concentration dependent reaction rate in a diffusion-reaction model

Numerical methods and mathematical models of Elmer
reactionrate
Posts: 1
Joined: 20 May 2020, 21:28
Antispam: Yes

concentration dependent reaction rate in a diffusion-reaction model

Hello.

I am new to Elmer and trying to determine if what I want to do is possible. I am modelling the diffusion of oxygen through a tissue. As a part of this I have a reaction rate that depends on the current concentration of oxygen:

R = density*(Vmax*[O2])/(Km+[O2])

where density, Vmax, and Km are scalar constants and [O2] is the oxygen concentration.

I have seen in the documentation that the reaction rate can depend on variables like temperature and concentration of other reactants, but is it possible to solve for oxygen concentration at the same time that you have a reaction rate that is dependent on oxygen?

I would really appreciate it if anyone could point me toward any information on this topic!

Many, many thanks!
kevinarden
Posts: 663
Joined: 25 Jan 2019, 01:28
Antispam: Yes

Re: concentration dependent reaction rate in a diffusion-reaction model

You may be interested in section 18.3 of the Elmer Solver manual where you can write your own user functions

http://www.nic.funet.fi/pub/sci/physics ... Manual.pdf
annier
Posts: 1141
Joined: 27 Aug 2013, 13:51
Antispam: Yes

Re: concentration dependent reaction rate in a diffusion-reaction model

Hi,
The variable-dependent equation for reaction rate that you provide is similar to modeling Eq. 1.12 of heat equation in Elmer Models Manual (http://www.nic.funet.fi/pub/sci/physics ... Manual.pdf). The relevant code for the Heat Equation is provided at https://github.com/ElmerCSC/elmerfem/bl ... tSolve.F90.

Now, you can implement the term for reaction rate in the analogous way of Eq. 1.12 in the existing ModelPDE solver (Advection, Diffusion, Reaction Solver). The source code of ModelPDE equation is https://github.com/ElmerCSC/elmerfem/bl ... delPDE.F90 .

Yours Sincerely,
Anil Kunwar
Anil Kunwar
Department of Materials Engineering, KU Leuven, Belgium