What coefficients can I use in a Reaction-Diffusion Equation?
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I am qualitatively analyzing an abstract chemical reaction
A+B→2AA+B→2A
where AA and BB are some liquid substances that undergo Reaction-Diffusion with a second order reaction (actually my model is much more complicated than that, but this is for simplicity). I have Reaction-Diffusion Equation that models this reaction:
u=(ab),u(0)=u0,d∈R+,k∈R+u=(ab),u(0)=u0,d∈R+,k∈R+,
at=dΔa+kabat=dΔa+kab,
bt=dΔb−kabbt=dΔb−kab.
However, I need some specific coefficients dd and kk, and starting densities for uu to do my simulations on.
What would be a decent Fermi estimate for diffusion coefficient dd, reaction rate kk and density u0u0 for reactions present in reality?
In terms of speed, I'm interested in reactions like one of reactions present in the Belousov–Zhabotinsky Reaction-Diffusion model and I just need a very, very rough estimate of values (with physical units) to put in my model so that I keep studying behavior of reactions that might plausibly happen in reality for some specific substances. So far I used k≈1dm3kg⋅sk≈1dm3kg⋅s, d≈1dm2sd≈1dm2s, and u0≈1kgdm3u0≈1kgdm3, but I'm particularly unsure if this ratio of kk to dd is anywhere near realistic. I know I could just scale time, space, and mass in this equation, but I'm interested in specific value ranges or examples.
A+B→2AA+B→2A
where AA and BB are some liquid substances that undergo Reaction-Diffusion with a second order reaction (actually my model is much more complicated than that, but this is for simplicity). I have Reaction-Diffusion Equation that models this reaction:
u=(ab),u(0)=u0,d∈R+,k∈R+u=(ab),u(0)=u0,d∈R+,k∈R+,
at=dΔa+kabat=dΔa+kab,
bt=dΔb−kabbt=dΔb−kab.
However, I need some specific coefficients dd and kk, and starting densities for uu to do my simulations on.
What would be a decent Fermi estimate for diffusion coefficient dd, reaction rate kk and density u0u0 for reactions present in reality?
In terms of speed, I'm interested in reactions like one of reactions present in the Belousov–Zhabotinsky Reaction-Diffusion model and I just need a very, very rough estimate of values (with physical units) to put in my model so that I keep studying behavior of reactions that might plausibly happen in reality for some specific substances. So far I used k≈1dm3kg⋅sk≈1dm3kg⋅s, d≈1dm2sd≈1dm2s, and u0≈1kgdm3u0≈1kgdm3, but I'm particularly unsure if this ratio of kk to dd is anywhere near realistic. I know I could just scale time, space, and mass in this equation, but I'm interested in specific value ranges or examples.
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