Development of FBMINC model for particle diffusion in fluids

Abstract

Abstract An accurate particle tracking method using FBMINC (new fractional Brownian motion) is outlined. It generates non-Fickian diffusion rather than Fickian diffusion as traditional particle tracking model does. The FBMINC model is based on fractional Brownian motion (fBm) which is generalization of regular Brownian motion. The two models of fBms (FBM model and FBMINC model) were explored and the differences of the two models are compared from the three aspects: the standard deviation of each step, the small memory and the effect of the number of particles in the cloud. The results show the FBMINC model is a better model as it produces more accurate statistics. The effect of simple shear dispersion for both Brownian and fBm was investigated. The power law scaling of fBm shear dispersion was correctly identified. In addition, a scaling coefficient was found numerically. The FBMINC model is then used for producing both superdiffusive and subdiffusive particle paths, therefore, the non-Fickian diffusion of soil particle clouds can be modelled. The particle clouds represent soil contaminant are released in an idealised coastal bay and the fBm particle tracking method is used for simulation the particle cloud spreading in the bay. There is a noticeable increase in the spreading rate of the cloud. In addition, owning to the spreading rate of the cloud, a noticeable part of it has escaped the bay area and transported downstream. The variation of the Hurst exponent can lead to an area of the flow being affected by a contaminant cloud which is not picked up by the regular Brownian motion models. The purpose of this paper is to bring soil transport engineers a new angle on soil particle transport research in fluids. Using FBMINC particle tracking model allows more flexibility in simulation of diffusion in soil contaminant spread in coastal bay or ocean surface.