A polymer solution is applied to a horizontal surface as a film of thickness $H.$ As the film dries, a polymer "skin" develops. The skin slows down the drying as the solvent must diffuse through the skin. Assume that a skin of thickness $"h"$ has developed on the film. The diffusion coefficient of the solvent through the skin is known $D_{AS}.$ The concentration of the solvent at the bottom of the skin is small and is known $x_{A_0}.$ As the solvent reaches the top of the skin, it is carried away by air flow.

A$)$ Given an expression for the rate of drying of the film assuming that diffusions through the skin of some thickness $h$ limits the drying rate.

B$)$ If the rate that the skin increase in thickness $(d\frac{h}{d}t)$ is equal to some constant $K$ times the rate of drying, give an expression for the rate of increase of $h$ as a function of time. Show

how you could get an expression for the time needed to dry to reach a final skin thickness of $h_{\text{f}\text{i}\text{n}\text{a}\text{l}\text{.}}.$