Dynamics of Liquid Spreading on Solid Surfaces

Using simple scaling arguments and a precursor film model, we show that the appropriate macroscopic contact angle θ during the slow spreading of a completely or partially wetting liquid under conditions of viscous flow and small slopes should be described by tan θ = [tan 3 θ e − 9 log η Ca ] 1/3 where θ e is the static contact angle, Ca is the capillary number, and η is a scaled Hamaker constant. Using this simple relation as a boundary condition, we are able to quantitatively model, without any empirical parameter, the spreading dynamics of several classical spreading phenomena (capillary rise, sessile, and pendant drop spreading) by simply equating the slope of the leading order static bulk region to our dynamic contact angle boundary condition without performing a matched asymptotic analysis for each case independently as is usually done in the literature.