Diffusion from an instantaneous point source
Input(s)
\(\boldsymbol{m}_{A}\): Mass of Species A \((\mathrm{g})\)
\(\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}\): Binary Diffusivity for System A-B \(\left(\mathrm{cm}^{2} / \mathrm{s}\right)\)
\(\mathrm{t}\): Time (s)
r: Radial Coordinate, L (m)
Output(s)
\(\boldsymbol{\rho}_{A}\): Density of Species A \(\left(\mathrm{g} / \mathrm{cm}^{3}\right)\)
Formula(s)
\[
\rho_{\mathrm{A}}=\left(\frac{\mathrm{m}_{\mathrm{A}}}{\left(4 * \pi * \mathrm{D}_{\mathrm{AB}} * \mathrm{t}\right)^{\frac{3}{2}}}\right) * \exp \left(-\frac{\mathrm{r}^{2}}{4 * \mathrm{D}_{\mathrm{AB}} * \mathrm{t}}\right)
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley & Sons, Chapter: 20, Page: 650.