Thermo-capillarity in microfluidic binary systems via phase modulated sinusoidal thermal stimuli

Abstract

In this article, we have explored the theoretical aspects of thermo-capillarity driven hydrodynamics at the interface of an immiscible binary-fluid system within a microfluidic domain. The top and bottom walls of the microfluidic confinement are exposed to sinusoidal thermal stimuli with different mean values, wave numbers, and phase differences. We explore the influence of different governing parameters on the thermal and hydrodynamic transport due to interfacial thermo-capillarity and within the constituent fluids. To this end, we deduce the full solutions for the temperature field, hydrodynamics, and the interfacial deformation characteristics in an analytical framework, by appealing to the assumption of the creeping flow (vanishingly small Reynolds, Marangoni, and Capillary number regime) and nearly un-deformed interface. Complicated spatial distribution of the isotherms is generated across the fluids, leading to spatially varying thermal gradients across and along the interface. This leads to periodic circulation of the fluids within the microchannel due to the sinusoidal thermal stimulus. It is observed that the interfacial flow strength depends on the relative film thickness and the thermal conductivities of the two fluids. Vortex enveloping phenomenon is observed for lower values of film thickness ratio when the thermal conductivity of the lower fluid is higher relative to the upper fluid. The findings may hold significance for the design and development of thermal stimulus-controlled spatial mixing and solute transport mechanisms in reactive micro- and nano-fluidic devices.