Diffusion, convection, and chemical reaction

Input(s)

k1\boldsymbol{k}_{\mathbf{1}}: Homogeneous Chemical Reaction Rate Coefficient (1/s)

DAB\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}: Diffusivity (cm2/s)\left(\mathrm{cm}^{2} / \mathrm{s}\right)

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

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

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

Output(s)

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

Formula(s)

cA=(cAO)exp(((1+4k1DABvo2)0.5)1)(voz2DAB)\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.


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