Diffusion from within a Spherical Body with Partially Blocked Surface: Diffusion through a Constant Surface Area

Diffusion from spherical bodies has been a subject of interest since the earliest times of modern sciences and a few equivalent analytical formulations of the problem are taught in engineering textbooks dealing with cooling rates of hot spheres. However, all these former studies assume that the diffusing material is transferable to/from the surrounding space through the whole surface of the spherical body. Conversely, the development of nanoscience and the improved knowledge of microscopic biological events have evidenced that diffusion from spherical bodies is a ubiquitous problem. It often occurs in situations where the nanosphere surfaces are not isotropic and partly impermeable to diffusing materials. This work elaborates on this issue and theoretically establishes that—with some specific allowance—the basic analytical equation of diffusion from/to fully accessible spherical bodies may be used.