2009, Peschka, Dirk, Münch, Andreas, Niethammer, Barbara

This paper studies the rupture of thin liquid films on hydrophobic substrates, assuming large slip at the liquidsolid interface. Using a recently developed em strong slip lubrication model, it is shown that the rupture passes through up to three self-similar regimes with different dominant balances and different scaling exponents. For one of these regimes the similarity is of second kind, and the similarity exponent is determined by solving a boundary value problem for a nonlinear ODE. For this regime we also prove finite-time rupture.

2015, Ahnert, Tobias, Münch, Andreas, Niethammer, Barbara, Wagner, Barbara

The stability of two-dimensional Poiseuille flow and plane Couette flow for concentrated suspensions is investigated. Linear stability analysis of the twophase flow model for both flow geometries shows the existence of a convectively driven instability with increasing growth rates of the unstable modes as the particle volume fraction of the suspension increases. In addition it is shown that there exists a bound for the particle phase viscosity below which the two-phase flow model may become ill-posed as the particle phase approaches its maximum packing fraction. The case of two-dimensional Poiseuille flow gives rise to base state solutions that exhibit a jammed and unyielded region, due to shear-induced migration, as the maximum packing fraction is approached. The stability characteristics of the resulting Bingham-type flow is investigated and connections to the stability problem for the related classical Bingham-flow problem are discussed.

2009, Peschka, Dirk, Münch, Andreas, Niethammer, Barbara

We consider rupture of thin viscous films in the strong-slip regime with small Reynolds numbers. Numerical simulations indicate that near the rupture point viscosity and van-der-Waals forces are dominant and that there are self-similar solutions of the second kind. For a corresponding simplified model we rigorously analyse self-similar behaviour. There exists a one-parameter family of self-similar solutions and we establish necessary and sufficient conditions for convergence to any self-similar solution in a certain parameter regime. We also present a conjecture on the domains of attraction of all self-similar solutions which is supported by numerical simulations.