A comprehensive theoretical model of capillary transport in rectangular microchannels

A detailed theoretical model of capillary transport in rectangular microchannels is proposed. Two important aspects of capillary transport are revisited, which are considered with simplified assumption in the literature. The capillary flow is assumed as a low Reynolds number flow and hence creeping flow assumptions are considered for majority of analyses. The velocity profile used with this assumption results into a steady state fully developed velocity profile. The capillary flow is inherently a transient process. In this study, the capillary flow analysis is performed with transient velocity profile. The pressure field expression at the entrance of the microchannel is another aspect which is not often accurately represented in the literature. The approximated pressure field expression at the entrance of the rectangular microchannel is widely used in the literature. An appropriate entrance pressure field expression for a rectangular microchannel is proposed. For both analyses, the governing equation of the capillary transport in rectangular microchannel is derived by applying the momentum equation to the fluid control volume along the microchannel. The non-dimensional governing equations are obtained, each for a transient velocity profile and a newly proposed pressure field, for analyzing the importance of such velocity profile and pressure field expression.