1. Consider the case where a tissue sample sheet disk with an initial solute concentration distribution of c (x,0) - 0 is placed in a well-mixed bath of fixed concentration co and allowed to fill up with diffusing solutes. Assume the solute has partition coefficient of K I within the tissue sheet: (25%) a) Write the mathematical problem statement for c (x,t) corresponding to this physical situation. including the initial and boundary conditions this is a good practice for your course project, b) What will be c (x,?) for very large r (i.e., at equilibrium)? Write this down and let's call it ca (x,() c) Define ci (x,?) = c (x,?) - c. (x,/). Must c (x,?) satisfy the diffusion equation? What boundary and initial conditions must it obey? d) Find a solution for ci (x,/), using any means available e) Use that solution to determine c (x,!)