Optimal design of open capillary channel arrays to maximize evaporative mass flux

Plant leaves and heat pipes commonly involve microscale flow systems where liquids wicking into open channels undergo evaporation. Here we are interested in obtaining the optimal design of open capillary channel arrays to maximize evaporative mass flux. To increase the liquid evaporation, the liquid flux via wicking into the channel arrays should be enhanced. In addition, the evaporative mass transfer from liquid to surrounding gas should be facilitated, which is sensitive to the effects of contact line. That is, for hydrophilic channels, the evaporation flux is greatly enhanced near the solid-liquid-gas contact line. Thus, increasing the contact lines can be more effective than simply increasing the liquid-gas interfacial area. We experimentally measure and theoretically rationalize the evaporation flux from various widths of microscale open channels under the effects of contact line. We further consider the effects of overlapping diffusion boundary layers caused by too narrowly spaced channels. Then we provide a mathematical rule to optimize the channel width and spacings that can maximize the evaporative mass flux of liquid wicking into open capillaries.