Dr. U. Thiele (Max-Planck-Institut für Physik komplexer Systeme, Dresden)

Thin liquid films on a slightly inclined heated plate: From Cahn-Hilliard to Kuramoto-Sivashinsky behaviour

After formulating the basic mathematical problem for a thin liquid film on a uniformly heated substrate we discuss the stationary solutions in the case of a horizontal substrate. These are time-independent and of two types: continuous solutions with thickness bounded away from zero, and discontinuous solutions consisting of drops separated by dry spots. We describe a construction that generates all such solutions and illustrate it with explicit examples. We then discuss how the solution landscape collapses once the substrate is inclined. The solutions are now devoid of dry spots and all slide down the substrate. These states are obtained by solving a nonlinear eigenvalue problem, and their stability properties can be mapped out by solving an additional linear eigenvalue problem. The results shed light on the multiplicity of states accessible to systems of this type and on the possible transitions among them.