Deposition Of Brownian Particles Research Articles

Effect of particle size on collision efficiency in the deposition of Brownian particles with electrostatic energy barriers

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTEffect of particle size on collision efficiency in the deposition of Brownian particles with electrostatic energy barriersMenachem Elimelech and Charles R. O'MeliaCite this: Langmuir 1990, 6, 6, 1153–1163Publication Date (Print):June 1, 1990Publication History Published online1 May 2002Published inissue 1 June 1990https://doi.org/10.1021/la00096a023RIGHTS & PERMISSIONSArticle Views1866Altmetric-Citations321LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts Get e-Alerts

Mixing and deposition of Brownian particles in model alveolus.

Inhaled submicron particles readily penetrate into alveolar regions of the human lung, where the behavior of these particles is largely influenced by mixing between inhaled air and residual air. In the present work, an experimental technique to study mixing and deposition of Brownian particles in an expanding/contracting balloon as a model alveolus was developed by employing a “wash-out” experimental technique. Further, applying a simple number balance equation of particles, the mixing volume and deposition coefficient during a breath were obtained. It was found that (i) there exists a critical value in the duration of balloon expansion/contraction over which Brownian diffusion of aerosol enhances mixing between aerosol and clean air, and the critical duration of balloon expansion/contraction is longer for a larger expansion/contraction volume of the balloon; and (ii) at the same expansion/contraction volume of the balloon, the deposition coefficient per breath is larger for a larger expansion/contraction volume.

Enhanced deposition of particles under attractive double-layer forces

The kinetics of Brownian particle deposition from flowing suspensions in the vicinity of a stagnation point (rotating disk, spherical, cylindrical, and impinging jet collectors) was studied theoretically and experimentally. On the basis of the numerical solutions of governing transport equations a considerable enhancement of particle deposition was predicted for particle and collectors bearing opposite surface charge (zeta potentials). The initial deposition rate of particles can be increased by many times when decreasing the ionic strength of the suspension to the value 10 −5–10 −6 M. This effect, which we shall refer to as the reverse salt effect, is completely opposite to what one commonly observed for equally charged particle and collector surfaces (as well as in coagulation kinetic studies). These theoretical predictions were confirmed quantitatively by the direct microscope observation method using mica collector (modified by chemisorption of silano compounds) and a monodisperse suspension of submicrometer latex particles (negatively charged). The experiments also furnished a direct evidence of the coupling between macroscopic hydrodynamic flow and the microscopic colloid forces and proved that the asymmetric double-layer dynamics cannot be properly described by the constant surface charge boundary conditions.

Adsorption of interacting Brownian particles onto surfaces: I. General formulation of the macroscopic diffusion equation and results for nonhydrodynamic force interactions

Previous studies on the adsorption or deposition of Brownian particles onto surfaces have been carried out in the limit of infinite particle dilution. In the present study we have examined the effects of finite particle concentrations on the transport and adsorption of Brownian particles onto surfaces. A macroscopic diffusion equation for the collection of particles in a nonuniform host fluid is derived beginning with the n-particle Fokker-Planck equation. Both hydrodynamic interparticle interactions and hydrodynamic interactions of the particles with the adsorbing surface are included in the theoretical formulation. In agreement with previous methods, the resulting convective-diffusion equation is similar in form to the single-particle equation (Smoluchowski equation) with the Einstein diffusion coefficient replaced by the mutual diffusion tensor for the interacting Brownian particles. Solutions to the convective-diffusion equation were carried out for the problem of Brownian particle adsorption onto a large sphere under the conditions of low Reynolds number fluid motion and large particle Peclet numbers. In this first study, we have neglected the effects of hydrodynamic interactions on the solution behavior, and have thus focused our attention on the effects of attractive- and repulsive-type colloidal force interactions on the transport and deposition of Brownian particles onto a spherical collector. Our semianalytic solutions to the convective-diffusion equation show a general behavior of interparticle interactions: attractive-type interactions lead to a decrease in the total particle number flux to the sphere surface as compared to the noninteracting case, whereas repulsive-type interactions result in a relative increase in the flux. This behavior is explained by examining the “force environment” of a particle near the collecting sphere surface. The effects of colloidal interaction forces were further quantified by considering two specific interaction potentials: hard-sphere and electric double-layer interactions. Typical parameters of this latter potential show a most dramatic change in the total particle number flux, resulting in some cases in as much as a 100% increase over the noninteracting case at a particle volume fraction of 10 −2. Finally, we have also summarized our assumptions which have led to the results reported here, including the neglect of hydrodynamic interactions to be investigated in the second part of this study.

Deposition of Brownian particles in packed beds

An analysis is presented to describe the deposition of Brownian particles from suspensions flowing through granular media. The constricted tube porous media model recently proposed by Payatakes et al.[8] was used to characterize the media and the deposition process was assumed to be controlled by convective diffusion as well as the nature of the surface interaction between the media grains and the Brownian particles. Three different tube configurations were considered and the differences among the results were found to be relatively unimportant. Agreement between the analysis and available experimental data was found to be reasonably good for the limiting case when the surface effect is favorable.

Collection of submicron particles in electro-flotation

A theoretical analysis is presented to describe the deposition of Brownian particles onto hydrogen bubbles under surface interactions. Single collection efficiency has been numerically calculated for zeta potentials, having assumed that the effective Hamaker constant is equal to 3.0 × 10 −14erg though our choice of Hamaker constant is rather arbitrary. From a mass balance, total collection efficiency or the rate of flotation has been determined. In this way, electro-flotation process is quantitatively described. Experimentally, the electro-flotation of polystyrene latices of mean diameter 0.6 μm has been studied to examine the effect of the charge on both particles and bubbles on the total collection efficiency. The bubbles were of mean diameter 20 μm. The electrolyte was AlCl 3. To measure the charge on the bubbles, we directly sampled solution including very small bubbles with a glass tube from a flotation vessel and poured into a micro-electrophoresis cell. The horizontal velocity measured when the bubbles rose up a “stationary level” in the cell under the known potential gradient gave the electromobility. The charge on the latex particles were found to change its sign from negative to positive as flotation time went on. The theoretical total collection efficiency has been in close agreement with the experimentally determined one.

Collection of submicron particles by H 2 bubbles

A theoretical analysis is presented to describe the deposition of Brownian particles onto H 2 bubbles (flotation) by analogy with classical filtration theory. Experimentally, it is shown that submicron and smaller particles of MnO 2 are collected by H 2 bubbles without using the special collector or chemicals usually employed in flotation. The experimental technique for determining the total collection efficiency is described. A comparison between the theory and our experiment makes it clear that there are cases in which the simpler filtration theory is adaptable to a complicated flotation analysis. In addition, we find that the collection mechanisms of submicron particles of MnO 2 is predominantly characterized by interception and Brownian diffusion.

Rates of deposition of brownian particles calculated by lumping interaction forces into a boundary condition

Double-layer repulsion, van der Waals attractions, and hydrodynamic resistance can be lumped into a boundary condition on the convective-diffusion equation only if (1) they act over sufficiently short distances, and (2) double-layer repulsion is sufficiently strong. Otherwise, the complete transport equations must be solved.

Effect of London forces upon the rate of deposition of Brownian particles

AbstractRates of deposition of particles onto a spherical collector, immersed in a creeping fluid, are calculated as a function of Peclet number, aspect ratio, and the ratio of Hamaker's constant to kT for all cases of practical importance involving convective‐diffusion and London forces. Boundaries of regions where London forces or Brownian motion may be neglected are established in terms of the above dimensionless groups. Gravitational forces were included in the calculations for some representative conditions but may be neglected for small or neutrally buoyant particles or for high flow rates.Close agreement was noted between deposition rates calculated by summing individual contributions from each transport mechanism and deposition rates calculated from a rigorous consideration of their combined effect. Thus the additivity rule was verified for the cases studied.

Role of the electrical double layer in particle deposition by convective diffusion

A theoretical analysis is presented to describe the deposition of Brownian particles which interact with collectors through an attractive-repulsive potential. When the interactions are confined sufficiently near the collector surface, it is shown that the process is equivalent to ordinary convective diffusion in the bulk with a first-order surface reaction at the collector; a formula for the surface reaction coefficient is derived in terms of the net interaction potential. Large Peclet solutions appropriate to hydrocolloid collection by spheres and cylinders with first-order surface reaction are obtained and available solutions are discussed. The ratio of overall deposition to deposition under diffusion control proves to be a function of a single dimensionless parameter. At extreme values of this parameter collection becomes surface reaction controlled or diffusion controlled.

Rate of deposition of Brownian particles under the action of London and double-layer forces

The rate of collection of Brownian particles under the influence of interaction forces between the collector surface and the particles is calculated by (a) incorporating the interaction forces in the rate constant of a virtual, first order, chemical reaction taking place on the surface of the collector, and by (b) solving the convective diffusion equation subject to that chemical reaction as a boundary condition. Several geometries (sphere, cylinder, rotating disc) are considered for the collector.An Arrhenius type equation is obtained for the apparent reaction rate constant. Equations for the apparent activation energy and for the frequency factor are established as functions of Hamaker's constant, ionic strength, surface potentials and particle radius.