I am qualitatively analyzing an abstract chemical reaction
$A + B \rightarrow 2A$
where $A$ and $B$ 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:
$u = \left(\begin{array}{c}a\\b\end{array}\right), \quad u(0) = u_0, \quad d \in \mathbb{R}_+, k \in \mathbb{R}_+$,
$a_t = d \Delta a + k a b$,
$b_t = d \Delta b - k a b$.
However, I need some specific coefficients $d$ and $k$, and starting densities for $u$ to do my simulations on.
What would be a decent Fermi estimate for diffusion coefficient $d$, reaction rate $k$ and density $u_0$ 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 $k \approx 1 \frac{dm^3}{kg \cdotp s}$, $d \approx 1 \frac{dm^2}{s}$, and $u_0 \approx 1 \frac{kg}{dm^3}$, but I'm particularly unsure if this ratio of $k$ to $d$ 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.