Boundary Condition for Particle Diffusion

Thus the energy of attraction becomes infinite as the particle approaches a flat surface. For this reason, it is usually assumed that a surface acts as a p erfect sink in the theory of aerosol diffusion that is, when a particle penetrates to a distance one radiu.s from the surface, the particles adhere. This holds best for submicron particles moving at thermal velocities. Rebound occurs for larger particles moving at high velocities (Chapter 4). This analysis does not lake into account the effects of surface roughness of the scale of the particle size or of layers or patches of adsorbed gases or liquids. Such factors may be important in practical applications. 

We consider particle transport from a gas to a body with a flat bounding surface by Brownian diffusion under the influence of van der Waals forces exerted by the body. The relative contributions of the two mechanisms can be estimated as follows The total flux normal to the surface is given by the x component of the flux 

The solution for the concentration distribution assuming Jx is constant near the surface is (Spielman and Friedlander, 1974) 

Values of A often range between 10 and 10 ergs. For T = 25 C and taking the smaller 

Because the dispersion forces are attractive, they tend to increase the rate of particle transport to the surface. When the diffusion path is long compared with the range of operation of the dispersion forces, the attractive effects on diffusion can be neglected (Fig. 2,11). The sink boundary condition is retained, however, and the particle flux can be calculated by solving the diffusion equation in the absence of an external force field with the condition = 0 at a distance dp/2 from the surface. The particle flux is 

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The boundary condition for particle diffusion differs from the condition for molecular dilTusion becau.se of the finite diameter of the particle. For certain classes of problems, such as flows around cylinders and spheres, the particle concentration is assumed to vanish at one particle radiu.s from the surface ... 

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