2017, Kitavtsev, Georgy, Münch, Andreas, Wagner, Barbara

In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamics in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Leslie-Erickson-Parodi theory. Analytic expressions are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure.

2010, Münch, Andreas, Please, Colin P., Wagner, Barbara

We consider a mathematical model of spin coating of a single polymer blended in a solvent. The model describes the one-dimensional development of the thin layer of the mixture as the layer thins due to flow created by a balance of viscous forces and centrifugal forces and due to evaporation of the solvent. In the model both the diffusivity of the solvent in the polymer and the viscosity of the mixture are very rapidly varying functions of the solvent volume fraction. Guided by numerical solutions an asymptotic analysis reveals a number of different possible behaviours of the thinning layer dependent on the nondimensional parameters describing the system. The main practical interest is in controlling the appearance and development of a ``skin'' on the polymer where the solvent concentration reduces rapidly on the outer surface leaving the bulk of the layer still with high concentrations of solvent. The critical parameters controlling this behaviour are found to be eps the ratio of the diffusion to advection time scales, delta the ratio of the evaporation to advection time scales and exp(-gamma), the ratio of the diffusivity of the initial mixture and the pure polymer. In particular, our analysis shows that for very small evaporation with delta ll exp(-3/(4gamma)) eps^3/4 skin formation can be prevented

2012, Korzec, Maciek D., Münch, Andreas, Wagner, Barbara

In this paper we revisit models for the description of the evolution of crystalline films with anisotropic surface energies. We prove equivalences of symmetry properties of anisotropic surface energy models commonly used in the literature. Then we systematically develop a framework for the derivation of surface diffusion models for the self-assembly of quantum dots during Stranski-Krastanov growth that include surface energies also with large anisotropy as well as the effect of wetting energy, elastic energy and a randomly perturbed atomic deposition flux. A linear stability analysis for the resulting sixth-order semilinear evolution equation for the thin film surface shows that that the new model allows for large anisotropy and gives rise to the formation of anisotropic quantum dots. The nonlinear three-dimensional evolution is investigated via numerical solutions. These suggest that increasing anisotropy stabilizes the faceted surfaces and may lead to a dramatic slow-down of the coarsening of the dots.

2020, Celora, Giulia L., Hennessy, Matthew G., Münch, Andreas, Wagner, Barbara, Waters, Sarah L.

In this study we use non-equilibrium thermodynamics to systematically derive a phase-field model of a polyelectrolyte gel coupled to a thermodynamically consistent model for the salt solution surrounding the gel. The governing equations for the gel account for the free energy of the internal interfaces which form upon phase separation, as well as finite elasticity and multi-component transport. The fully time-dependent model describes the evolution of small changes in the mobile ion concentrations and follows their impact on the large-scale solvent flux and the emergence of long-time pattern formation in the gel. We observe a strong acceleration of the evolution of the free surface when the volume phase transition sets in, as well as the triggering of spinodal decomposition that leads to strong inhomogeneities in the lateral stresses, potentially leading to experimentally visible patterns.

2013, Ahnert, Tobias, Münch, Andreas, Wagner, Barbara

A new two-phase model is derived that make use of a constitutive law combining non-Brownian suspension with granular rheology, that was recently proposed by Boyer et al. [PRL, 107(18),188301 (2011)]. It is shown that for the simple channel flow geometry, the stress model naturally exhibits a Bingham type flow property with an unyielded finite-size zone in the center of the channel. As the volume fraction of the solid phase is increased, the various transitions in the flow fields are discussed using phase space methods for a boundary value problem, that is derived from the full model. The predictions of this analysis is then compared to the direct finite-element numerical solutions of the full model.

2015, Jachalski, Sebastian, Münch, Andreas, Wagner, Barbara

In 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.

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.

2018, Hennessy, Matthew G., Münch, Andreas, Wagner, Barbara

We present a formulation of the free boundary problem for a hydrogel that accounts for the interfacial free energy and finite strain due to the large deformation of the polymer network during solvent transport across the free boundary. For the geometry of an initially dry layer fixed at a rigid substrate, our model predicts a phase transition when a critical value of the solvent concentration has been reached near the free boundary. A one-dimensional case study shows that depending on the flux rate at the free boundary an initial saturation front is followed by spinodal decomposition of the hydrogel and the formation of an interfacial front that moves through the layer. Moreover, increasing the shear modulus of the elastic network delays or even suppresses phase separation.

2012, Jachalski, Sebastian, Peschka, Dirk, Münch, Andreas, Wagner, Barbara

In 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.

2014, Korzec, Maciek, Münch, Andreas, Süli, Endre, Wagner, Barbara

Anisotropy is an essential feature of phase-field models, in particular when describing the evolution of microstructures in solids. The symmetries of the crystalline phases are reflected in the interfacial energy by introducing corresponding directional dependencies in the gradient energy coefficients, which multiply the highest order derivative in the phase-field model. This paper instead considers an alternative approach, where the anisotropic gradient energy terms are replaced by a wavelet analogue that is intrinsically anisotropic and linear. In our studies we focus on the classical coupled temperature