Numerical simulation of wall mass transfer rates in capillary-driven flow in microchannels

Microchannels are believed to open up the prospect of precise control of fluid flow and chemical reactions. The high surface to volume ratio of micro size channels allows efficient mass transfer rates. The capillary effect can be used to pump fluids in microchannels and the flow generated can dissolve chemicals previously deposited on the walls of the channel. The purpose of this work is to analyze the wall mass transfer rates generated by a capillary driven flow in a microchannel. The results have implications in the optimization and design of devices for biological assays. We performed simulations of the capillary-driven flow in two-dimensional rectangular and circular microchannels by solving numerically the governing momentum and mass transfer equations with a second order accuracy finite volume code. The effects of the Reynolds number, of the contact angle and of the channel geometry on the time evolution of the local and averaged wall mass transfer rates are reported and analyzed. The flow field behind the meniscus, viewed from a reference frame moving at the velocity of the meniscus, showed to have two recirculations that enhance the wall mass transfer rates close to the triple point. A correlation between the Sherwood number and the Reynolds number, the contact angle and the time is reported. The correlation can be a useful tool for design purposes of microfluidic devices with capillary driven flows in which a fast heterogeneous reaction occurs on the wall.