Search Results
Impact of slippage on the morphology and stability of a dewetting rim
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.
Gradient structures for flows of concentrated suspensions
2018, Peschka, Dirk, Thomas, Marita, Ahnert, Tobias, Münch, Andreas, Wagner, Barbara
In this work we investigate a two-phase model for concentrated suspensions. We construct a PDE formulation using a gradient flow structure featuring dissipative coupling between fluid and solid phase as well as different driving forces. Our construction is based on the concept of flow maps that also allows it to account for flows in moving domains with free boundaries. The major difference compared to similar existing approaches is the incorporation of a non-smooth twohomogeneous term to the dissipation potential, which creates a normal pressure even for pure shear flows.
Stationary solutions for two-layer lubrication equations
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.
Signatures of slip in dewetting polymer films
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.
Equilibrium shapes of poly-crystalline silicon nanodots
2013, Korzec, Maciek D., Roczen, Maurizio, Schade, Martin, Wagner, Barbara, Rech, Bernd
This study is concerned with the topography of nanostructures consisting of arrays of poly-crystalline nanodots. Guided by transmission electron microscopy (TEM) measurements of crystalline Si (c-Si) nanodots that evolved from a dewetting process of an amorphous Si (a-Si) layer from a SiO2 coated substrate, we investigate appropriate formulations for the surface energy density and transitions of energy density states at grain boundaries. We introduce a new numerical minimization formulation that allows to account for adhesion energy from an underlying substrate. We demonstrate our approach first for the free standing case, where the solutions can be compared to well-known Wulff constructions, before we treat the general case for interfacial energy settings that support partial wetting. We then use our method to predict the morphologies of poly-crystalline silicon nanodots.
Spinodal dewetting of thin films with large interfacial slip : implications from the dispersion relation
2008, Rauscher, Markus, Blossey, Ralf, Münch, Andreas, Wagner, Barbara
We compare the dispersion relations for spinodally dewetting thin liquid films for increasing magnitude of interfacial slip length in the lubrication limit. While the shape of the dispersion relation, in particular the position of the maximum, are equal for no-slip up to moderate slip lengths, the position of the maximum shifts to much larger wavelengths for large slip lengths. Here, we discuss the implications of this fact for recently developed methods to assess the disjoining pressure in spinodally unstable thin films by measuring the shape of the roughness power spectrum. For PS films on OTS covered Si wafers (with slip length $bapprox 1,mu$m) we predict a 20% shift of the position of the maximum of the power spectrum which should be detectable in experiments.
Models for the two-phase flow of concentrated suspensions
2014, Ahnert, Tobias, Münch, Andreas, Wagner, Barbara
A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model naturally exhibits a Bingham-type flow property. This property is investigated in detail for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady state of this problem, the governing equation are reduced to a boundary value problem for a system of ordinary differential equations and the dependence of its solutions are analyzed by using phase-space methods. For the general time-dependent case a new drift-flux model is derived for the first time using matched asymptotic expansions that take account of the boundary layers at the walls and the interface between the yielded and unyielded region. Using the drift-flux model, the behavior of the suspension flow, in particular the appearance and evolution of unyielded or jammed regions is then studied numerically for different choices of the parameters.
Influence of slip on the Rayleigh-Plateau rim instability in dewetting viscous films
2013, Bäumchen, Oliver, Marquant, Ludovic, Blossey, Ralf, Münch, Andreas, Wagner, Barbara, Jacobs, Karin
A dewetting viscous film develops a characteristic fluid rim at its receding edge due to mass conservation. In the course of the dewetting process the rim becomes unstable via an instability of Rayleigh-Plateau type. An important difference exists between this classic instability of a liquid column and the rim instability in the thin film as the growth of the rim is continuously fueled by the receding film. We explain how the development and macroscopic morphology of the rim instability are controlled by the slip of the film on the substrate. A single thin-film model captures quantitatively the characteristics of the evolution of the rim observed in our experiments.
Interface morphologies in liquid/liquid dewetting
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.
Anisotropic surface energy formulations and their effect on stability of a growing thin film
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.