Condsider the timed drug-release pill illustrated below. The pill is ingested into the stomach. The pill is a slab, 0.36 cm per side, that has an array of 16 cylindrical pores in it. Each pore is 0.4...

Condsider the timed drug-release pill illustrated below.

The pill is ingested into the stomach. The pill is a slab, 0.36 cm per side, that has an array of 16 cylindrical pores in it. Each pore is 0.4 mm in diameter and 2.0 mm deep. Pure solid drug A is loaded into each pore to a depth of 1.2 mm, which provides a total initial drug loading of 2.65 mg in all of the pores. The density of the solid drug A is 1.10 g/cm³. The drug dissolves into the fluid inside the stomach, which approximates the properties of water (component B). The maximum solubility of drug A in water is
 (i.e., not very soluble) and the diffusion coefficient of the drug is
 at body temperature of 37C. The molecular weight of the drug is 120 g/mol.

a. Starting with the general differential equation for mass transfer and Fick’s flux equation, develop a simple model, in final integrated form, for predicting the flux of the drug from one pore. You may assume that the diffusion process is pseudo-steady state, the stomach fluid serves as an infinite sink for the drug so that
, and the drug does not chemically degrade inside the pore.

b. From your model, determine the total transfer rate of the drug from the whole pill, W_A, to the body when each 0.2 cm pore is filled to a depth of 0.12 cm with solid drug.

c. How many hours will it take for all of the drug to be released?