Adaptive Grid Formulation of Thermocapillary Convection in a Microfluidic Two-Phase Flow

ABSTRACT

A new adaptive grid formulation is developed for heat transfer predictions of thermocapillary droplet transport in a microchannel. Unlike past studies with open microchannels, this article applies a sliding grid in the liquid (droplet) with an adaptive deforming grid in the compressed and expanded gas (air) phases of a closed microchannel. Thermocapillary forces in the corners of the droplet lead to pressure changes and bulk motion of the droplet. The fluid flow equations are solved with a staggered grid and adaptive mesh refinement at the liquid/gas interfaces. This refinement uses Bernstein polynomials and control points to adjust the grid spacing. Heat transfer through a thermal bridge within the substrate generates cyclic heating and cooling periods during the microdroplet transport. Numerical simulations indicate that a recirculating cell is observed within the lower half-domain of the microchannel. Close agreement between finite-volume and theoretical (slug-flow approximation) results provides useful validation of the formulation.

Support of this research from the NSERC (Canada), as well as a University of Manitoba Graduate Fellowship (P. S. Glockner), is gratefully acknowledged.