What coefficients can I use in a Reaction-Diffusion Equation? - Chemistry Stack Exchange most recent 30 from chemistry.stackexchange.com 2019-08-18T23:20:52Z https://chemistry.stackexchange.com/feeds/question/99961 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://chemistry.stackexchange.com/q/99961 1 What coefficients can I use in a Reaction-Diffusion Equation? Xilexio https://chemistry.stackexchange.com/users/63816 2018-07-28T03:13:57Z 2018-07-28T04:35:10Z <p>I am qualitatively analyzing an abstract chemical reaction</p> <p>$A + B \rightarrow 2A$</p> <p>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:</p> <p>$u = \left(\begin{array}{c}a\\b\end{array}\right), \quad u(0) = u_0, \quad d \in \mathbb{R}_+, k \in \mathbb{R}_+$,</p> <p>$a_t = d \Delta a + k a b$,</p> <p>$b_t = d \Delta b - k a b$.</p> <p>However, I need some specific coefficients $d$ and $k$, and starting densities for $u$ to do my simulations on.</p> <p>What would be a decent <strong>Fermi estimate</strong> for diffusion coefficient $d$, reaction rate $k$ and density $u_0$ for reactions present in reality?</p> <p>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.</p>