Porous particulate film deposition in the transition regime

We examine the formation of particulate films via Langevin dynamic simulations of monodisperse particle deposition onto flat substrates. In simulations, we consider particle inertia, thermal motion, and a constant advective force directing particles towards the substrate. These conditions effectively mimic the formation of dust cakes during filtration, as well as the production of nanostructured films at the outlet of gas phase synthesis reactors. Parameterization of the equations of motion shows that the movement of each particle depends only upon Kn_D (the diffusive Knudsen number, proportional to the particle[U+05F3]s mean persistence distance to its radius) and χ_F (the ratio of the particle[U+05F3]s translational energy at the advective velocity to the thermal energy). Use of these ratios is advantageous because one dimensionless number (Kn_D) is independent of the advective velocity, while the second (χ_F) is independent of background gas pressure. This is in contrast with the traditionally employed Peclet and Stokes numbers, both of which are dependent upon the advective velocity and gas pressure. The film structures resulting from simulations are quantified in terms of their porosities, and results are reported for simulations over a wide range of Kn_D (10^-3-10¹) and χ_F (10^-4-10³), deposition areas 1000×1000 particle radii in size, and with more than 10⁶ deposited particles. For each simulated deposit, three distinct regions are observed: (I) a region close to the substrate (within 50 primary particle radii), wherein the porosity begins at a minimum and increases to constant value; (II) a region where this constant porosity is maintained (which is dependent on Kn_D and χ_F), constantly increasing in height and encompassing the majority of the film after sufficient deposition; and (III) the outer region, in which the film is still growing, and the porosity increases from the region II value to unity, spanning less than 100 particle radii in height in most circumstances. A regression equation is provided to describe the film porosity as a function of Kn_D and χ_F in region II, facilitating a priori predictions of film porosities from deposition parameters.