A spherical tissue engineered device is being explored. It would be a pellet of radius L containing insulin-producing cells for use as an implant to treat diabetes. This implant would be cultured in a bath with a constant oxygen concentration of c ₀ .

Fick’s 2nd law in spherical coordinates is: 

  

When integrated at steady state, it yields the following equation, with A and B designating the unknown integration constants. (You don’t have to integrate this yourself!) 

  

Using symmetry and the known concentration where the device is in contact with the bath, solve for A and B and show that: 

dc Dij a dc + Ri r2 dr