I'm just now learning the diffusion model and it seems that we aren't taking into account the acceleration due to gravity of the particles. Is this a shortcoming of the model or irrelevant? I don't have much experience with physics but this seems like an important factor.
Effects of gravity on diffusion
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0This question might be better suited for http://physics.stackexchange.com/. – 2012-09-14
1 Answers
Most models of physical processes, expressed as PDEs in most textbooks, are very model and do not take into account some external forces. These are 'model' equations, for example, the heat equation or a wave equation. In most cases, one can think that the right part $F$ of the equation, for example, $ {\partial \phi \over \partial t} - D \nabla^2 \phi = F $ contains all the external forces (including gravity, air resistance, etc.)
I most 1D or 2D cases, we just ignore the 'vertical' forces, such as gravity. For a 3D diffusion equations, considering external forces like gravity, consult the fluid dyncamics stacialists, but keep in mind these equation will be much more complex and very nonlinear (and hard to investigate!)
P.S. Remember the derivation of a wave equation from most PDE textbooks, You'll notice we always skip lots of forces there.
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0Add: You could also take a look at a *convection-diffusion equation*, which is a more generic model for heat&mass transfer. – 2012-09-30