Evaporative capillary rise

The capillary rise in vertically situated open microchannels can be severely limited by liquid evaporation. Here we quantitatively study the rise dynamics using a combination of experiment and theory. On evaluating the effects of the enhanced evaporation near the solid-liquid-gas contact line on the mass transfer rate from liquid in a microchannel, we set up a differential equation for the temporal evolution of rise height by considering mass conservation of evaporating viscous liquid drawn against gravity via capillarity. It is found that there exists an optimal channel width that maximizes the equilibrium rise height under a given channel depth, unlike nonevaporative rise whose equilibrium height monotonically increases with the reduction of channel width. Our work can lay a foundation for understanding the evaporative capillary rise dynamics occurring in various porous media of biological, natural, and artificial settings.