An axisymmetric model for diffusion of nano-particles

Abstract

An axisymmetric model was presented which was capable of predicting the diffusion of nano-particles with accuracy comparable to that of a 3-D model. Both analytical and numerical approaches were presented. An Eulerian approach was first presented where the concentration distribution equation was solved analytically. It was shown that the mean-square radial displacements of the nano- and micro-particles are equal to 4Dt, which is twice that of one-dimensional Cartesian directions. The Langvein equation for Brownian motion of particles in radial direction was then analyzed. An axisymmetric coordinate was used and the appropriate spectral intensity for Brownian motion of the particles in radial direction was presented. Three dimensional and axisymmetric computational models for the Brownian motion of nano-particles were also described. Lagrangian particle trajectory analysis was performed assuming a one-way coupling model. The particle equation of motion used included the drag and Brownian forces. Trajectories of different size nano-particles in a uniform flow were analyzed, and the particles radial dispersions were studied. The predictions of the 3-D model for variance of the particle radial displacement were shown to be in agreement with the results of analytical solution. The results of the axisymmetric computational model was also found to be in agreement with the exact solution of diffusion equation and 3-D Lagrangian simulation results provided that the appropriate spectral intensity for the radial direction be used.