Effects of Cage-Breaking Events in Single-File Diffusion on Elongation Correlation

Collective motion of caged particles is studied by calculating correlations of elongations (i.e., excess distances between two tagged particles) in a one-dimensional colloidal system, with the focus on the effect of overtaking events by which particles can hop out of the cage. It is shown analytically and verified numerically that the effect of overtaking is more prominent in shorter lengthscales, and also that the two-time elongation correlation exhibits ageing behavior due to overtaking

Two-tag correlations and nonequilibrium fluctuation-response relation in ageing single-file diffusion

Spatiotemporally correlated motions of interacting Brownian particles, confined in a narrow channel of infinite length, are studied in terms of statistical quantities involving two particles. A theoretical framework that allows analytical calculation of two-tag correlations is presented on the basis of the Dean–Kawasaki equation describing density fluctuations in colloidal systems. In the equilibrium case, the time-dependent Einstein relation holds between the two-tag displacement correlation and the response function corresponding to it, which is a manifestation of the fluctuation–dissipation theorem for the correlation of density fluctuations. While the standard procedure of closure approximation for nonlinear density fluctuations is known to be obstructed by inconsistency with the fluctuation–dissipation theorem, this difficulty is naturally avoided by switching from the standard Fourier representation of the density field to the label-based Fourier representation of the vacancy field. In the case of ageing dynamics started from equidistant lattice configuration, the time-dependent Einstein relation is violated, as the two-tag correlation depends on the waiting time for equilibration while the response function is not sensitive to it. Within linear approximation, however, there is a simple relation between the density (or vacancy) fluctuations and the corresponding response function, which is valid even if the system is out of equilibrium. This non-equilibrium fluctuation–response relation can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field

Solitary waves on falling liquid films in the inertia-dominated regime

We offer new insights and results on the hydrodynamics of solitary waves on inertia-dominated falling liquid films using a combination of experimental measurements, direct numerical simulations (DNS) and low-dimensional (LD) modelling. The DNS are shown to be in very good agreement with experimental measurements in terms of the main wave characteristics and velocity profiles over the entire range of investigated Reynolds numbers. And, surprisingly, the LD model is found to predict accurately the film height even for inertia-dominated films with high Reynolds numbers. Based on a detailed analysis of the flow field within the liquid film, the hydrodynamic mechanism responsible for a constant, or even reducing, maximum film height when the Reynolds number increases above a critical value is identified, and reasons why no flow reversal is observed underneath the wave trough above a critical Reynolds number are proposed. The saturation of the maximum film height is shown to be linked to a reduced effective inertia acting on the solitary waves as a result of flow recirculation in the main wave hump and in the moving frame of reference. Nevertheless, the velocity profile at the crest of the solitary waves remains parabolic and self-similar even after the onset of flow recirculation. The upper limit of the Reynolds number with respect to flow reversal is primarily the result of steeper solitary waves at high Reynolds numbers, which leads to larger streamwise pressure gradients that counter flow reversal. Our results should be of interest in the optimisation of the heat and mass transport characteristics of falling liquid films and can also serve as a benchmark for future model development

Internal Stress in a Model Elasto-Plastic Fluid

Plastic materials can carry memory of past mechanical treatment in the form of internal stress. We introduce a natural definition of the vorticity of internal stress in a simple two-dimensional model of elasto-plastic fluids, which generates the internal stress. We demonstrate how the internal stress is induced under external loading, and how the presence of the internal stress modifies the plastic behavior.Comment: 4 pages, 3 figure

Effect of Interaction on the Formation of Memories in Paste

A densely packed colloidal suspension with plasticity, called paste, is known to remember directions of vibration and flow. These memories in paste can be visualized by the morphology of desiccation crack patterns. Here, we find that paste made of charged colloidal particles cannot remember flow direction. If we add sodium chloride into such paste to screen the Coulombic repulsive interaction between particles, the paste comes to remember flow direction. That is, one drop of salt water changes memory effect in the paste and thereby we can tune the morphology of desiccation crack patterns more precisely.Comment: 10 pages, 11 figures, Title change