Analysis of Capillary Flow in a Parallel Microchannel-Based Wick Structure with Circular and Noncircular Geometries

Capillary flow in porous media is of great significance to many different applications including microfluidics, chromatography, and passive thermal management. For example, heat pipe has been widely used in the thermal management of electronic system due to its high flexibility and low thermal resistance. However, the critical heat flux of heat pipe is often limited by the maximum capillary-driven liquid transport rate through the wicking material. A significant number of novel porous material with complex structures have been proposed in past studies to provide enhanced capillary-driven flow without substantial reduction in pore size and porosity. However, the increasing level of structural complexity often leads to a more tortuous flow path, which deprives the merits of enhanced capillarity. In this study, we examined the capillary performance of a porous material with simple geometric structures both analytically and numerically. Specifically, the capillary rate of rise of water in parallel hollow microchannels with different cross-sectional shapes is derived by solving the momentum transport equation. The relationships between the capillary flow rate and wicking height are further validated by two-phase flow simulation based on the conservative level-set method. The results demonstrate that parallel microchannel configuration, despite its geometric simplicity, provides superior capillary performance than most existing porous media in terms of both capillary flow rate and ultimate wicking height. In addition, design of noncircular cross section reduces the viscous drag and increases the packing density of the microchannels in the bulk solid without affecting the capillary pumping pressure. These features contribute to a further enhancement in the capillary performance by up to 32%. These results provide important guidance to the rational design of porous material with enhanced fluid transport property in a variety of microfluidic systems.