Prediction of hemiwicking dynamics in micropillar arrays

Dynamic hemiwicking behavior is observable in both nature and a wide range of industrial applications ranging from biomedical devices to thermal management. We present a semi-analytical modeling framework (without empirical fitting coefficients) to predict transient capillary-driven hemiwicking behavior of a liquid through a nano/microstructured surface, specifically a micropillar array. In our model framework, the liquid domain is discretized into micropillar unit cells to enable the time marching of the hemiwicking front. A simplified linear pressure drop is assumed along the hemiwicking length such that the local meniscus curvature, contact angle, and effective liquid height are determined at each time step in our transient model. This semi-analytical model is validated with experimental data from our own experiments and from published literature for different fluids. Our model predicts hemiwicking dynamics with <20% error over a broad range of micropillar geometries with height-to-pitch ratio ranging between approximate to 0.34 and 6.7 and diameter-to-pitch ratio in the range of approximate to 0.25-0.7 and without any fitting parameters. For lower diameter-to-pitch ratio data points related to sparse micropillar array arrangements, we suggest modifications to the semi-analytical model. This work sheds light on complex and dynamic solid-liquid-vapor interfacial interactions which could serve as a guide for the design of textured surfaces for wicking enhancement in multi-phase thermal and mass transport technologies and applications.