I am a biochemist by profession and not very experienced in working with programming codes.

I am currently trying to develop a model to describe the mass transport and antigen binding of a biosensor. This involves a flow channel over a biologically activated surface. The aim is to simulate how long it takes for the analyte molecules diffusing freely in the system to bind completely to the biologically activated surface.

I have already set up the corresponding partial differential equation and defined the necessary boundary conditions. However, I need help with the implementation of the FEM.

Would anyone be willing to help me?

Yes if is no to difficult,

Post your data and equation.

Hello Frederic, thanks for replying

This is the general set-up:

I got it from a paper but I need to change the parameters and one boundary condition for my application.

Myszka, David G., et al. "Extending the range of rate constants available from BIACORE: interpreting mass transport-influenced binding data. Biophysical journal 75.2 (1998): 583-594.

Here is the PDE they used:

with these boundary conditions:

these are the nondimensionalized forms:

This is a exemplary result they got:

Maybe this is to complex but it would be great if you can help me. Thank you in advance

Probably look at the laplace equation examples and add the flow term at end up eqn 6.

Time stepping is usually done in the examples for forward or backward Euler where

a solution for C give the time derivative. You have another variable b which would

have to be updated at each time step too. I guess they assume a flow velocity profile,

Maybe see some of this or related pages,

https://doc.freefem.org/models/evolution-problems.html

Most of the code is pretty self-explanatory although if you are not familiar

with integration by parts the weak formulation may be confusing.

IIRC Equation 6 comes from continuity equation applied to diffusion equation and

AFAICT the term at the end is not going to be common in the examples.