A kinematic evolution equation for the dynamic contact angle

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Résumé : We investigate the moving contact line problem for two-phase incompressible flows by a kinematic approach, where the key idea is to derive an evolution equation for the contact angle assuming the transporting velocity field to be given. The resulting equation expresses the time derivative of the contact angle in terms of the gradients of the fluid velocity and the local mass transfer rate at the solid wall. Combined with the additionally imposed boundary conditions for the velocity and, furthermore, exploiting the interfacial transmission condition for the viscous stress, we derive an explicit form of the contact angle evolution for sufficiently smooth solutions to a large class of models. From this equation we can read off the qualitative behavior of the contact angle evolution for this class of models, which turns out to be unphysical! We discuss consequences from this observation and possible generalizations of the model.

Joint work with Mathis Fricke (Darmstadt) and Matthias Köhne (Düsseldorf)