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In a previous paper (1) the effects of particle inertia on the diffusional deposition of Brownian particles onto a surface in viscous, axisymmetric stagnation-point flow were investigated using the method of Brownian dynamics. Following Fernandez de la Mora and Rosner (2), under the conditions of large Schmidt numbers and small Stokes numbers (less than the critical Stokes number), an approximate analytical solution is obtained here that also includes an arbitrary external force acting on the particles. This solution is shown to be in excellent agreement with the results from Brownian dynamics simulations. An important characteristic of these solutions is inertial particle concentration “enrichment” outside the diffusion boundary layer near the adsorbing surface at subcritical Stokes numbers. In general, it is shown that attractive external particle forces only slightly reduce the amount of this enrichment. On the other hand, in the absence of inertia, attractive external particle forces increase the surface flux of particles beyond that for solely diffusional deposition. The combination of inertial particle concentration enrichment and an attractive external particle force leads to a synergistic-type increase in the surface flux of particles beyond that for solely diffusional deposition. Finally, Robinson's theorem (6) is extended to formally prove these results for inviscid-type flows.

By raising the temperature of a surface above that of the ambient fluid, a temperature gradient that results in a thermophoretic force that repels particles from the surface is created. It has been recommended that this effect be used to reduce the contamination of product surfaces during manufacturing. It has been shown that even modest levels of electrostatic interactions between particles and surfaces can overwhelm the thermophoretic repulsion available by raising the temperature of the surface 10% above that of the ambient fluid. We present an analysis for axisymmetric, viscous stagnation-point flow, extending the work of Friedlander et al. (1988, J. Colloid Interface Sci.125, 351), and show the temperature differences that must be achieved to succeed in preventing particle deposition due to diffusion, gravitation, and electrostatic attraction. Simple algebraic relationships are established that allow for a ready determination of the temperature differences needed to suppress particle diffusional deposition onto surfaces under the action of uniform external forces, such as gravitational and coulombic forces, and a spatially dependent external force, which for this study we have chosen to be the electrostatic image force. These relationships are further verified through approximate analytical and “exact” numerical solutions also given here. Various results of practical interest are discussed. For example, for a flow intensity of 6.67 s−1 in air, an electric field as small as 100 V/cm makes it unlikely that particles with a minimal charge distribution (Boltzmann) will be kept from deposition on a surface by raising the surface temperature 10 or 20% above the ambient temperature. This emphasizes the importance of reducing the electric charge levels of product surfaces during manufacturing.

In this study, an idealized pore model is used to examine the salient features of Brownian particle adsorption onto the inner pore walls in unsteady-state flow. An important example is the expansion/contraction of the alveolar region of the lung that gives rise to the unsteady-state gas flow and can have a significant effect on the transport and adsorption of submicron particles. An idealized pore model with an oscillating outer wall is developed to systematically study fluid and Brownian particle motion as well as adsorption. The unsteady-state gas flow is derived in a general way using a Fourier series representation of the oscillating outer wall in order to simulate various patient specific breathing patterns. The Smoluchowski–Chandrasekhar equation is used to describe the convective-diffusion of a solution of non-interacting Brownian particles. A perturbation method is adopted to obtain analytical solutions for the Brownian particle concentration and flux behavior. The leading order solution describes pure unsteady-state diffusion, while the first-order solution takes into account the effects of fluid convection. As expected, the adsorption of Brownian particles is enhanced during inhalation cycles and is reduced during exhalation cycles. An interesting feature of the first-order solution is the appearance of local particle concentration maximum (“hot spots”) between the wall and centerline of the pore due to large zero-order concentration gradients in those regions. These solutions can be used to maximize or minimize deposition by controlling the various parameters such as breathing pattern, flow rate, and particle concentration. We also summarize the general domains of the problem of Brownian particle motion for unsteady-state flows in pores.

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.

The inclusion of Brownian motion in aerosol deposition studies has often been treated separately from deposition due to other causes (e.g., inertial and electrical forces). A unified approach based on the full solution to the so-called ordinary Langevin equation of motion is presented to study particle deposition on a single spherical collector. The “Brownian dynamics” method given here is useful when the inertial, external, and particle-particle interaction forces are comparable to the diffusive, or Brownian, force. Several example calculations are considered for both the clean, or steady-state, deposition efficiencies, as well as for the unsteady-state efficiencies (particle-particle deposition problem). In particular, for the steady-state behavior, the classic Levich-Lighthill solution to the problem of convective-diffusion to a freely falling sphere has been reproduced. Additionally, an approximate analytical solution for the combined case of inertial and diffusional deposition, recently given by J. Fernandez de la Mora and D. E. Rosner [J. Fluid Mech. 125, 379 (1982)], has been verified and the so-called principle of superposition for the combined case of inertial and electrostatic deposition has been criticized. For the unsteady-state problem, the charge neutralization of an initially uniform charged collecting sphere by the deposition of oppositely charged Brownian particles has been examined. This latter study represents a generalization of the previously proposed “aerosol dynamics” method (M. H. Peters, R. K. Jalan, and D. Gupta, Chem. Eng. Sci., in press) which now includes the Brownian motion of the aerosol particles.