A generalized mass transfer law unifying various particle transport mechanisms in dilute dispersions

A generalized mass transfer law for dilute dispersion of particles (or droplets) of any sizes suspended in a fluid has been described, which can be applied to turbulent or laminar flow. The generalized law reduces to the Fick’s law of diffusion in the limit of very small particles. Thus the study shows how the well-known and much-used Fick’s law of diffusion fits into the broader context of particle transport. The general expression for particle flux comprises a diffusive flux due to Brownian motion and turbulent fluctuation, a diffusive flux due to temperature gradient (thermophoresis plus stressphoresis) and a convective flux that arises primarily due to the interaction of particle inertia and the inhomogeneity of the fluid turbulence field (turbophoresis). Shear-induced lift force, electrical force, gravity, etc. also contribute to the convective flux. The present study includes the effects of surface roughness, and the calculations show that the presence of small surface roughness even in the hydraulically smooth regime significantly enhances deposition especially of small particles. Thermophoresis can have equally strong effects, even with a modest temperature difference between the wall and the bulk fluid. For particles of the intermediate size range, turbophoresis, thermophoresis and roughness are all important contributors to the overall deposition rate. The paper includes a parametric study of the effects of electrostatic forces due to mirror charging. The present work provides a unified framework to determine the combined effect of various particle transport mechanisms on mass transfer rate and the inclusion of other mechanisms not considered in this paper is possible.