Miniaturization is a necessity in today's world. Size reduction through the advent of microfluidics has facilitated the integration and intensification of multiple processes over a single microfluidic chip. In droplet-based microfluidics, incorporation of external electric field provides control over the mixing, transport and manipulation of droplets. Dynamics of sessile droplets is primarily governed by the dynamics of the triple phase contact line (TPCL).  We investigate the statics and dynamics of TPCL under electric field using a three-pronged approach including calculus of variation (CV), thin film modelling and molecular dynamics simulations. The work has implications in internal mixing at low Reynolds number, electrovariable optics, droplet actuation, and bioassays.

The method of calculus of variations is integral in the study of statics of TPCL at a continuum level. The classical Young-Dupre equation as well as the Young Lippmann equation for electrowetting can be derived using CV by constrained energy minimization. The utility of such a method to arrive at the statics of TPCL of different liquids and substrates differentiable on the basis of electrochemical and physical properties will be attempted. Non-linear dynamics of TPCL under electric field can be captured using WRIBL (Weighted Residual Integral Boundary Layer) theory. The role of bulk charges in a vast class of fluids such as electrolytes also remains largely unexplored. Electrowetting of nano-scale droplets, wherein the continuum description fails, requires understanding that can only be derived from molecular simulations. The role of electric field on contact angle saturation, contact line friction and contact line tension are key areas that warrant investigation. 

Relevant Publications:

1. Pillai, D. S., Sahu, K. C., & Narayanan, R. (2021). Electrowetting of a leaky dielectric droplet under a time-periodic electric field. Physical Review Fluids, 6(7), 073701.

2. Kainikkara, M. A., Pillai, D. S., & Sahu, K. C. (2021). Equivalence of sessile droplet dynamics under periodic and steady electric fields. npj Microgravity, 7(1), 47.

3. Goel, Shreyank, Pillai, D. S.  (2023). An electrokinetic thin-film model for electrowetting: role of bulk charges. Langmuir

4. Goel, Shreyank, Pillai, D. S., (2023). A reduced-order model for surfactant-laden electrified sessile droplets. Langmuir

Surface oxide films are formed on metals such as aluminum, titanium, and tantalum, during oxidation in electrochemical cells, a process known as anodization. Anodic oxide films may form two different morphologies, viz., nonporous barrier-type oxide films and porous-type oxide films, depending mainly on the nature of the anodizing electrolyte. Under the right conditions, films can be obtained with highly regular arrangements of pores with submicron diameters. Numerous devices for example energy, optical, catalytic, and biological applications have been constructed from these porous anodic oxide (PAO) films, taking advantage of their high specific surface area and the ability to tune the porous layer geometry by adjusting the anodizing voltage and solution composition. Many desirable engineering properties such as excellent hardness, corrosion, and abrasion resistance can be obtained by anodizing metals in acid electrolytes. 

Our research focuses on the fundamental interfacial reactions, ion migration process, and the electrochemical factors that determine the geometric and chemical structures of PAOs. Our research involves theoretical modeling studies to investigate various mechanisms that play a significant role in the formation of porous anodic oxide. These mechanisms include field-assisted oxide dissolution, flow mechanism, and stress generation mechanism. However, our extensive modeling studies provide valuable insights into these processes. Furthermore, we explore the use of linear and weakly nonlinear stability analyses to identify specific regimes of self-ordering.

A smooth stream of water breaking into droplets as it exits from a faucet is a common experience. Numerous research on the dynamics of jetting to dripping transition have shown that global linear stability analysis is an efficient method to theoretically obtain the critical flow rate at which the transition takes place. The critical flow rate depends on the liquid density, kinematic viscosity, interfacial tension, radius of the injector and the acceleration due to gravity.

The absolute or convective character of the instabilities can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. The character of the instability can be determined theoretically using the Briggs-Bers criterion. A flow is absolutely unstable when the branch-point singularities lie in the upper half of complex-frequency plane, while the flow is convectively unstable when the branch-point singularities lie in the lower half of complex-frequency plane.

Our current study focusses on employing global linear stability analysis to determine the critical flow rate at which the jetting to dripping transition takes place for a surfactant-laden jet, the frequency of the self-sustained oscillations experienced by the jet at the critical condition, as well as the periodicity of droplet formation from the time return map.