Density scaling laws for the structure of granular deposits

Abstract

The structure of granular deposits growing by arriving particles is analyzed using three-dimensional on-lattice Monte Carlo modeling of convective-diffusive particle deposition. The deposit density profile $\rho \left(h\right)$ depends on the particle dynamics and becomes formed by three different regions: a denser near-wall region at the deposit bottom in contact with the original plain surface, a middle uniform region with constant mean density, and an open and lighter active-growth region at the deposit outer surface. Fitting expressions for $\rho \left(h\right)$ valid in each region are proposed, based on the known features of deposits formed in the two limiting cases: ballistic deposition and diffusion-limited deposition. Also, a composite expression for $\rho \left(h\right)$ fitting the density profile throughout the deposit is given. All these expressions are written in terms of a length scale $l\left(\mathrm{Pe}\right)$ dependent on the particle Péclet number, which provides the relative importance of the convective motion to the diffusive transport for the particle.