A spherical capsule has an outer membrane thickness with inner and outer radii \(r_{\mathrm{i}}\) and \(r_{\mathrm{o}}\), respectively. A solute is diffusing across this capsule. Consider the case where the diffusion coefficient is a function of concentration and can be represented in a general form as \(D\left(C_{\mathrm{A}}\right)\) and is not a constant.

Derive an expression for the (total) rate of mass transport across this spherical shell. Use the low-flux model.