# Time dependent PDEs - mathematical modelling - diffusion equation

## Homework Statement

Porous membranes are used to separate mixtures in industry, because smaller
compounds permeate through them more easily than larger ones. KnoGas Pty
Ltd are trialling an experimental separation process, using a membrane to sep-
arate compounds A and B: compound A permeates the membrane, while com-
pound B cannot. The ratio of A to B in the original mixture is held constant,
and any compound A that has di used through the membrane is instantly re-
moved for storage when it emerges at the other side.
It is discovered, however, that compound A interacts with the membrane:
during this interaction, some (but not necessarily all) of compound A turns
into a useless by-product. This reaction doesn't a ect the rate of di usion of
compound A, but the permeation process is no longer described by di usion
alone. Importantly for KnoGas, the production rate of compound A { the rate
at which it leaves the membrane { is changed as a result of this reaction.
You have been asked by KnoGas to develop and solve a model for this
process, in order to advise them on
1. how the production rate of compound A changes with time; and
2. how the interaction rate between compound A and the membrane aff ects
this change in the production rate over time.

## Homework Equations

Diffusion equation: dc/dt=D(d^2c/dx^2) these should be partial derivatives

## The Attempt at a Solution

dA/dt = D(d^2A/dx^2) + R(A)

R(A) is the interaction term.

Don't know if i'm going about this the wrong way?
kind of confused by the wording. Please help!