Browsing by Author "Jachalski, Sebastian"
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- ItemDroplets on liquids and their long way into equilibrium(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bommer, Stefan; Jachalski, Sebastian; Peschka, Dirk; Seemann, Ralf; Wagner, BarbaraThe morphological paths towards equilibrium droplets during the late stages of the dewetting process of a liquid film from a liquid substrate is investigated experimentally and theoretically. As liquids, short chained polystyrene (PS) and polymethyl-methacrylate (PMMA) are used, which can be considered as Newontian liquids well above their glass transition temperatures. Careful imaging of the PS/air interface of the droplets during equilibration by in situ scanning force microscopy and the PS/PMMA interface after removal of the PS droplets reveal a surprisingly deep penetration of the PS droplets into the PMMA layer. Droplets of sufficiently small volumes develop the typical lens shape and were used to extract the ratio of the PS/air and PS/PMMA surface tensions and the contact angles by comparison to theoretical exact equilibrium solutions of the liquid/liquid system. Using these results in our dynamical thin-film model we find that before the droplets reach their equilibrium they undergo several intermediate stages each with a well-defined signature in shape. Moreover, the intermediate droplet shapes are independent of the details of the initial configuration, while the time scale they are reached depend strongly on the droplet volume. This is shown by the numerical solutions of the thin-film model and demonstrated by quantitative comparison to experimental results
- ItemExistence of solutions to an anisotropic degenerate Cahn-Hilliard-type equation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dziwnik, Marion; Jachalski, SebastianWe prove existence of solutions to an anisotropic Cahn-Hilliard-type equation with degenerate diffusional mobility. In particular, the mobility vanishes at the pure phases, which is typically used to model motion by surface diffusion. The main difficulty of the present existence result is the strong non-linearity given by the fourth-order anisotropic operator. Imposing particular assumptions on the domain and assuming that the strength of the anisotropy is sufficiently small enables to establish appropriate auxiliary results which play an essential part in the present existence proof. In addition to the existence we show that the absolute value of the corresponding solutions is bounded by 1.
- ItemGradient flow perspective of thin-film bilayer flows(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Huth, Robert; Jachalski, Sebastian; Kitavtsev, Georgy; Peschka, DirkWe study gradient flow formulations of thin-film bilayer flows with triple-junctions between liquid/liquid/air. First we highlight the gradient structure in the Stokes free-boundary flow and identify its solutions with the well-known PDE with boundary conditions. Next we propose a similar gradient formulation for the corresponding thin-film model and formally identify solutions with those of the corresponding free-boundary problem. A robust numerical algorithm for the thin-film gradient flow structure is then provided. Using this algorithm we compare the sharp triple-junction model with precursor models. For their stationary solutions a rigorous connection is established using [Gamma]-convergence. For time-dependentsolutions the comparison of numerical solutions shows a good agreement for small and moderate times. Finally we study spreading in the zero-contact angle case, where we compare numerical solutions with asymptotically exact source-type solutions.
- ItemImpact of energy dissipation on interface shapes and on rates for dewetting from liquid substrates([London] : Macmillan Publishers Limited, part of Springer Nature, 2018) Peschka, Dirk; Bommer, Stefan; Jachalski, Sebastian; Seemann, Ralf; Wagner, BarbaraWe revisit the fundamental problem of liquid-liquid dewetting and perform a detailed comparison of theoretical predictions based on thin-film models with experimental measurements obtained by atomic force microscopy. Specifically, we consider the dewetting of a liquid polystyrene layer from a liquid polymethyl methacrylate layer, where the thicknesses and the viscosities of both layers are similar. Using experimentally determined system parameters like viscosity and surface tension, an excellent agreement of experimentally and theoretically obtained rim profile shapes are obtained including the liquid-liquid interface and even dewetting rates. Our new energetic approach additionally allows to assess the physical importance of different contributions to the energy-dissipation mechanism, for which we analyze the local flow fields and the local dissipation rates. Using this approach, we explain why dewetting rates for liquid-liquid systems follow no universal power law, despite the fact that experimental velocities are almost constant. This is in contrast to dewetting scenarios on solid substrates and in contrast to previous results for liquid-liquid substrates using heuristic approaches.
- ItemImpact of interfacial slip on the stability of liquid two-layer polymer films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Jachalski, Sebastian; Peschka, Dirk; Münch, Andreas; Wagner, BarbaraIn this study systems of coupled thin-film models for two immiscible liquid polymer layers on a solid substrate that account for interfacial slip and intermolecular forces are derived. On the scale of tens to hundred nanometers such two-layer systems are susceptable to instability and may rupture and dewet. The stability of the two-layer system and its significant dependence on the order of magnitude of slip is investigated via these thin-film models. With no-slip at both, the liquid-liquid and liquid-solid interface and polymer layers of comparable thickness, the dispersion relation typically shows two local maxima, one in the long-wave regime and the other at moderate wavenumbers. The former is associated with perturbations that mainly affect the gas-liquid interface and the latter with higher relative perturbation amplitudes at the liquid-liquid interface. Slip at the liquid-liquid interface generally favors the former perturbations. However, when the liquid-liquid and the liquidsolid interface exhibit large slip, the maxima shift to small wavenumbers for increasing slip and hence may significantly change the spinodal patterns.
- ItemLiquid-liquid dewetting: Morphologies and rates(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Bommer, Stefan; Seemann, Ralf; Jachalski, Sebastian; Peschka, Dirk; Wagner, BarbaraThe 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.
- ItemStationary solutions for two-layer lubrication equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Jachalski, Sebastian; Huth, Robert; Kitavtsev, Georgy; Peschka, Dirk; Wagner, BarbaraWe 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.
- ItemStructure formation in thin liquid-liquid films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Bommer, Stefan; Jachalski, Sebastian; Peschka, Dirk; Seemann, Ralf; Wagner, BarbaraWe revisit the problem of a liquid polymer that dewets from another liquid polymer substrate with the focus on the direct comparison of results from mathematical modeling, rigorous analysis, numerical simulation and experimental investigations of rupture, dewetting dynamics and equilibrium patterns of a thin liquid-liquid system. The experimental system uses as a model system a thin polystyrene (PS) / polymethylmethacrylate (PMMA) bilayer of a few hundred nm. The polymer systems allow for in situ observation of the dewetting process by atomic force microscopy (AFM) and for a precise ex situ imaging of the liquidliquid interface. In the present study, the molecular chain length of the used polymers is chosen such that the polymers can be considered as Newtonian liquids. However, by increasing the chain length, the rheological properties of the polymers can be also tuned to a viscoelastic flow behavior. The experimental results are compared with the predictions based on the thin film models. The system parameters like contact angle and surface tensions are determined from the experiments and used for a quantitative comparison. We obtain excellent agreement for transient drop shapes on their way towards equilibrium, as well as dewetting rim profiles and dewetting dynamics.
- ItemThin-film models for viscoelastic liquid bi-layers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Jachalski, Sebastian; Münch, Andreas; Wagner, BarbaraIn this work we consider a two-layer system of viscoelastic liquids of corotational Jeffreys type dewetting from a Newtonian liquid substrates. We derive conditions that allow for the first time the asymptotically consistent reduction of the free boundary problem for the two-layer system to a system of coupled thin-film equations that incorporate the full nonlinear viscoelastic rheology. We show that these conditions are controlled by the order of magnitude of the viscosity ratio of the liquid layers and their thickness ratio. For pure Newtonian flow, these conditions lead to a thin-film model that couples a layer with a parabolic flow field to a layer described by elongational flow. For this system we establish asymptotic regimes that relate the viscosity ratio to a corresponding apparent slip. We then use numerical simulations to discuss the characteristic morphological and dynamical properties of viscoelastic films of corotational Jeffreys type dewetting from a solid as well as liquid substrate.
- ItemWeak solutions to lubrication systems describing the evolution of bilayer thin films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Jachalski, Sebastian; Kitavtsev, Georgy; Taranets, RomanThe existence of global nonnegative weak solutions is proved for coupled one-dimensional lubrication systems that describe the evolution of nanoscopic bilayer thin polymer films that take account of Navier-slip or no-slip conditions at both liquid-liquid and liquidsolid interfaces. In addition, in the presence of attractive van der Waals and repulsive Born intermolecular interactions existence of positive smooth solutions is shown.