On a simple model for surfactant-dominated contact-line movement

This paper presents a simple approximate continuum model for contact-line advance from Newtonian aqueous surfactant solution into oil. Geometrical complexity of the underlying solid surface and the liquid/liquid interface is included in the general formulation of model equations. A much simpler two-dimensional model for slow flow where interfaces are plane, the oil is inviscid and the contact angle is small, is then developed and analysed. In both models, the mechanics of the flow is dominated by surfactant concentration gradients in the three interfaces. It is concluded that quantitative predictions at the several length scales characterising the problem will require a hierarchy of models, and that a role will be played by molecular dynamic, Brownian dynamic, Lattice–Boltzmann and fully continuum-level FD/FE/FV simulations.