Fall and rise of small droplets on rough hydrophobic substrates

Liquid droplets on patterned hydrophobic substrates are typically observed either in the Wenzel or the Cassie state. Here we show that for droplets of comparable size to the roughness scale an additional local equilibrium state exists, where the droplet is immersed in the texture, but not yet contacts the bottom grooves. Upon evaporation, a droplet in this state enters the Cassie state, leading to a qualitatively new self-cleaning mechanism. The effect is of generic character and is expected to occur in any hydrophobic capillary wetting situation where a spherical liquid reservoir is involved.Comment: 6 pages, 6 figures, version as published in EP

The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments

The rotation ${\rm polar}(F) \in {\rm SO}(3)$ arises as the unique orthogonal factor of the right polar decomposition $F = {\rm polar}(F) \cdot U$ of a given invertible matrix $F \in {\rm GL}^+(3)$. In the context of nonlinear elasticity Grioli (1940) discovered a geometric variational characterization of ${\rm polar}(F)$ as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli's variational approach with weights (material parameters) $\mu > 0$ and $\mu_c \geq 0$ (Grioli: $\mu = \mu_c$). The energy subject to minimization coincides with the Cosserat shear-stretch contribution arising in any geometrically nonlinear, isotropic and quadratic Cosserat continuum model formulated in the deformation gradient field $F := \nabla\varphi: \Omega \to {\rm GL}^+(3)$ and the microrotation field $R: \Omega \to {\rm SO}(3)$. The corresponding set of non-classical energy-minimizing rotations $${\rm rpolar}^\pm_{\mu,\mu_c}(F) := \substack{{\rm argmin}\\ R\,\in\,{\rm SO(3)}} \Big\{ W_{\mu, \mu_c}(R\,;F) := \mu\, || {\rm sym}(R^TF - 1)||^2 + \mu_c\, ||{\rm skew}(R^TF - 1)||^2 \Big\}$$ represents a new relaxed-polar mechanism. Our goal is to motivate this mechanism by presenting it in a relevant setting. To this end, we explicitly construct a deformation mapping $\varphi_{\rm nano}$ which models an idealized nanoindentation and compare the corresponding optimal rotation patterns ${\rm rpolar}^\pm_{1,0}(F_{\rm nano})$ with experimentally obtained 3D-EBSD measurements of the disorientation angle of lattice rotations due to a nanoindentation in solid copper. We observe that the non-classical relaxed-polar mechanism can produce interesting counter-rotations. A possible link between Cosserat theory and finite multiplicative plasticity theory on small scales is also explored.Comment: 28 pages, 11 figure

Maintaining the equipartition theorem in small heterogeneous molecular dynamics ensembles

It has been reported recently that the equipartition theorem is violated in molecular dynamics simulations with periodic boundary condition [Shirts et al, J. Chem. Phys. 125, 164102 (2006)]. This effect is associated with the conservation of the center of mass momentum. Here, we propose a fluctuating center of mass molecular dynamics approach (FCMMD) to solve this problem. Using the analogy to a system exchanging momentum with its surroundings, we work out --and validate via simulations-- an expression for the rate at which fluctuations shall be added to the system. The restoration of equipartition within the FCMMD is then shown both at equilibrium as well as beyond equilibrium in the linear response regime

Aging in Structural Changes of Amorphous Solids: A Study of First Passage Time and Persistence Time Distribution

The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(\Delta t)$, and the persistence time, $p(\tau)$. In contrast to previous reports, both $p_1$ and $p$ are found to evolve with time upon aging. The age dependence of the persistence time distribution is shown to be sensitive to the details of the algorithm used to extract it from particle trajectories. By updating the reference point in event detection algorithm and accounting for the event specific aging time, we uncover age dependence of $p(\tau)$, hidden to previous studies. Moreover, the apparent age-dependence of $p_1$ in continuous time random walk with an age independent $p(\tau)$ is shown to result from an implicit synchronization of all the random walkers at the starting time

Heterogeneous shear in hard sphere glasses

There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. Via event driven molecular dynamics simulations of a hard sphere glass, we provide the first direct evidence for a correlation between the fluctuations of the local volume-fraction and the fluctuations of the local shear rate. Higher shear rates do preferentially occur at regions of lower density and vice versa. The temporal behavior of fluctuations is governed by a characteristic time scale, which, when measured in units of strain, is independent of shear rate in the investigated range. Interestingly, the correlation volume is also roughly constant for the same range of shear rates. A possible connection between these two observations is discussed.Comment: 5 pages, 4 figures, accepted at Phys. Rev. Let

Single particle fluctuations and directional correlations in driven hard sphere glasses

Via event driven molecular dynamics simulations and experiments, we study the packing fraction and shear-rate dependence of single particle fluctuations and dynamic correlations in hard sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies [Chikkadi et al, Europhys. Lett. (2012)], we further address the issue of anisotropy of the dynamic correlations.Comment: 8 pages, 10 figure

Shear stress in lattice Boltzmann simulations

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time-dependence of the fluid density in terms of the Reynolds number, Mach number and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.Comment: 15 pages, 4 figures, 2 table

Wetting gradient induced separation of emulsions: A combined experimental and lattice Boltzmann computer simulation study

Guided motion of emulsions is studied via combined experimental and theoretical investigations. The focus of the work is on basic issues related to driving forces generated via a step-wise (abrupt) change in wetting properties of the substrate along a given spatial direction. Experiments on binary emulsions unambiguously show that selective wettability of the one of the fluid components (water in our experiments) with respect to the two different parts of the substrate is sufficient in order to drive the separation process. These studies are accompanied by approximate analytic arguments as well as lattice Boltzmann computer simulations, focusing on effects of a wetting gradient on internal droplet dynamics as well as its relative strength compared to volumetric forces driving the fluid flow. These theoretical investigations show qualitatively different dependence of wetting gradient induced forces on contact angle and liquid volume in the case of an open substrate as opposed to a planar channel. In particular, for the parameter range of our experiments, slit geometry is found to give rise to considerably higher separation forces as compared to open substrate.Comment: 34 pages, 12 figure

On the spheroidized carbide dissolution and elemental partitioning in a high carbon bearing steel 100Cr6

We report on the characterization of high carbon bearing steel 100Cr6 using electron microscopy and atom probe tomography in combination with multi-component diffusion simulations (DICTRA). Scanning electron micrographs show that around 14 vol.% spheroidized carbides are formed during soft annealing and only 3 vol.% remain after dissolution into the austenitic matrix by austenitization at 1123 K (850 {\deg}C) for 300 s. The spheroidized particles are identified as (Fe, Cr)3C by transmission electron microscopy. Atom probe analyses reveal the redistribution and partitioning behaviors of elements, i.e. C, Si, Mn, Cr, Fe in both, the spheroidized carbides and the bainitic matrix in the sample isothermally heat-treated at 773 K (500 {\deg}C) after austenitization. A homogeneous distribution of C and gradual gradient of Cr was detected within the spheroidized carbides. Due to its limited diffusivity in (Fe, Cr)3C, Cr exhibits a maximum concentration at the surface of spheroidized carbides (16 at.%) and decreases gradually from surface towards the core down to a level of about 2 at.%. The atom probe results also indicate that the partially dissolved spheroidized carbides during austenitization may serve as nucleation sites for intermediate temperature cementite within bainite, which results in a relatively softer surface and harder core in spheroidized particles. This microstructure may contribute to the good wear resistance and fatigue propertie