Example passive permeation across a membrane

If a biological membrane is treated as a homogeneous isotropic medium, then transport of a solute in the membrane is governed by the diffusion equation 

If the membrane has width d and the concentrations on either side of the membrane are given by c(0) = Co, c(d) = a, then the concentration profile in the membrane is given by 

Therefore the steady state flux through the membrane is linearly proportional to the concentration difference across the membrane. Defining the membrane permeability p = Dm/d, we have T = pAc. 

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