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Author: Peschka, Dirk × Subject: lubrication theory ×

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Now showing 1 - 2 of 2
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    Dynamics of particle settling and resuspension in viscous liquids
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Murisic, Nebojsa; Pausader, Benoit; Peschka, Dirk; Bertozzi, Andrea L.
    We derive and study a dynamical model for suspensions of negatively buoyant particles on an incline. Our theoretical model includes the settling/sedimentation due to gravity as well as the resuspension of particles induced by shear-induced migration, leading to disaggregation of the dense sediment layer. Out of the three different regimes observed in the experiments, we focus on the so-called settled case, where the particles settle out of the flow, and two distinct fronts, liquid and particle, form. Using an approach relying on asymptotics, we systematically connect our dynamic model with the previously developed equilibrium theory for particle-laden flows. We show that the resulting transport equations for the liquid and the particles are of hyperbolic type, and study the dilute limit, for which we derive the analytic solution. We also carry out a systematic experimental study of the settled regime, focusing on the motion of the liquid and the particle fronts. Finally, we carry out numerical simulations of our transport equations. We show that the model predictions for small to moderate values of the particle volume fraction and the inclination angle of the solid substrate agree well with the experimental data.
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    Interface morphologies in liquid/liquid dewetting
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Kostourou, Konstantina; Peschka, Dirk; Münch, Andreas; Wagner, Barbara; Herminghaus, Stephan; Seemann, Ralf
    The dynamics and morphology of a liquid polystyrene (PS) film on the scale of a hundred nanometer dewetting from a liquid polymethylmethacrylate (PMMA) film is investigated experimentally and theoretically. The polymers considered here are both below their entanglement lengths and have negligible elastic properties. A theoretical model based on viscous Newtonian flow for both polymers is set up from which a system of coupled lubrication equations is derived and solved numerically. A direct comparison of the numerical solution with the experimental findings for the characteristic signatures of the cross-sections of liquid/air and liquid/liquid phase boundaries of the dewetting rims as well as the dewetting rates is performed and discussed for various viscosity ratios of the PS and PMMA layers.