Diffusion from an instantaneous point source

Input(s)

mA\boldsymbol{m}_{A}: Mass of Species A (g)(\mathrm{g})

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

t\mathrm{t}: Time (s)

r: Radial Coordinate, L (m)

Output(s)

ρA\boldsymbol{\rho}_{A}: Density of Species A (g/cm3)\left(\mathrm{g} / \mathrm{cm}^{3}\right)

Formula(s)

ρA=(mA(4πDABt)32)exp(r24DABt)\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.

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