I am reading the book The Mathematics of Diffusion by J. Crank (cf. Crank_1975_Diffusion) and, at page 89, I could not understand the equation of radial diffusion:
$$\dfrac{\partial C}{\partial t}=D\bigg(\dfrac{\partial^2C}{\partial r^2}+\boxed{\dfrac{2}{r}\dfrac{\partial C}{\partial r}}\bigg).$$
What is the physical meaning of the boxed term?
Many thanks in advance.
The diffusion equation is
$$ \frac{\partial C}{\partial t}=D\Delta C\;. $$
The boxed term arises from expressing the Laplacian $\Delta C$ of a radially symmetric function $C$ in spherical coordinates; you can derive it from the more symmetric expression $\frac1{r^2}\frac\partial{\partial r}\left(r^2\frac{\partial C}{\partial r}\right)$ by carrying out the outer differentiation. See Wikipedia here and here.