Unsaturated hemiwicking dynamics on surfaces with irregular roughness

Spreading of wetting liquids on rough surfaces can occur in a regime termed hemiwicking in which liquid advances ahead of the bulk liquid droplet front under the influence of capillary forces induced by the surface topography. When the surface topography is periodic as in the case for micropillar arrays, the wetting front is sharp and models describing the wetting dynamics can be derived directly from the periodic geometry. For materials with a highly irregular surface topography, the wetting front is diffuse and deriving analytical spreading model parameters directly from the surface topography is not generally possible.

In this work, a previously published model for liquid spreading on thin porous materials is modified to incorporate unsaturated spreading ahead of the bulk liquid droplet using Richards equation. The permeability, K, and capillary pressure, p_c, of the liquid in the surface roughness are the primary model parameters describing the spreading dynamics in Richards equation. These are determined by fitting to one-dimensional spreading experiments of silicone oil on a polyurethane-based paint coating with roughness on the scale of microns.

The resulting predictions of spreading dynamics for droplets with different initial sizes is good. It is also shown that reasonable model parameters can also be determined from the irregular surface topography by spatial filtering over 10 µm wavelength increments covering the range 10-500 µm. Approximate periodic micropillar arrays are defined from the filtered topography for each wavelength increment, enabling analytical estimates of the permeability and capillary pressure. Although using only the surface topography results in somewhat less accurate predictions, the savings in experimental and computational effort make it an attractive method for determining spreading model parameters.