Predicting Hemiwicking Dynamics on Textured Substrates

The ability to predict liquid transport rates on textured surfaces is key to the design and optimization of devices and processes such as oil recovery, coatings, reaction-separation, high-throughput screening, and thermal management. In this work we develop a fully analytical model to predict the propagation coefficients for liquids hemiwicking through micropillar arrays. This is carried out by balancing the capillary driving force and a viscous resistive force and solving the Navier-Stokes equation for representative channels. The model is validated against a large data set of experimental hemiwicking coefficients harvested from the literature and measured in-house using high-speed imaging. The theoretical predictions show excellent agreement with the measured values and improved accuracy compared to previously proposed models. Furthermore, using lattice Boltzmann (LB) simulations, we demonstrate that the present model is applicable over a broad range of geometries. The scaling of velocity with texture geometry, implicit in our model, is compared against experimental data, where good agreement is observed for most practical systems. The analytical expression presented here offers a tool for developing design guidelines for surface chemistry and microstructure selection for liquid propagation on textured surfaces.