Effect of surface roughness on wettability and displacement curvature in tubes of uniform cross-section

A fundamental problem in interpretation of the capillary properties of porous media is the effect of the interaction of wetting properties and pore geometry on interface curvature. Contact angles provide a fundamental measure of wetting. However, circumstances under which contact angles are reproducible and unambiguous are limited. Contact angles commonly exhibit hysteresis between advancing and receding conditions. The origin of the contact angle hysteresis may be related to either chemical or geometric properties or a combination of both. Small scale geometric features, such as surface roughness, can have a dominant effect on the effective contact angles at the three phase lines of contact and determine the local interface curvature. In this paper, the effect of roughness on the effective contact angle is studied by applying the MS–P (Mayer and Stowe, and Princen) method of computing interface curvatures, for the first time, to geometric models of surface roughness that include small scale periodic variation and retained fluid in grooves along the walls of tubes of constant cross section. The method provides a consistent account of interface behavior for wetting regimes commonly identified with Wenzel or Cassie and Baxter. The theoretical results are also shown to be consistent with experimental results on the wetting behavior of combinations of roughened polymeric tubes and pure liquids that give a range of well-defined intrinsic contact angles.