Interfacial thermocapillary pressure of an accelerated droplet in microchannels: Part I. Fluid flow formulation

Fluid flow and thermocapillary heat transfer near a droplet/air interface in microchannels is studied analytically and numerically in this set of two companion papers. Thermocapillary forces generate a pressure difference across the droplet, which drives two symmetric re-circulation cells in the upper and lower half-portions of the droplet. The numerical formulation uses a sliding grid for the accelerating droplet, as well as an expanding/contracting grid in the gas region and an adaptive grid in the substrate below the closed-end microchannel. In contrast to past studies with a uniform interfacial pressure, this paper accommodates a varying interfacial pressure along the receding edge of the droplet.