Interplay between hydrodynamic and Brownian fluctuations in sedimenting colloidal suspensions

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet number (Pe) ranging from 0.08 to 12. Hydrodynamic backflow causes a reduction of the average sedimentation velocity relative to the Stokes velocity. We find that this effect is independent of Pe number. Velocity fluctuations show the expected effects of thermal fluctuations at short correlation times. At longer times, nonequilibrium hydrodynamic fluctuations are visible, and their character appears to be independent of the thermal fluctuations. The hydrodynamic fluctuations dominate the diffusive behavior even for modest Pe number, while conversely the short-time fluctuations are dominated by thermal effects for surprisingly large Pe numbers. Inspired by recent experiments, we also study finite sedimentation in a horizontal planar slit. In our simulations distinct lateral patterns emerge, in agreement with observations in the experiments

The crossover from single file to Fickian diffusion

The crossover from single-file diffusion, where the mean-square displacement scales as ~t^(1/2), to normal Fickian diffusion, where ~t$, is studied as a function of channel width for colloidal particles. By comparing Brownian dynamics to a hybrid molecular dynamics and mesoscopic simulation technique, we can study the effect of hydrodynamic interactions on the single file mobility and on the crossover to Fickian diffusion for wider channel widths. For disc-like particles with a steep interparticle repulsion, the single file mobilities for different particle densities are well described by the exactly solvable hard-rod model. This holds both for simulations that include hydrodynamics, as well as for those that don't. When the single file constraint is lifted, then for particles of diameter \sigma and pipe of width$L$ such that (L- 2 \sigma)/\sigma = \delta_c << 1 the particles can be described as hopping past one-another in an average time t_{hop}. For shorter times t << t_{hop} the particles still exhibit sub-diffusive behaviour, but at longer times t > t_{hop}, normal Fickian diffusion sets in with an effective diffusion constant D_{hop} ~ t_{hop}^(1/2). For the Brownian particles, t_{hop} ~ 1/\delta_c^(2) when \delta << 1, but when hydrodynamic interactions are included, we find a stronger dependence than \delta_c^{-2}. We attribute this difference to short-range lubrication forces that make it more difficult for particles to hop past each other in very narrow channels

Computer Simulation of Entanglements in Viscoelastic Polymer Melts

In this thesis we report on computer simulations of polymer melts. Polymers in a melt can be viewed as long molecules which coil around each other and hinder each other’s motions: they are “entangled”. Entanglements occur because bonds between two adjacent atoms in a polymer chain can never be crossed by other such bonds. The goal of our study was to simulate and to understand the dynamical and rheological behavior resulting from this entanglement effect. Because of its relative simplicity, we have chosen polyethylene (PE) as our primary system of interest

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 Effects of Inter-particle Attractions on Colloidal Sedimentation

We use a mesoscopic simulation technique to study the effect of short-ranged inter-particle attraction on the steady-state sedimentation of colloidal suspensions. Attractions increase the average sedimentation velocity $v_s$ compared to the pure hard-sphere case, and for strong enough attractions, a non-monotonic dependence on the packing fraction $\phi$ with a maximum velocity at intermediate $\phi$ is observed. Attractions also strongly enhance hydrodynamic velocity fluctuations, which show a pronounced maximum size as a function of $\phi$. These results are linked to a complex interplay between hydrodynamics and the formation and break-up of transient many-particle clusters.Comment: 4 pages 4 figure

Hydrodynamic and Brownian fluctuations in sedimenting suspensions

The interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1-15 was studied using a mesoscopic computer simulation. A stochastic rotation dynamics (SRD) to the problem of sedimenting HS was adapted to perform the simulations. It was shown that the hydrodynamic interactions (HI) induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction, even when the they were an order of magnitude weaker than Brownian forces. It was observed that the velocity fluctuations begin to show nonequilibrium hydrodynamic character for Pe&gt;1

Mesoscale modeling of the rheology of pressure sensitive adhesives through inclusion of transient forces

For optimal application, pressure-sensitive adhesives must have rheological properties in between those of a viscoplastic solid and those of a viscoelastic liquid. Such adhesives can be produced by emulsion polymerisation, resulting in latex particles which are dispersed in water and contain long-chain acrylic polymers. When the emulsion is dried, the latex particles coalesce and an adhesive film is formed. The rheological properties of the dried samples are believed to be dominated by the interface regions between the original latex particles, but the relation between rheology and latex particle properties is poorly understood. In this paper we show that it is possible to describe the bulk rheology of a pressure-sensitive adhesive by means of a mesoscale simulation model. To reach experimental time and length scales, each latex particle is represented by just one simulated particle. The model is subjected to oscillatory shear flow and extensional flow. Simple order of magnitude estimates of the model parameters already lead to semi-quantitative agreement with experimental results. We show that inclusion of transient forces in the model, i.e. forces with memory of previous configurations, is essential to correctly predict the linear and nonlinear properties.Comment: 29 pages, 8 figure

Force calculation on walls and embedded particles in multiparticle collision dynamics simulations

Colloidal solutions posses a wide range of time and length scales, so that it is unfeasible to keep track of all of them within a single simulation. As a consequence some form of coarse-graining must be applied. In this work we use the Multi-Particle Collision Dynamics scheme. We describe a particular implementation of no-slip boundary conditions upon a solid surface, capable of providing correct force s on the solid bypassing the calculation of the velocity profile or the stre ss tensor in the fluid near the surface. As an application we measure the friction on a spherical particle, when it is placed in a bulk fluid and when it is confined in a slit. We show that the implementation of the no-slip boundary conditions leads to an enhanced Ensko g friction, which can be understood analytically. Because of the long-range nature of hydrodynamic interactions, the Stokes friction obtained from the simulations is sensitive of the simulation box size. We address this topic for the slit geometry, showing that that the dependence on the system size differs very much from what is expected in a 3D system, where periodic boundary conditions are used in all directions.Comment: To appear in Physical Review