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
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.