Dynamics of hemiwicking

Abstract

Hemiwicking refers to the spreading of a liquid on a rough hydrophilic surface driven by capillarity. Here, we construct scaling laws to predict the velocity of hemiwicking on a rough substrate and experimentally corroborate them with various arrangements and dimensions of micropillar arrays. At the macroscopic scale, where the wetting front appears parallel to the free surface of the reservoir, the wicking distance is shown to grow diffusively, i.e. like $t^{1/2}$ with $t$ being time. We show that our model is consistent with pillar arrays of a wide range of pitch-to-height ratios, either square or skewed. At the microscopic scale, where the meniscus extension from individual pillars at the wetting front is considered, the extension distance begins to grow like $t$ but the spreading slows down to behave like $t^{1/3}$ when the meniscus is far from the pillar. Our microscopic flow modelling allows us to find pillar spacing conditions under which the assumption of densely spaced pillars is valid.