Diffusion, convection, and chemical reaction

Input(s)

$\boldsymbol{k}_{\mathbf{1}}$: Homogeneous Chemical Reaction Rate Coefficient (1/s)

$\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}$: Diffusivity $\left(\mathrm{cm}^{2} / \mathrm{s}\right)$

$v_{\boldsymbol{o}}$: Velocity $(\mathrm{cm} / \mathrm{s})$

$\boldsymbol{c}_{\boldsymbol{A} \boldsymbol{o}}$: Fraction of Initial Concentration (dimensionless)

z: Vertical Distance $(\mathrm{cm})$

Output(s)

$\boldsymbol{c}_{\boldsymbol{A}}$: Fraction of Initial Concentration remaining (dimensionless)

Formula(s)

$$ \mathrm{c}_{\mathrm{A}}=\left(\mathrm{c}_{\mathrm{AO}}\right) * \exp \left(-\left(\left(1+\frac{4 * \mathrm{k}_{1} * \mathrm{D}_{\mathrm{AB}}}{\mathrm{v}_{\mathrm{o}}^{2}}\right)^{0.5}\right)-1\right) *\left(\frac{\mathrm{v}_{\mathrm{o}} * \mathrm{z}}{2 * \mathrm{D}_{\mathrm{AB}}}\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 19, Page: 586.