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Author: Niethammer, Barbara ×

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    Thin film rupture for large slip
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.
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    Stability of concentrated suspensions under Couette and Poiseuille flow
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.
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    Self-similar rupture of viscous thin films in the strong slip regime
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.