Transport of Brownian particles confined to a weakly corrugated channel

We investigate the average velocity of Brownian particles driven by a constant external force when constrained to move in two-dimensional, weakly-corrugated channels. We consider both the geometric confinement of the particles between solid walls as well as the soft confinement induced by a periodic potential. Using perturbation methods we show that the leading order correction to the marginal probability distribution of particles in the case of soft confinement is equal to that obtained in the case of geometric confinement, provided that the (configuration) integral over the cross-section of the confining potential is equal to the width of the solid channel. We then calculate the probability distribution and average velocity in the case of a sinusoidal variation in the width of the channels. The reduction on the average velocity is larger in the case of soft channels at small P\'eclet numbers and for relatively narrow channels and the opposite is true at large P\'eclet numbers and for wide channels. In the limit of large P\'eclet numbers the convergence to bulk velocity is faster in the case of soft channels. The leading order correction to the average velocity and marginal probability distribution agree well with Brownian Dynamics simulations for the two types of confinement and over a wide range of P\'eclet numbers

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

Hysteresis, force oscillations and non-equilibrium effects in the adhesion of spherical nanoparticles to atomically smooth surfaces

Molecular dynamics simulations are used to examine hysteretic effects and distinctions between equilibrium and non-equilibrium aspects of particle adsorption on the walls of nano-sized fluidfilled channels. The force on the particle and the system's Helmholtz free energy are found to depend on the particle's history as well as on its radial position and the wetting properties of the fluid, even when the particle's motion occurs on time scales much longer than the spontaneous adsorption time. The hysteresis is associated with changes in the fluid density in the gap between the particle and the wall, and these structural rearrangements persist over surprisingly long times. The force and free energy exhibit large oscillations with distance when the lattice of the structured nanoparticle is held in register with that of the tube wall, but not if the particle is allowed to rotate freely. Adsorbed particles are trapped in free energy minima in equilibrium, but if the particle is forced along the channel the resulting stick-slip motion alters the fluid structure and allows the particle to desorb