Aggregation of self-propelled colloidal rods near confining walls

Non-equilibrium collective behavior of self-propelled colloidal rods in a confining channel is studied using Brownian dynamics simulations and dynamical density functional theory. We observe an aggregation process in which rods self-organize into transiently jammed clusters at the channel walls. In the early stage of the process, fast-growing hedgehog-like clusters are formed which are largely immobile. At later stages, most of these clusters dissolve and mobilize into nematized aggregates sliding past the walls.Comment: 5 pages, 4 figure

Translational and rotational friction on a colloidal rod near a wall

We present particulate simulation results for translational and rotational friction components of a shish-kebab model of a colloidal rod with aspect ratio (length over diameter) $L/D = 10$ in the presence of a planar hard wall. Hydrodynamic interactions between rod and wall cause an overall enhancement of the friction tensor components. We find that the friction enhancements to reasonable approximation scale inversely linear with the closest distance $d$ between the rod surface and the wall, for $d$ in the range between $D/8$ and $L$. The dependence of the wall-induced friction on the angle $\theta$ between the long axis of the rod and the normal to the wall is studied and fitted with simple polynomials in $\cos \theta$.Comment: 8 pages, 8 figure

The probability distribution of a trapped Brownian particle in plane shear flows

We investigate the statistical properties of an over-damped Brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and they are substantiated by numerical results. There is a good agreement between the two approaches for a wide range of parameters.Comment: 5 pages, 4 figur

Particles held by springs in a linear shear flow exhibit oscillatory motion

The dynamics of small spheres, which are held by linear springs in a low Reynolds number shear flow at neighboring locations is investigated. The flow elongates the beads and the interplay of the shear gradient with the nonlinear behavior of the hydrodynamic interaction among the spheres causes in a large range of parameters a bifurcation to a surprising oscillatory bead motion. The parameter ranges, wherein this bifurcation is either super- or subcritical, are determined.Comment: 4 pages, 5 figure

Hydrodynamic induced deformation and orientation of a microscopic elastic filament

We describe simulations of a microscopic elastic filament immersed in a fluid and subject to a uniform external force. Our method accounts for the hydrodynamic coupling between the flow generated by the filament and the friction force it experiences. While models that neglect this coupling predict a drift in a straight configuration, our findings are very different. Notably, a force with a component perpendicular to the filament axis induces bending and perpendicular alignment. Moreover, with increasing force we observe four shape regimes, ranging from slight distortion to a state of tumbling motion that lacks a steady state. We also identify the appearance of marginally stable structures. Both the instability of these shapes and the observed alignment can be explained by the combined action of induced bending and non-local hydrodynamic interactions. Most of these effects should be experimentally relevant for stiff micro-filaments, such as microtubules.Comment: three figures. To appear in Phys Rev Let

Stick boundary conditions and rotational velocity auto-correlation functions for colloidal particles in a coarse-grained representation of the solvent

We show how to implement stick boundary conditions for a spherical colloid in a solvent that is coarse-grained by the method of stochastic rotation dynamics. This allows us to measure colloidal rotational velocity auto-correlation functions by direct computer simulation. We find quantitative agreement with Enskog theory for short times and with hydrodynamic mode-coupling theory for longer times. For aqueous colloidal suspensions, the Enskog contribution to the rotational friction is larger than the hydrodynamic one when the colloidal radius drops below 35nm.Comment: new version with some minor change

Reentrance effect in the lane formation of driven colloids

Recently it has been shown that a strongly interacting colloidal mixture consisting of oppositely driven particles, undergoes a nonequilibrium transition towards lane formation provided the driving strength exceeds a threshold value. We predict here a reentrance effect in lane formation: for fixed high driving force and increasing particle densities, there is first a transition towards lane formation which is followed by another transition back to a state with no lanes. Our result is obtained both by Brownian dynamics computer simulations and by a phenomenological dynamical density functional theory.Comment: 4 pages, 2 figure

Depletion forces in non-equilibrium

The concept of effective depletion forces between two fixed big colloidal particles in a bath of small particles is generalized to a non-equilibrium situation where the bath of small Brownian particles is flowing around the big particles with a prescribed velocity. In striking contrast to the equilibrium case, the non-equilibrium forces violate Newton's third law, are non-conservative and strongly anisotropic, featuring both strong attractive and repulsive domains.Comment: 4 pages, 3 figure

From Equilibrium to Steady-State Dynamics after Switch-On of Shear

A relation between equilibrium, steady-state, and waiting-time dependent dynamical two-time correlation functions in dense glass-forming liquids subject to homogeneous steady shear flow is discussed. The systems under study show pronounced shear thinning, i.e., a significant speedup in their steady-state slow relaxation as compared to equilibrium. An approximate relation that recovers the exact limit for small waiting times is derived following the integration through transients (ITT) approach for the nonequilibrium Smoluchowski dynamics, and is exemplified within a schematic model in the framework of the mode-coupling theory of the glass transition (MCT). Computer simulation results for the tagged-particle density correlation functions corresponding to wave vectors in the shear-gradient directions from both event-driven stochastic dynamics of a two-dimensional hard-disk system and from previously published Newtonian-dynamics simulations of a three-dimensional soft-sphere mixture are analyzed and compared with the predictions of the ITT-based approximation. Good qualitative and semi-quantitative agreement is found. Furthermore, for short waiting times, the theoretical description of the waiting time dependence shows excellent quantitative agreement to the simulations. This confirms the accuracy of the central approximation used earlier to derive fluctuation dissipation ratios (Phys. Rev. Lett. 102, 135701). For intermediate waiting times, the correlation functions decay faster at long times than the stationary ones. This behavior is predicted by our theory and observed in simulations.Comment: 16 pages, 12 figures, submitted to Phys Rev

A dynamic density functional theory for particles in a flowing solvent

We present a dynamic density functional theory (dDFT) which takes into accou nt the advection of the particles by a flowing solvent. For potential flows we can use the same closure as in the absence of solvent flow. The structure of the resulting advected dDFT suggests that it could be used for non-potential flows as well. We apply this dDFT to Brownian particles (e.g., polymer coils) in a solvent flowing around a spherical obstacle (e.g., a colloid) and compare the results with direct simulations of the underlying Brownian dynamics. Although numerical limitations do not allow for an accurate quantitative check of the advected dDFT both show the same qualitative features. In contrast to previous works which neglected the deformation of the flow by the obstacle, we find that the bow-wave in the density distribution of particles in front of the obstacle as well as the wake behind it are reduced dramatically. As a consequence the friction force exerted by the (polymer) particles on the colloid can be reduced drastically.Comment: 7 pages, 5 figures, 2 tables, submitte