Nanoscale simulations of directional locking

When particles suspended in a fluid are driven through a regular lattice of cylindrical obstacles, the particle motion is usually not simply in the direction of the force, and in the high Peclet number limit particle trajectories tend to lock along certain lattice directions. By means of molecular dynamics simulations we show that this effect persists in the presence of molecular diffusion for nanoparticle flows, provided the Peclet number is not too small. We examine the effects of varying particle and obstacle size, the method of forcing, solid roughness, and particle concentration. While we observe trajectory locking in all cases, the degree of locking varies with particle size and these flows may have application as a separation technique

Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions

The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of sheared suspensions can be characterized as a chaotic motion in phase space and determine the dependence of the largest Lyapunov exponent on the volume fraction $\phi$. The loss of memory at the microscopic level of individual particles is also shown in terms of the autocorrelation functions for the two transverse velocity components. Moreover, a negative correlation in the transverse particle velocities is seen to exist at the lower concentrations, an effect which we explain on the basis of the dynamics of two isolated spheres undergoing simple shear. In addition, we calculate the probability distribution function of the velocity fluctuations and observe, with increasing $\phi$, a transition from exponential to Gaussian distributions. The simulations include a non-hydrodynamic repulsive interaction between the spheres which qualitatively models the effects of surface roughness and other irreversible effects, such as residual Brownian displacements, that become particularly important whenever pairs of spheres are nearly touching. We investigate the effects of such a non-hydrodynamic interparticle force on the scaling of the particle tracer diffusion coefficient $D$ for very dilute suspensions, and show that, when this force is very short-ranged, $D$ becomes proportional to $\phi^2$ as $\phi \to 0$. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of $D$ on $\phi$, from $\phi^2$ to $\phi$ as $\phi \to 0$.Comment: Submitted to J. Fluid Mec

Microstructure and velocity fluctuations in sheared suspensions

The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant, non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only for the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity components, and for three different concentrations, showing a transition from a Gaussian to an Exponential and finally to a Stretched Exponential functional form as the volume fraction is decreased. We also show that, although the pair distribution function recovers its fore-aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately described by assuming the complete absence of any permanent doublets of spheres. We finally present a simple correction to the analysis of laser-Doppler velocimetry measurements.Comment: Submitted to Journal of Fluid Mechanic

Extensional rupture of model non-Newtonian fluid filaments

We present molecular dynamics computer simulations of filaments of model non-Newtonian liquid stretched in a uniaxial deformation to the point of breaking. The liquid consists of Lennard-Jones monomers bound into chains of 100 monomers by nonlinear springs, and several different constant velocity and constant strain rate deformations are considered. Generally we observe nonuniform extensions originating in an interplay between the stretching forces and elastic and capillary restoring mechanisms, leading to highly uneven shapes and alternating stretched and unstretched regions of liquid. Except at the fastest pulling speeds, the filaments continue to thin indefinitely and break only when depleted of molecules, rather than common viscoelastic rupture mechanisms.Comment: 7 pages text, 14 pages (eps) figure

Microscopic Motion of Particles Flowing through a Porous Medium

We use Stokesian Dynamics simulations to study the microscopic motion of particles suspended in fluids passing through porous media. We construct model porous media with fixed spherical particles, and allow mobile ones to move through this fixed bed under the action of an ambient velocity field. We first consider the pore scale motion of individual suspended particles at pore junctions. The relative particle flux into different possible directions exiting from a single pore, for two and three dimensional model porous media is found to approximately equal the corresponding fractional channel width or area. Next we consider the waiting time distribution for particles which are delayed in a junction, due to a stagnation point caused by a flow bifurcation. The waiting times are found to be controlled by two-particle interactions, and the distributions take the same form in model porous media as in two-particle systems. A simple theoretical estimate of the waiting time is consistent with the simulations. We also find that perturbing such a slow-moving particle by another nearby one leads to rather complicated behavior. We study the stability of geometrically trapped particles. For simple model traps, we find that particles passing nearby can ``relaunch'' the trapped particle through its hydrodynamic interaction, although the conditions for relaunching depend sensitively on the details of the trap and its surroundings.Comment: 16 pages, 19 figure

Universal and Non-Universal First-Passage Properties of Planar Multipole Flows

The dynamics of passive Brownian tracer particles in steady two-dimensional potential flows between sources and sinks is investigated. The first-passage probability, $p(t)$, exhibits power-law decay with a velocity-dependent exponent in radial flow and an order-dependent exponent in multipolar flows. For the latter, there also occur diffusive ``echo'' shoulders and exponential decays associated with stagnation points in the flow. For spatially extended dipole sinks, the spatial distribution of the collected tracer is independent of the overall magnitude of the flow field.Comment: 7 pages, LaTe

Molecular Dynamics Simulation of Compressible Fluid Flow in Two-Dimensional Channels

We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream reservoir is kept at vacuum. The channel is sufficiently long in the direction of the flow that the finite length has little effect on the properties of the fluid in the central region. The simulated system is represented by an efficient data structure, whose internal elements are created and manipulated dynamically in a layered fashion. Consequently the code is highly efficient and manifests completely linear performance in simulations of large systems. We obtain the steady-state velocity, temperature, and density distributions in the system. The velocity distribution across the channel is very nearly a quadratic function of the distance from the center of the channel and reveals velocity slip at the boundaries; the temperature distribution is only approximately a quartic function of this distance from the center to the channel. The density distribution across the channel is non-uniform. We attribute this non-uniformity to the relatively high Mach number, approximately 0.5, in the fluid flow. An equation for the density distribution based on simple compressibility arguments is proposed; its predictions agree well with the simulation results. Validity of the concept of local dynamic temperature and the variation of the temperature along the channel are discussed.Comment: 16 pages (in latex) + 8 figures (in a single ps file). Submitted to the Physical Review

Hybrid method for simulating front propagation in reaction-diffusion systems

We study the propagation of pulled fronts in the $A \leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we concentrate on the corrections to the deterministic behavior due to the number of particles per site $\Omega$. By means of a new hybrid simulation scheme, we manage to reach large macroscopic values of $\Omega$ which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation.Comment: 5 pages, 4 figure