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Type: report × Author: Wagner, Barbara ×

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    Impact of slippage on the morphology and stability of a dewetting rim
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Münch, Andreas; Wagner, Barbara
    In this study lubrication theory is used to describe the stability and morphology of the rim that forms as a thin polymer film dewets from a hydrophobized silicon wafer. Thin film equations are derived from the governing hydrodynamic equations for the polymer to enable the systematic mathematical and numerical analysis of the properties of the solutions for different regimes of slippage and for a range of time scales. Dewetting rates and the cross sectional profiles of the evolving rims are derived for these models and compared to experimental results. Experiments also show that the rim is typically unstable in the spanwise direction and develops thicker and thinner parts that may grow into ``fingers''. Linear stability analysis as well as nonlinear numerical solutions are presented to investigate shape and growth rate of the rim instability. It is demonstrated that the difference in morphology and the rate at which the instability develops can be directly attributed to the magnitude of slippage. Finally, a derivation is given for the dominant wavelength of the bulges along the unstable rim.
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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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    Signatures of slip in dewetting polymer films
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Peschka, Dirk; Haefner, Sabrina; Jacobs, Karin; Münch, Andreas; Wagner, Barbara
    Thin liquid polymer films on hydrophobic substrates are susceptable to rupture and formation of holes, which in turn initiate a complex dewetting process that eventually evolves into characteristic stationary droplet patterns. Experimental and theoretical studies suggest that the specific type of droplet pattern largely depends on the nature of the polymer-substrate boundary condition. To follow the morphological evolution numerically over long time scales and for the multiple length scales involved has so far been a major challenge. In this study a highly adaptive finite-element based numerical scheme is presented that allows for large-scale simulations to follow the evolution of the dewetting process deep into the nonlinear regime of the model equations, capturing the complex dynamics including shedding of droplets. In addition, the numerical results predict the previouly unknown shedding of satellite droplets during the destabilisation of liquid ridges, that form during the late stages of the dewetting process. While the formation of satellite droplets is well-known in the context of elongating fluid filaments and jets, we show here that for dewetting liquid ridges this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip.
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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.
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    Stationary solutions for two-layer lubrication equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Jachalski, Sebastian; Huth, Robert; Kitavtsev, Georgy; Peschka, Dirk; Wagner, Barbara
    We investigate stationary solutions of flows of thin liquid bilayers in an energetic formulation which is motivated by the gradient flow structure of its lubrication approximation. The corresponding energy favors the liquid substrate to be only partially covered by the upper liquid. This is expressed by a negative spreading coefficient which arises from an intermolecular potential combining attractive and repulsive forces and leads to an ultra-thin layer of thickness e. For the corresponding lubrication models existence of stationary solutions is proven. In the limit e to 0 matched asymptotic analysis is applied to derive sharp-interface models and the corresponding contact angles, i.e. the Neumann triangle. In addition we use G-convergence and derive the equivalent sharp-interface models rigorously in this limit. For the resulting model existence and uniqueness of energetic minimizers are proven. The minimizers agree with solutions obtained by matched asymptotics.
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    Sharp-interface problem of the Ohta--Kawasaki model for symmetric diblock copolymers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Barua, Amlam K.; Chew, Ray; Shuwang, Li; Lowengrub, John; Münch, Andreas; Wagner, Barbara
    The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space.
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    Controlled topological transitions in thin film phase separation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hennessy, Mathew G.; Burlakov, Victor M.; Münch, Andreas; Wagner, Barbara; Goriely, Alain
    In this paper the evolution of a binary mixture in a thin-film geometry with a wall at the top and bottom is considered. Bringing the mixture into its miscibility gap so that no spinodal decomposition occurs in the bulk, a slight energetic bias of the walls towards each one of the constituents ensures the nucleation of thin boundary layers that grow until the constituents have moved into one of the two layers. These layers are separated by an interfacial region, where the composition changes rapidly. Conditions that ensure the separation into two layers with a thin interfacial region are investigated based on a phase-field model and using matched asymptotic expansions a corresponding sharp-interface problem for the location of the interface is established. It is then argued that a thus created two-layer system is not at its energetic minimum but destabilizes into a controlled self-replicating pattern of trapezoidal vertical stripes by minimizing the interfacial energy between the phases while conserving their area. A quantitative analysis of this mechanism is carried out via a new thin-film model for the free interfaces, which is derived asymptotically from the sharp-interface model.
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    Dynamic formation of oriented patches in chondrocyte cell cultures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Grote, Marcus; Palumberi, Viviana; Wagner, Barbara; Barbero, Andrea; Martin, Ivan
    Growth factors have a significant impact not only on the growth dynamics but also on the phenotype of chondrocytes (Barbero et al. , J. Cell. Phys. 204, pp. 830-838, 2005). In particular, as chondrocyte populations approach confluence, the cells tend to align and form coherent patches. Starting from a mathematical model for fibroblast populations at equilibrium (Mogilner et al., Physica D 89, pp. 346-367, 1996), a dynamic continuum model with logistic growth is developed. Both linear stability analysis and numerical solutions of the time-dependent nonlinear integro-partial differential equation are used to identify the key parameters that lead to pattern formation in the model. The numerical results are compared quantitatively to experimental data by extracting statistical information on orientation, density and patch size through Gabor filters.
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    Linear stability analysis of ta sharp-interface model for dewetting thin films
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) King, John R.; Münch, Andreas; Wagner, Barbara
    The topic of this study concerns the stability of the three-phase contact-line of a dewetting thin liquid film on a hydrophobised substrate driven by van der Waals forces. The role of slippage in the emerging instability at the three-phase contact-line is studied by deriving a sharp-interface model for the dewetting thin film via matched asymptotic expansions. This allows for a derivation of travelling waves and their linear stability via eigenmode analysis. In contrast to the dispersion relations typically encountered for the finger-instabilty, where the dependence of the growth rate on the wave number is quadratic, here it is linear. Using the separation of time scales of the slowly growing rim of the dewetting film and time scale on which the contact line destabilises, the sharp-interface results are compared to earlier results for the full lubrication model and good agreement for the most unstable modes is obtained.
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    Liquid-liquid dewetting: Morphologies and rates
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Bommer, Stefan; Seemann, Ralf; Jachalski, Sebastian; Peschka, Dirk; Wagner, Barbara
    The dependence of the dissipation on the local details of the flow field of a liquid polymer film dewetting from a liquid polymer substrate is shown, solving the free boundary problem for a two-layer liquid system. As a key result we show that the dewetting rates of such a liquid bi-layer system can not be described by a single power law but shows transient behaviour of the rates, changing from increasing to decreasing behaviour. The theoretical predictions on the evolution of morphology and rates of the free surfaces and free interfaces are compared to measurements of the evolution of the polystyrene(PS)-air, the polymethyl methacrylate (PMMA)-air and the PS-PMMA interfaces using in situ atomic force microscopy (AFM), and they show excellent agreement.