Thermocapillary convection in superimposed fluids confined within superhydrophobic surfaces of a microchannel - Radi A. Alsulami; Kanchathan Wasuwatthanakul; Kannan Premnath; Mutabe Aljaghtham; Saad Adam (Case Studies in Thermal Engineering)
Microfluidic applications based on thermocapillary effects have recently gained considerable attention due to the transport phenomena driven by the dominant surface tension forces. Furthermore, two-layer fluids, used in various applications, e.g., biomedical engineering, microfluidics, and chemical processing, enhance flow dynamics control by manipulating flow mixing and characteristics. Since prior works did not consider slip effects, this work addresses this phenomenon by investigating the thermocapillary-driven convection in two superimposed fluids in a microchannel while simulating the behavior of superhydrophobic surfaces. This is achieved by deriving a new analytical solution for thermocapillary convection between two solid walls, uniquely subject to the Navier slip condition and where the bottom surface is heated nonuniformly via a sinusoidal variation, under the limit of zero Reynolds and Marangoni numbers. The derived expressions for the flow field arising from the prevailing surface tension gradient are then explicitly parameterized by a dimensionless slip coefficient obtained by combining the Navier slip length and the wavenumber of the imposed temperature variation on the bottom surface, along with the ratios of the properties of fluids and their thicknesses. We study the effect of the various characteristic parameters on the thermocapillary flow patterns and the maximum interfacial velocity currents. In particular, it is shown that thermo-capillarity generates convective currents with nominally a pair of counter-rotating vortices in each fluid, which is sometimes increased and accompanied by a change in their sense of rotation and the magnitude of the peak velocities by variations in the dimensionless slip coefficient. These results elucidate the role of the competing effects of the wall shear variations due to slip and the thermocapillary motions in the bulk regions facilitated by the viscous forces, which can be exploited in modulating mixing and transport in microchannels.