Diffusion through membrane, which boundary condition to implement?

In summary, the individual is using explicit finite difference to simulate the diffusion of an analyte through a membrane and is specifically interested in the analyte's concentration over time on the opposite side of the membrane. One side of the membrane has an initial concentration, represented as a Dirichlet boundary condition, while the other side has zero concentration in a blank solution. The individual is unsure of what the boundary condition for this side should be, but their initial assumption is a Neumann zero-flux boundary condition. However, the other person clarifies that if the solution is meant to flow through the boundary, a Neumann condition cannot be used. Otherwise, the individual's assumption is correct.
  • #1
baseball1234
3
0
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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  • #2
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:
 

FAQ: Diffusion through membrane, which boundary condition to implement?

What is diffusion through a membrane?

Diffusion through a membrane is the process by which particles or molecules move from an area of higher concentration to an area of lower concentration across a semi-permeable membrane. This movement occurs due to the random motion of particles and does not require the input of energy.

Why is diffusion through a membrane important?

Diffusion through a membrane is important because it is a vital process for the survival of cells. It allows for the exchange of essential molecules such as oxygen and nutrients, as well as the removal of waste products, across the cell membrane.

What is a boundary condition in diffusion?

A boundary condition in diffusion is a set of rules or conditions that are applied at the boundary or interface between two different environments. In the context of diffusion through a membrane, boundary conditions determine the movement of particles across the membrane and can affect the rate of diffusion.

How do I determine which boundary condition to implement for diffusion through a membrane?

The boundary condition to implement for diffusion through a membrane depends on the characteristics of the membrane and the particles involved. The two most commonly used boundary conditions are the no-flux boundary condition, where there is no net movement of particles across the membrane, and the flux boundary condition, where there is a constant flow of particles across the membrane.

Can different types of molecules diffuse through a membrane at the same rate?

No, different types of molecules cannot diffuse through a membrane at the same rate because diffusion is dependent on the size, charge, and solubility of the molecules. Smaller, non-polar molecules will diffuse more easily through a membrane compared to larger, polar molecules.

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