Roughness gradient induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study

The effect of a step wise change in the pillar density on the dynamics of droplets is investigated via three-dimensional lattice Boltzmann simulations. For the same pillar density gradient but different pillar arrangements, both motion over the gradient zone as well as complete arrest are observed. In the moving case, the droplet velocity scales approximately linearly with the texture gradient. A simple model is provided reproducing the observed linear behavior. The model also predicts a linear dependence of droplet velocity on surface tension. This prediction is clearly confirmed via our computer simulations for a wide range of surface tensions.Comment: 6 pages, 8 figure

Amorphous silica between confining walls and under shear: a computer simulation study

Molecular dynamics computer simulations are used to investigate a silica melt confined between walls at equilibrium and in a steady-state Poisseuille flow. The walls consist of point particles forming a rigid face-centered cubic lattice and the interaction of the walls with the melt atoms is modelled such that the wall particles have only a weak bonding to those in the melt, i.e. much weaker than the covalent bonding of a Si-O unit. We observe a pronounced layering of the melt near the walls. This layering, as seen in the total density profile, has a very irregular character which can be attributed to a preferred orientational ordering of SiO4 tetrahedra near the wall. On intermediate length scales, the structure of the melt at the walls can be well distinguished from that of the bulk by means of the ring size distribution. Whereas essentially no structural changes occur in the bulk under the influence of the shear fields considered, strong structural rearrangements in the ring size distribution are present at the walls as far as there is a slip motion. For the sheared system, parabolic velocity profiles are found in the bulk region as expected from hydrodynamics and the values for the shear viscosity as extracted from those profiles are in good agreement with those obtained in pure bulk simulations from the appropriate Green-Kubo formula.Comment: 23 pages of Late

Diffuse interface models of solidification with convection: The choice of a finite interface thickness

The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original formulation of this problem is restricted to transport by diffusion, we consider here the case of melt convection. Using an analysis of the coupled phase field-fluid dynamic equations, we show here that such a thin interface limit does also exist if transport contains both diffusion and convection. This prediction is tested by comparing simulation studies, which make use of the thin-interface condition, with an analytic sharp-interface theory for dendritic tip growth under convection. © 2020, The Author(s)

Shear-induced anisotropic decay of correlations in hard-sphere colloidal glasses

Spatial correlations of microscopic fluctuations are investigated via real-space experiments and computer simulations of colloidal glasses under steady shear. It is shown that while the distribution of one-particle fluctuations is always isotropic regardless of the relative importance of shear as compared to thermal fluctuations, their spatial correlations show a marked sensitivity to the competition between shear-induced and thermally activated relaxation. Correlations are isotropic in the thermally dominated regime, but develop strong anisotropy as shear dominates the dynamics of microscopic fluctuations. We discuss the relevance of this observation for a better understanding of flow heterogeneity in sheared amorphous solids.Comment: 6 pages, 4 figure

Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids

With the eventual aim of describing flowing elasto-plastic materials, we focus on the elementary brick of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear strain. We characterize the effect of a nearby wall on this perturbation, and quantify the importance of finite size effects. Although for the sake of simplicity most of our explicit formulae deal with a 2D situation, our statements hold for 3D situations as well.Comment: submitted to EPJ

Nonequilibrium fluctuation dissipation relations of interacting Brownian particles driven by shear

We present a detailed analysis of the fluctuation dissipation theorem (FDT) close to the glass transition in colloidal suspensions under steady shear using mode coupling approximations. Starting point is the many-particle Smoluchowski equation. Under shear, detailed balance is broken and the response functions in the stationary state are smaller at long times than estimated from the equilibrium FDT. An asymptotically constant relation connects response and fluctuations during the shear driven decay, restoring the form of the FDT with, however, a ratio different from the equilibrium one. At short times, the equilibrium FDT holds. We follow two independent approaches whose results are in qualitative agreement. To discuss the derived fluctuation dissipation ratios, we show an exact reformulation of the susceptibility which contains not the full Smoluchowski operator as in equilibrium, but only its well defined Hermitian part. This Hermitian part can be interpreted as governing the dynamics in the frame comoving with the probability current. We present a simple toy model which illustrates the FDT violation in the sheared colloidal system.Comment: 21 pages, 13 figures, submitted to Phys. Rev.

Thin interface limit of the double-sided phase-field model with convection

The thin interface limit of the phase-field model is extended to include transport via melt convection. A double-sided model (equal diffusivity in liquid and solid phases) is considered for the present analysis. For the coupling between phase-field and Navier-Stokes equations, two commonly used schemes are investigated using a matched asymptotic analysis: (i) variable viscosity and (ii) drag force model. While for the variable viscosity model, the existence of a thin interface limit can be shown up to the second order in the expansion parameter, difficulties arise in satisfying no-slip boundary condition at this order for the drag force model. Nevertheless, detailed numerical simulations in two dimensions show practically no difference in dendritic growth profiles in the presence of forced melt flow obtained for the two coupling schemes. This suggests that both approaches can be used for the purpose of numerical simulations. Simulation results are also compared to analytic theory, showing excellent agreement for weak flow. Deviations at higher fluid velocities are discussed in terms of the underlying theoretical assumptions. © 2020 The Author(s) Published by the Royal Society. All rights reserved.European Space Agency, ESADeutsche Forschungsgemeinschaft, DFGRussian Science Foundation, RSF: 16-11-10095Deutsche Forschungsgemeinschaft, DFGData accessibility. This article has no additional data. Authors’ contributions. All the authors have contributed equally to this work. Competing interests. We declare we have no competing interest. Funding. P.K.G. acknowledges the support by the European Space Agency (ESA) under research project MULTIPHAS grant no. (AO-2004) and the German Aerospace Center (DLR) Space Management undercontract no. 50WM1541 and also from the Russian Science Foundation under project no. 16-11-10095. A.S. and F.V. acknowledges financial support by the German Research Foundation (DFG) under the project no. Va205/17-1