The lubrication approximation for moving contact lines in thin liquid films

Prof. Andrea Bertozzi

Department of Mathematics, Duke University

When the interface between two immiscible liquids, or liquid and a gas meet at a solid boundary, the triple juncture, or contact line, plays a strong role in the evolution of the entire liquid/solid interface. When the system is at rest, as in the case of a nonwetting or partial wetting fluid in equilibrium, the local interfacial energies of the three interfaces determine the preferred state of the system via Young's law. However, when the system is not at rest, as in the case of a wetting fluid, energy from the bulk of the fluid dissipates at the contact line, in a fashion that is not very well understood. We study continuum models for moving contact lines in situations far from equilibrium. By examining the robustness of various models, using rigorous analysis, asymptotic and scaling methods, and high resolution numerical simulations, we can learn more about their validity.