title: Quasistatic evolution and contact-angle hysteresis
in capillarity
4 lectures at the "ITN-Winterschool on Mathematical Models for
Wetting: Analysis and Numerics". Veilbronn (near Erlangen, Germany),
February 13-17, 2012.
abstract: In these lectures I describe a model for quasistatic
evolution of capillary drops, studied in a joint work with Antonio
De Simone (Arch. Rational Mech. Anal. 202 (2011), pp. 295-348).
We consider a drop sitting on a solid surface and subject to the usual
capillary forces, and assume the existence of a frictional force acting
on the line where the free surface of the drop meets the solid (contact
line). This simple dissipation mechanism accounts for a widely observed
hysteresis of the contact angle. Among other results, we prove the
existence of solutions for the corresponding quasistatic evolution.
In the first lecture and half of the second one I recall the notion of
quasistatic evolution (or rate-independent dissipative process) focusing
on some simple mechanical model, and describe the standard approach to
existence results by time-discretization.
In the rest of the second lecture and in the third one I describe the
classical (that is, geometric) model for capillarity, and show how the
hysteresis of contact angle can be modelled by a simple frictional force
on the contact line.
The last lecture is devoted to a review of the main abstract tool needed
in proofs (the theory of finite perimeter sets) and to the proof of the
basic existence result for the geometric model of capillarity, which is
actually the first step in the proof of existence of solutions for our
quasistatic evolution.