Thin fluid films heated from below

Thin fluid films find various applications in industrial processes. These films, ranging from nanometers to micrometers in thickness, are often exposed to temperature gradients, which compete with stabilising surface tension effects. A mathematical model describing the evolution of thin fluid film's height resting on a horizontal, heated plate can be derived via lubrication approximation, constituting a quasilinear, degenerate, fourth-order partial differential equations.

When a critical temperature disparity between the heated plate and the surrounding environment is reached, the flat steady state becomes spectrally unstable and periodic stationary solutions bifurcate. Using a Hamiltonian formulation of the stationary problem and analytic bifurcation theory, we prove the existence of a global bifurcation curve converging to a weak stationary periodic solution exhibiting film rupture.

Based on a joint work with B. Hilder (Munich) and J. Jansen (Lund).