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

Active droplets are liquid droplets suspended in another immiscible liquid that can move autonomously without any external force or torque. They serve as minimal, highly controllable model systems for mimicking biological microswimmers and have attracted growing interest for applications such as targeted drug delivery, microscale transport, and soft microrobotics. These droplets can propel through diverse environments, including Newtonian fluids and complex viscoelastic media like polymer solutions, mucus, blood, and other industrial or biological fluids. Their motion arises from self-generated physicochemical gradients, including interfacial tension gradients, induced surface slip velocities, and chemical or pH gradients in the surrounding fluid, which together drive force-free propulsion.

Our research seeks to understand the fundamental mechanisms governing how active droplets propel, deform, and interact with their environment. We develop theoretical and computational models to study chemically driven propulsion. These models identify conditions under which droplets transition between stationary, steadily swimming, and oscillatory states. In parallel, we investigate droplet deformation during swimming in complex viscoelastic fluids, revealing how fluid elasticity and swimmer type influence stress localization and shape evolution. By linking interfacial chemistry, hydrodynamics, and soft-matter rheology, our work aims to establish physical design principles for tunable microswimmers and active fluid systems relevant to future biomedical and engineering applications.

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.

Relevant Publications:

1. Wankhede S., Pillai, D. S., (2024). Nature of instability in flow-driven porous anodic oxide. Chaos 34, 073136.

2. Wankhede S., Pillai, D. S., (2024). Electrokinetics-driven anodic oxide pore formation: linear and weakly nonlinear analysis. Journal of The Electrochemical Society, (171) 112501.

3. Wankhede S., Pillai, D. S., (2025). A Hybrid Model for Electrokinetic and Stress-Induced Flow Mechanisms in Porous Anodic Oxide Formation . Journal of The Electrochemical Society (172) 083501