The motion of Brownian particles suspended in a non-uniform fluid flow

Abstract

The effect of the type of fluid flow velocity profile on the motion of a Brownian particle in a circular tube has been studied using a Monte Carlo technique to simulate particle trajectories. Three types of fluid flow were studied: uniform (UF), parabolic (PF), and an initial uniform flow which evolves and may eventually attain the parabolic velocity profile, i.e. transient flow (TF). For UF and PF, radial and axial particle diffusion were simultaneously considered in some cases; for TF, where fluid dynamics equations had to be solved in addition to the Monte Carlo simulations, axial diffusion was neglected for fluid and particles, so that calculations had to be restricted to tube aspect ratios (radius/length) smaller than 0.1, a common scenario in most practical aerosol applications. A first series of simulations were performed to determine the overall particle penetration through the tube. For fixed tube geometry and particle diffusion coefficient, penetration in TF lied between those in PF (highest) and UF (lowest), in such a manner that, for a given value of the diffusion coefficient, the larger the degree of flow development (i.e., the smaller the values of the tube aspect ratio and the Reynolds number), the larger the penetration. These findings are coherent with those found in a former investigation dealing with the particle residence time in the tube. In a second series of simulation runs, calculations were done for selected initial locations of the particle within the tube entrance cross section, to examine the effect that the proximity of the particle starting position to the tube wall or to the tube axis has on variables such as penetration, mean first hitting time and length, mean first exit time, and mean axial velocity of lost and survived particles. When the fluid flow is not uniform but varies from place to place, the mean particle axial velocity is larger than that of the fluid. This counterintuitive fundamental result allows interpretation of the trends observed in penetration and residence time.