The Mathematics of Moving Contact Lines in Thin Liquid Films

Thin Films and Moving Contact Lines The motion of a liquid under the influence of surface tension is a phenomenon we experience every day when we take a shower, drink a cup of coffee, or turn on the windshield wipers. All of these realworld situations involve not only the motion of the liquid and surrounding air but also their interaction with adjacent hard surfaces. As we know from waxing our cars and cooking with nonstick cookware, the dynamics of a fluid coating a solid surface depend heavily on the surface chemistry. Many industrial processes, ranging from spin coating of microchips to de-icing of airplane wings, rely on the ability to control these interactions. An ongoing challenge is to explain the underlying physics of the motion of a contact line, a triple juncture of the solid/air, solid/liquid, and liquid/air interfaces. When the system is at rest, the three interfacial energies, determined by the energy per unit area γS (S = sa, sl, or la) on each surface, are in balance, and an equilibrium contact angle θ satisfying