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Boundary Conditions in Diffusional Growth and Sedimentation

In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or sediments, particles in the suspension outside the surface or aggregate boundary can be considered as diffusing under the influence of applied forces, such as the double-layer interactions or gravity. However, the diffusion equation cannot be used at the substrate or inside the aggregate. One convenient and widely used approach has been to impose boundary conditions at the surface, to supplement and completely define the diffusion problem outside it. This short survey describes some theoretical results on the use of such boundary conditions and their physical interpretation.