A simple analytic model for predicting the wicking velocity in micropillar arrays

Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers ( 10 − 7 ≲ Re ≲ 10 − 3 ) . Fluid drag is conceptualized via a critical Reynolds number: Re = v 0 x 0 ν , where v 0 corresponds to the maximum wetting speed on a flat, dry surface and x 0 is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction with v 0 and x 0 measurements using Water ( v 0 ≈ 2 m / s , 25 µ m ≲ x 0 ≲ 28 µ m ) , viscous FC-70 ( v 0 ≈ 0.3 m / s , 18.6 µ m ≲ x 0 ≲ 38.6 µ m ) and lower viscosity Ethanol ( v 0 ≈ 1.2 m / s , 11.8 µ m ≲ x 0 ≲ 33.3 µ m ) .