Thermo-capillarity of immiscible binary fluids within serpentine micro-confinements

Abstract

The thermocapillary flow of multiple liquid layers over contoured substrates finds applications in many industrial phenomena via micro-electromechanical systems/nano-electromechanical systems devices. This study theoretically explores the thermocapillary transport of binary-liquid layers in a wavy microchannel with serpentine wall profiles. Sinusoidal profiles are considered for the microchannel walls' temperature and surface topology. Patterned slip conditions at the walls are also accounted for in the analysis to make the problem more realistic. We semi-analytically solve the energy and momentum equations to understand the system's thermal and hydrodynamic characteristics for the limiting conditions of Ma, Re, and Ca. The leading- and higher-order solutions of the temperature and flow field are separately shown to demonstrate the advection terms' contribution to the transport equations. The circulatory flow obtained due to periodic thermal stimuli can be used to enhance the mixing efficiency of the system. We also present how the parameters like phase difference between the thermal stimulus, relative thermal conductivity, and relative film thickness ratio of the liquid layers can be altered to control the flow characteristics to obtain the most potent thermocapillary effect.