Thermocapillary oscillations in liquid thin films: Interplay of substrate topography and thermal wave

Liquid flows over patterned and/or contoured substrates is utilized in many practical applications e.g., lubrication flow in MEMS (micro-electromechanical systems) /NEMS (nano-electromechanical systems) devices, cell sorting operations in biology, etc. The topological gradients in such geometries induce thermal gradients, which in turn generates Marangoni hydrodynamics. Here, we theoretically showcase the interplay of substrate topology, imposed wavy temperature stimulus, and chemically patterned wall slip to generate thermo-capillarity in thin liquid films. We obtain analytical solutions for the thermal and the hydrodynamic fields for low Marangoni (Ma) and Reynolds (Re) number thermocapillary effect. Vorticity is observed to generate and transport at the liquid-gas interface, and further transported to the bulk film by vertical diffusion and convection. We also study further to understand the significance of different geometric and physical parameters on the Marangoni thermo-fluid-dynamics. Interplay of constructive and destructive interference between the wave forms of the substrate topology and imposed periodic thermal stimulus may yield maximum interfacial temperature gradients and strong thermo-capillarity. It is also observed that the lower values of system Biot number (Bi) enables better diffusion of heat from the patterned substrate to obtain stable thermo-capillarity. Further, the presence of optimal slip patterning allows for stronger and tuned circulations in the liquid film.