7 results
Search Results
Now showing 1 - 7 of 7
- ItemEquilibrium shapes of poly-crystalline silicon nanodots(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Korzec, Maciek D.; Roczen, Maurizio; Schade, Martin; Wagner, Barbara; Rech, BerndThis 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.
- ItemInfluence of slip on the Rayleigh-Plateau rim instability in dewetting viscous films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bäumchen, Oliver; Marquant, Ludovic; Blossey, Ralf; Münch, Andreas; Wagner, Barbara; Jacobs, KarinA 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.
- ItemControlled 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, AlainIn 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.
- ItemStability analysis of non-constant base states in thin film equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dziwnik, Marion; Korzec, Maciek D.; Münch, Andreas; Wagner, BarbaraWe address the linear stability of non-constant base states within the class of mass conserving free boundary problems for degenerate and non-degenerate thin film equations. Well-known examples are the finger-instabilities of growing rims that appear in retracting thin solid and liquid films. Since the base states are time dependent and do not have a simple travelling wave or self-similar form, a classical eigenvalue analysis fails to provide the dominant wavelength of the instability. However, the initial fronts evolve on a slower time-scale than the typical perturbations. We exploit this time-scale separation and develop a multiple-scale approach for this class of stability problems. We show that the value of the dominant wavelength is rapidly attained once the base state has entered an approximately self-similar scaling. We note that this value is different from the one obtained by the linear stability analysis with "frozen modes", frequently found in the literature. Furthermore we show that for the present class of stability problems the dispersion relation behaves linear for large wavelengths, which is in contrast to many other instability problems in thin film flows.
- 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
- ItemTwo-phase flow model for concentrated suspensions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Ahnert, Tobias; Münch, Andreas; Wagner, BarbaraA 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.
- ItemPropagating topological transformations in thin immiscible bilayer films(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hennessy, Mathew G.; Burlakov, Victor M.; Münch, Andreas; Wagner, Barbara; Goriely, AlainA physical mechanism for the topological transformation of a two-layer system confined by two substrates is proposed. Initially the two horizontal layers, A and B, are on top of each other, but upon a sufficiently large disturbance, they can rearrange themselves through a spontaneously propagating sectioning to create a sequence of vertical alternating domains ABABAB. This generic topological transformation could be used to control the morphology of fabricated nanocomposites by first creating metastable layered structures and then triggering their transformation. The generality is underscored by formulating conditions for this topological transformation in terms of the interface energies between phases and substrates. The theoretical estimate for the width of the domains is confirmed by simulations of a phase-field model and its thin-film/sharp-interface approximation.