Irreversible Adsorption of particles after diffusing in a gravitational field

In this paper we analyze the influence of transport mechanisms (diffusion and sedimentation) on the structure of monolayers of particles irreversibly adsorbed on a line. We focus our attention on the dependence of the radial distribution function $g(r)$ and the saturation coverage $\theta_\infty$ on the gravitational P\'eclet number $N_g$. First, we study the probability density of adsorption onto an available interval using approximate solutions of the transport equation and computer simulations. Combining our results with an approximate general formalism, we can obtain values of $\theta_\infty$ and the gap density, which agree with our simulations. We also show that, for large gravity, the coverage $\theta_{\infty}$ approaches the ballistic limit following a power law in $N_g$ that is independent of the number of dimensions, as has been observed in simulations.