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Analytical Investigation in Brownian Diffusion of Airborne Particles with Slip/No-slip Interfaces

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Volume: 7 | Issue: 3 | Pages: 353-378
DOI: 10.4209/aaqr.2006.12.0030
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Jimmy Kuo1,2, Shih H. Chen 3

  • 1 Institute of Marine Biotechnology, National Dong Hwa University, Pingtung 944, Taiwan
  • 2 Department of Planning and Research, National Museum of Marine Biology and Aquarium, Pingtung 944, Taiwan
  • 3 Department of Biochemical Engineering, Hwa Hsia Institute of Technology, Chung-ho City, Taipei County 235, Taiwan

Abstract

The Brownian motion for an aerosol dispersion stating that suspending particles are rigid and the surrounding fluid may slip and/or not slip at the solid-fluid interface was investigated analytically. Particles were assumed to be close enough to interact hydrodynamically. Based on Einstein’s prescription of Brownian motion, the Brownian diffusivities in two different types of situation were deduced. The first concerned a homogeneous dilute suspension, and the relative diffusivity of two rigid slip/no-slip spheres with a given separation was derived. The second concerned a suspension in which there was a gradient in concentration of particles. The thermodynamic force on each particle in this case was shown to be equal to the gradient of the physical potential of particles, which brings considerations of the multiparticle-excluded volume into the problem. Determination of the sedimentation velocity of particles falling through fluid under gravity, for which a theoretical result corrected to the first order in volume fraction of the particles, was available. The diffusivity of the particles was found to increase slowly as the concentration rose from zero. These results were generalized to the case of an (dilute) inhomogeneous suspension of several different species of particle with slip/no-slip surfaces, and expressions were obtained for the diagonal and off-diagonal elements of the diffusivity matrix. Our results, presented in simple closed forms, agreed very well with the existing solutions for the limiting cases of no-slip at the particles’ surfaces. Also, the limiting diffusion situations of perfect-slip particles in gas or spherical gas bubbles in liquid were considered in this article.

Keywords

Diffusion Particle interactions, Concentration gradient Polydisperse


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