Effect of hydrodynamic interactions on the distribution of adhering Brownian particles

Abstract

Brownian dynamics simulations were used to study the adhesion of hard spheres on a solid surface by taking the hydrodynamic interactions into account. Special attention was paid to analyze the configuration of the assembly of adsorbed particles. These results were compared to configurations generated by the extensively studied random sequential adsorption (RSA) model. In our case the adsorption probability for a particle is almost uniform over the entire available surface. This surprising result shows that RSA provides a good approximation to generate adsorbed particle configurations. (DRSA) [2], where the adsorbing particle is allowed to diffuse in three-dimensional space subject to hard sphere interactions with previously adsorbed ones. The DRSA leads to an increased adsorption probability for an incoming sphere in the close vicinity of an already attached one as compared to RSA. The DRSA distribution of adsorbed particles is thus different at a given coverage from its RSA counterpart except near saturation (jamming limit) [3]. However, since the diffusion coeKcient is taken constant, the DRSA seems to model a particle as moving in "dry water" [4]. This Letter is devoted to take hydrodynamic interactions into account and should thus represent a significant jump toward reality.The effect of the hydrodynamic interaction is to increase the frictional force experienced by a particle when it approaches another one or a fiat surface [5]. This kind of interaction between a sphere and a clean wall is well known, and its effect on the rate of adsorption has already been studied [6]. The main goal of this Letter is to investigate the inHuence of the hydrodynamic interactions between an adsorbing particle and (i) the already adsorbed ones, and (ii) the planar adsorbing surface, on the distribution of the particles on this surface. It will in particular be compared to RSA distributions in order to investigate the degree of accuracy of this simple and now well-known algorithm.The Brownian motion of a spherical particle is completely described by the friction tensor, which is in general position dependent and nonisotropic.In particular, the normal component of the friction tensor diverges when the separation between the particle and any solid surface vanishes due to lubrication forces. As a consequence, contact of the particles with the adsorbing surface is impossible in the absence of a strong attractive force, like the van der Waals attraction. The latter becomes strong enough at small separations to overcome the lubrication effects. In general van der Waals, hard core, and electrostatic forces also act between the particles. However, in this study we will solely consider, besides the hydrodynamic interactions, the different hard core repulsions, and the van

Influence of hydrodynamic interactions on the adsorption process of large particles

“…[11] [10], considerably simplifies our treatment, and it is sufficient to make evident the effects of HI in the adsorption process.…”

“…Note that in eq. (1) we have not considered van der Waals forces with the plane since, contrary to what happens for Brownian particles [10], they are not relevant in the dynamics of large particles due to its short range nature. The expression of the mobility matrix takes into account the existence of HI.…”

Influence of hydrodynamic interactions on the ballistic deposition of colloidal particles on solid surfaces

“…It is worthnoting that at small particle-plane distances, ξ || diverges much more slowly than ξ ⊥ . Since the diffusion coefficient behaves as the inverse of the friction tensor, this fact is responsible for the "randomization" of the final position of an adhering sphere whose motion is controlled by Brownian motion, as commented in the introduction [13]. Regarding the expression for ξ ss ( r i ), we will use the friction coefficient of two spheres in an unbounded fluid as worked out at all distances by Jeffrey and Onishi [20].…”

“…The situation would be completely different for trajectories controlled by Brownian motion. The sphere would then have a large tendency to diffuse parallel to the line, leading to a randomization in its final position on the substrate [13].…”

“…Thus, in this case, n must exceed 1: one deposited particle cannot hinder another particle to adhere on the surface. On the other hand, the presence of HI favors the diffusion of the particle parallel to the plane, implying that the incoming particle can explore much larger distances along the surface than perpendicularly to it before adhering [13]. As a consequence, in first approximation, the incoming particle can be assumed to adsorb randomly on the surface.…”