A “bio film” (component B) coats the surface of a nonporous inert sphere. The diameter of the nonporous inert core is 4.0 mm, and the overall diameter of the spherical bio film particle is 8.0 mm. The spherical bio film particle is suspended within water containing a known, constant, dilute concentration of solute A (c_A∞). Within the bio film, a homogeneous, first-order reaction A → _k1 D takes place. 

a. Define the system, the source and sink for mass transfer of reactant A. Consider that the process is dilute with respect to species A and D. Propose three additional reasonable assumptions for this process. 

b. Develop the differential material balance for the process in terms of concentration profile c_A. State all boundary conditions necessary to completely specify this differential equation.