability.