Structural relaxation and rheological response of a driven amorphous system

The interplay between the structural relaxation and the rheological response of a binary LJ glass former is studied via MD simulations. In the quiescent state, the model is well known for its sluggish dynamics and a two step relaxation of correlation functions at low temperatures. An ideal glass transition temperature of $T_c = 0.435$ has been identified in the previous studies via the analysis of the system's dynamics in the frame work of the mode coupling theory of the glass transition [W. Kob and H.C. Andersen, PRE 51, 4626 (1995)]. Here, we test wether a signature of this ideal glass transition can also be found under shear. Indeed, the following distinction in the structural relaxation is found: In the supercooled state, the structural relaxation is dominated by the shear at relatively high shear rates, $\dot{\gamma}$, whereas at sufficiently low $\dot{\gamma}$ the (shear-independent) equilibrium relaxation is recovered. In contrast to this, the structural relaxation of a \emph{glass} is always driven by shear. This distinct behavior of the correlation functions is also reflected in the rheological response. In the supercooled state, the shear viscosity, $\eta$, decreases with increasing shear rate (shear thinning) at high shear rates, but then converges toward a constant as the $\dot{\gamma}$ is decreased below a (temperature-dependent) threshold value. Below $T_c$, on the other hand, the shear viscosity grows as $\eta \propto 1/\dot{\gamma}$ suggesting a divergence at $\dot{\gamma} =0$. Thus, within the accessible observation time window, a transition toward a non-ergodic state seems to occur in the driven glass as the driving force approaches zero.Comment: 12 pages, 9 figure

Interfacial roughening in non-ideal fluids: Dynamic scaling in the weak- and strong-damping regime

Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first analyzed by Flekkoy and Rothman [Phys. Rev. Lett. 75, 260 (1995)], where the dynamic scaling exponents in the weakly damped case in two dimensions were found to agree with the Kardar-Parisi-Zhang universality class. We extend this work by taking into account also the strong-damping regime and perform extensive fluctuating hydrodynamics simulations in two dimensions using the Lattice Boltzmann method. We show that the dynamic scaling behavior is different in the weakly and strongly damped case.Comment: 15 pages, 9 figure

Spreading Dynamics of Nanodrops: A Lattice Boltzmann Study

Spreading of nano-droplets is an interesting and technologically relevant phenomenon where thermal fluctuations lead to unexpected deviations from well-known deterministic laws. Here, we apply the newly developed fluctuating non-ideal lattice Boltzmann method [Gross et al., J. Stat. Mech., P03030 (2011)] for the study of this issue. Confirming the predictions of Davidovich and coworkers [PRL 95, 244905 (2005)], we provide the first independent evidence for the existence of an asymptotic, self-similar noise-driven spreading regime in both two- and three-dimensional geometry. The cross over from the deterministic Tanner's law, where the drop's base radius $b$ grows (in 3D) with time as $b \sim t^{1/10}$ and the noise dominated regime where $b \sim t^{1/6}$ is also observed by tuning the strength of thermal noise.Comment: 5 page

Shear-density coupling for a compressible single-component yield-stress fluid

Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive model. Focusing on the limit of low shear rates and high densities, the model approximates well---but is not limited to---gently sheared hard sphere colloidal glasses, where solvent effects are negligible. A detailed analysis of the linearized hydrodynamic equations for fluctuations and the resulting cubic dispersion relation reveals the existence of a range of densities and shear rates with growing flow heterogeneity. In this regime, after an initial transient, the velocity and density fields monotonically reach a spatially inhomogeneous stationary profile, where regions of high shear rate and low density coexist with regions of low shear rate and high density. The steady state is thus maintained by a competition between shear-induced enhancement of density inhomogeneities and relaxation via overdamped sound waves. An analysis of the mechanical equilibrium condition provides a criterion for the existence of steady state solutions. The dynamical evolution of the system is discussed in detail for various boundary conditions, imposing either a constant velocity, shear rate, or stress at the walls.Comment: 18 pages, 14 figure

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

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