Diffusion with a homogeneous chemical reaction
Input(s)
\(\mathrm{k}\): Rate Constant \((\mathrm{mol} \mathrm{cm} / \mathrm{s})\)
L: Length \((\mathrm{cm})\)
\(\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}\): Diffusivity \((\mathrm{cm} \mathrm{cm} / \mathrm{s})\)
c: Total Molar Concentration \(\left(\mathrm{mol} / \mathrm{ft}^{3}\right)\)
Output(s)
\(\emptyset\): Thiele Modulus (dimensionless)
\(\mathrm{N}\): Molar Flux \(\left(\mathrm{mol} \mathrm{L/ \textrm {cm } ^ { 2 } )}\right.\)
Formula(s)
\[
\begin{gathered}
\varnothing=\left(\frac{\mathrm{k} *\left(\mathrm{~L}^{2}\right)}{\mathrm{D}_{\mathrm{AB}}}\right)^{0.5} \\
\mathrm{~N}=\left(\frac{\mathrm{c} * \mathrm{D}_{\mathrm{AB}}}{\mathrm{L}}\right) * \varnothing * \tanh (\pi)
\end{gathered}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 18, Page: 555.