Diffusion through membrane, which boundary condition to implement?

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SUMMARY

The discussion centers on implementing boundary conditions for modeling diffusion through a membrane using explicit finite difference methods. The user applies a Dirichlet boundary condition for the initial concentration on one side of the membrane and seeks guidance on the appropriate boundary condition for the other side, which has zero concentration. The consensus indicates that a Neumann zero-flux boundary condition may be suitable if no flow is expected through the boundary; otherwise, a different approach is necessary to allow for analyte movement.

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  • Basic principles of diffusion and concentration gradients
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Hi, I am solving the diffusion equation using explicit finite difference to model the diffusion of an analyte through a membrane. I am interested in the concentration of the analyte on the other side vs time elapsed. On one side of the membrane is an initial concentration, which I am implementing as a Dirichlet boundary condition, and the other is zero concentration of the analyte, in a blank solution. The initial condition of this other side would be 0, however I am unsure what the boundary condition would be. My first assumption would be a Neumann zero-flux boundary condition, however I don't know if this is correct. Any help on this would be great, thanks.
 
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I'm not a chemical engineer, so I don't really know the physics of your problem, but if you want your solution to actually flow through that boundary, then you can't have a Neumann condition. If it is indeed supposed not to flow through it, then I would say that you are correct :smile:
 

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