Modeling Two-Phase Flow and Heat Transfer in Polygonal Microchannels

Abstract

Microfluidics is a burgeoning research area with applications ranging from microfluidic cooling to biomolecule synthesis. Here we study two problems to gain an improved understanding of two-phase flow and heat transfer in microfluidic devices. We also study a third problem on boundary layer flow out of theoretical interest. In the first problem, we study the heat and mass transfer in polygonal micro heat pipes under small imposed temperature differences. A micro heat pipe, used in electronics cooling, consists of a closed polygonal microchannel filled with a wetting liquid and a long vapor bubble. We model the evaporation, fluid flow, and heat transfer in these devices to derive an analytic solution that captures their performance in terms of two dimensionless parameters. The solution explains the reason behind their poor performance, and the dimensionless parameters provide a design criterion for the development of more efficient micro heat pipes. We compare our model with four published micro-heat-pipe experiments, and find encouraging support for our design criteria. We have obtained solutions for square, triangular, hexagonal, and rectangular micro heat pipes. In the second problem, we study the motion of long drops in rectangular microchannels at low capillary numbers. As the drop moves it deposits a thin liquid film on the sidewalls of the microchannel. The drag on the drop comes mainly from the shear force exerted by the wall on the thin films surrounding the drop. The drag is balanced by a liquid pressure difference across the drop. We solve for the drag in the limit of zero capillary number and derive a pressure-flow rate relation. We find encouraging comparison between our model and published experimental results. We have obtained solutions for rectangular microchannels with aspect ratios 1, 1.2, 1.5 and 2, each for different drop to carrier liquid viscosity ratios ranging from 0.001 to 100. In the third problem, we study the boundary layer over a semi-infinite flat plate under forced uniform flow at the leading edge. We derive self-similar solutions, to leading order, for the velocity and pressure fields near the leading edge where the Blasius solution does not apply.