Agar gel is a gel matrix formed from agarose that is a purified hydrocolloid isolated from agar or agar-bearing marine algae. This gel matrix is nearly ideal for diffusion and electrokinetic movement of biopolymers. Therefore, it is useful for studying processes such as electrophoresis and immunodiffusion. Consider a cylindrical shaped agar gel of 20 mm diameter that contains a uniform concentration of urea of 0.1 kmol/m3 . The cylinder is suddenly immersed in water containing no urea. The water flow is rapid enough that the surface convective mass transfer resistance can be assumed to be negligible. The diffusivity of urea in water (agar is mostly water) is 4.5 x 10-10 m2 /s. a. (3 points) Write down the simplified governing equation for the problem. List all the assumptions necessary to reduce the original equation to the governing equation. b. (3 points) Write down the initial and the boundary conditions. c. (4 points) Write down the solution to the equation you wrote in (a) subject to the initial and boundary conditions in (b). Define all the variables in the equation. d. (12 points) Using the solution in (c) calculate the concentration at a distance of 5 mm from the center of the cy