Reagent mixing is necessary for a microfluidic system to achieve quick biological reactions. Microfluidic systems have low Reynolds number (Re) flow, making passive mixing challenging and demanding an outside stimulus to disturb the system. The present study theoretically investigates how patterned wettability and sinusoidal thermal stimuli at the walls interact to enhance mixing of a thermo-capillarity-driven ternary- liquid system in a microchannel. Here, we use perturbation approach to solve the two-dimensional decoupled Navier-Stokes and energy equations semi-analytically to derive the microchannel flow field under creeping flow conditions. The paper illustrates the improved mixing achieved in the chosen design by demonstrating the participating fluids' vortex transport and stretching phenomena. Further, the species transport equation is solved for discrete inlet concentrations to all fluid layers in COMSOL Multiphysics. The variation of the cross-sectional concentration profile with the axial displacement from the entrance reveals how quickly the mixing is achieved in the current configuration.

We discuss the influence of the wall slip length and the relative thermal conductivity of the three fluid layers on the mixing performance of the system. The patterned nature of wall slip provokes disturbance, causing rich mixing. Due to the better interplay of the thermo-capillarity and the wall wettability for a weak flow, stronger mixing is observed in a fluid layer with relatively lower thermal conductivity.