Transport Phenomena Assignment -

1. Diffusion in a multilayer domain

Consider the following simplified model that was introduced in class. The tissue domain consists of two attached tissues. The applied drug reacts in one tissue and not in the second; see diagram. The associated diffusion-reaction model in the two connected tissue is given as follows:

At interface both concentration and flux are continuous

The concentration in the tissue is continuous with concentration in the surrounding fluid (same units). The topically applied drug does not specifically partition into the tissue.

[Partition coefficient is unity from surrounding fluid to tissue 1 and from tissue 1 to tissue 2, and from tissue 2 to surrounding fluid.]. Following are known parameters:

D₁ and D₂ are respectively 200 and 400 µm²/minute and may be treated as constants in the current problem. The thickness of the tissues one and two are, respectively 200 and 100 microns. Kinetic constant is k₁ = 0.02 min^-1(g/m³)^-1.

Consider non-dimensionalizing the model prior to numerical work.

1. Apply a Method of Weighted Residual and obtain concentration profiles as a function of time. Show at least three profiles. Obtain one, two and three interior collocation solutions. Second part of the problem is to determine flux into the anterior chamber (x = L). Plot flux as a function of time.