1. A drug is diffusing from the surface of a spherical pill through a radial shell with thickness d1. The radius of the pill is r1. The drug concentration at the pill surface is c1 and the concentration outside the shell is c2. The diffusion coefficient of the solute is D. From first principles, derive a steady state expression for the drug concentration c(r) and flux, J(r), inside the shell.
2. Estimate the diffusivity of a spherically shaped protein with a MW of 36,000 in water at 37oC.
3. Estimate the diffusivity of the same solute in problem # 2 through cylindrical pores of a membrane that is 28 nm in diameter. Assume that the molecule enters the pores of the membrane from a well-stirred bulk solution.
Thank you.