Reaction-Diffusion with flow

Hi all, i am new to the forum and this is my first post.
Essentially what i am doing is trying to work from the 2D cylinder matlab script and add multicomponent(miscible) LBM with reaction terms. What i am trying to eventually do is have flow and reaction of chemicals occuring at solid surfaces to simulate what happens in a packed bed reactor.
I have read papers by Kingdon and Schofield, though i dont know how they incorporate reaction term into the LB evoloution equation and papers by Chen, Doolen et al and by He/LiGoldstein, though they all say something different. What would be a good start for for simulating say three species and how do i get the reaction to occur only at the solid suraces, would i include the reaction term as part of the bounce rule?

Any help would be greatly appreciated



for reaction-diffusion you have more than one collision equation. You have the equation for advection (standard collision) and you have the collision for the diffusive part, which gives you the diffusion equation in the macroscopic limit. In the collision equation for the components, you have to add source terms describing the chemical reaction, since it changes the concentrations of the components. And of course you can add the condition that the additional reaction term does only apply when you are close to a wall, e.g.

if(is_close_to_wall(x, y, z)) {
else {

How exactly you can implement the chemical reaction depends on the chemicals. But I have never done it and do not now articles about that. However, my colleague is working on advection-diffusion-reaction problems with LBM. I will ask him tomorrow.


Yes thanks, i would also like to hear what your friend has to say, i guess the main part i am having difficulty with is exaclt how do i incorporate the reaction term.

Okay, I have talked to my colleague. Suppose you have a two component system with conserved mass. The components are called A and B. Then you have three collision equations:

  1. the equation for the total population, f[sub]i[/sub] = f[sup]A[/sup][sub]i[/sub] + f[sup]B[/sup][sub]i[/sub]; here you have no additional terms
  2. the equation for the component A, f[sup]A[/sup][sub]i[/sub]; here you have an additional term taking into account the increase or decrease of component A due to the reaction
  3. the same for B, but in such a way that an increase of f[sup]A[/sup][sub]i[/sub] is exactly compensated by an decrease of f[sup]B[/sup][sub]i[/sub] and vice versa (if the total mass is conserved)
    How this reaction term looks like in detail, I cannot tell you. You will find something in the literature.

Yes thanks that is the sort of thing i was thinking the papers i was reading described it as, the only thing is that different papers say slightly different things, but i suppose what i have got to do is just try to program each of the different ways and then see which one gives meaningful results. Thanks