Diffusion through a non-isothermal spherical film
Input(s)
P: Pressure (atm)
\(\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}\): Diffusivity \(\left(\mathrm{cm}^{2} / \mathrm{s}\right)\)
R: Gas Constant \((\mathrm{J} / \mathrm{mol} \mathrm{K})\)
\(\boldsymbol{T}_{1}\): Temperature (K)
\(\mathrm{n}\): Exponent (dimensionless)
\(r_{1}\): Radius of Gas Film \((\mathrm{cm})\)
\(\boldsymbol{r}_{\mathbf{2}}\): Radius of Film \((\mathrm{cm})\)
\(\boldsymbol{x}_{\boldsymbol{A} 1}\): Position of Gas (fraction)
\(x_{A 2}\): Position of Film (fraction)
Output(s)
\(\boldsymbol{W}_{\boldsymbol{A}}\): Mass Rate \((\mathrm{mol} / \mathrm{s})\)
Formula(s)
\[
\mathrm{W}_{\mathrm{A}}=\frac{4 * \pi *\left(\frac{\mathrm{P} * \mathrm{D}_{\mathrm{AB}}}{\mathrm{R} * \mathrm{~T}_{1}}\right) *\left(1+\left(\frac{\mathrm{n}}{2}\right)\right)}{\left(\mathrm{r}_{1}^{\frac{\mathrm{n}}{2}}\right) *\left(\left(\frac{1}{\mathrm{r}_{1}}\right)^{1+\frac{\mathrm{n}}{2}}-\left(\frac{1}{\mathrm{r}_{2}}\right)^{1+\frac{\mathrm{n}}{2}}\right)} * \ln \left(\frac{1-\mathrm{x}_{\mathrm{A} 2}}{1-\mathrm{x}_{\mathrm{A} 1}}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 18, Page: 551 .