Evaporative Capillary Rise in a Heated Microchannel.

Efficient liquid transport in microstructured evaporators is critical for thermal management and phase-change applications, including electronics cooling, solar-thermal desalination, and heat pipe technologies. Here, we study the effect of evaporation on the capillary wicking in a microchannel subjected to a constant heat flux. A theoretical framework incorporating coupled mass, momentum, and energy conservation equations is developed to examine the influence of geometrical parameters, such as the width and depth of the microchannel, on the wicking length and the evaporation rate. In contrast to the case without evaporation, where the wicking length decreases monotonically as the channel width increases, the presence of evaporation introduces a nonmonotonic behavior in the wicking length with channel width. For a particular depth of microchannels, the width at which the wicking length attains its peak varies with the applied heat flux. The wicking length and the channel width determine the evaporating surface area, an increase of which increases the evaporation rate. For a given width, channels with a greater depth exhibit extended wicking lengths, rendering them more favorable for enhanced evaporation rates. Consequently, a set of geometric parameters are obtained for different heat fluxes that yield peak values of evaporation rates, which can serve as design criteria for efficient evaporators in phase-change applications. Wicking experiments are performed in microchannels of rectangular cross sections with different widths, employing water and ethanol as the working fluids. The experimental results agree well with the theoretically predicted wicking lengths for different surface morphologies and applied heat flux.