The spreading of surfactant-laden liquids with surfactant transfer through the contact line

Abstract

We examine the spreading of a liquid on a solid surface when the liquid surface has a spread monolayer of insoluble surfactant, and the surfactant transfers through the contact line between the liquid surface and the solid. We show that, as in surfactant-free systems, a singularity appears at the moving contact line. However, unlike surfactant-free systems, the singularity cannot be removed by the same assumptions as long as surfactant transfer takes place. In an attempt to avoid modelling difficulties posed by the question of how the singularity might be removed, we identify parameters which describe the dynamics of the macroscopic spreading process. These parameters, which depend on the details of the fluid motion next to the contact line as in the pure-fluid case, also depend on the state of the spread surfactant in the macroscopic region, in sharp contrast to the pure-fluid case where actions at the macroscopic scale did not affect material spreading parameters. A model of the viscous-controlled region near the contact line which accounts for surfactant transfer shows that, at steady state, some ranges of dynamic contact angles and of capillary number are forbidden. For a given surfactant–liquid pair, these disallowed ranges depend upon the actual contact angle and on the transfer flux of surfactant.We also examine a possible inner model which accounts for the transfer via surface diffusivity and regularizes the stress via a slip model. We show that the asymptotic behaviour of this model at distances from the contact line large compared to the inner length scale matches to the viscous-controlled region. An example of how the information propagates is given.