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.