Hydrodynamics and Contact Angle Relaxation during Unsteady Spreading

Abstract

We have studied the unsteady spreading of a liquid on a solid surface by observing the liquid−air meniscus shape and analyzing it with the hydrodynamic theory for Stokes' flow. The unsteady spreading process exhibits both quasi-steady and unsteady regimes. The unsteadiness in our moderately high viscosity system arises from temporal relaxation of the contact angle rather than inertial effects or momentum diffusion. The quasi-steady regime can be accurately described by a model that ascribes a steady-state flow near the contact line. “Spontaneous” spreading, i.e., spreading to final state of zero contact line speed, is recognized as a special case of the general unsteady spreading process with the commonly used power laws for spreading occurring only under special conditions.