Determination of dynamic dispersion coefficient for particles flowing in a parallel-plate fracture

Abstract

A robust and pragmatic technique has been developed to determine dynamic dispersion coefficients for particles flowing in a parallel-plate fracture. By using local moment analyses, theoretical equations have been formulated to describe flow behaviour of solid particles flowing in a parallel-plate fracture on the basis of the Poiseuille flow under different source conditions. By using the random walk particle tracking (RWPT) algorithm, newly developed models have been verified to determine solute and particle dispersion coefficients agreeing with those obtained from RWPT simulations. At early times, particle dispersion coefficient is not only controlled by the source condition, but also negatively correlated with the center-of-mass velocity. Compared to a point source, at early times, dispersion coefficients of particles originating from a line source are larger; however, after a critical time, all dispersion coefficients approach the values obtained through the extended Taylor theory. Subsequently, the newly developed models have been extended to match experimental measurements, while particle dispersion coefficients are notably less than those calculated by the extended Taylor theory.