Consider the timed drug release pill shown in the figure below. The pill is ingested into the stomach. The pill is a slab of 0.36 cm per side, which has an array of 16 cylindrical pores in it. Each pore is 0.4 mm (0.04 cm) in diameter and 2.0 mm (0.20 cm) deep. Pure solid drug (species A) is loaded into each pore to a depth of 1.2 mm (0.12 cm), which provides a total initial drug loading of 2.65 mg in all of the pores. The density of the solid drug (ρ_A,solid) is 1.10 g/cm³. The drug dissolves into fluid inside the stomach, which approximates the properties of water (species B). The maximum solubility of drug in water is 2.0 × 10^-4gmol/cm³(not very soluble), and the diffusion coefficient of the drug in the fluid is 2.0 × l0^-5cm²/s at body temperature of 37°C. The molecular weight of the drug is 120 g/gmole. 

a. Determine the total transfer rate of the drug from the whole pill (W_A) to the body at when each 0.2 cm pore is filled to a depth of 0.12 cm with solid drug. You may assume that (1) the diffusion process is at a pseudo-steady-state, (2) the stomach fluid serves as an infinite sink for the drug so that c_A,ˆž ‰ˆ 0, and (3) the drug does not chemically degrade inside the pore. List all other assumptions you make as appropriate in the development of your mass-transfer model. 

b. How long will it take (in hours) for all of the drug material in the reservoir to be released? 

A = drug, B = water inside pore

T = 310 K

L_t = 0.2 cm, L_o = 0.12 cm, d_pore = 0.04 cm, h_pore = 0.20 cm

c. Propose adjustment of one of the variables in the process that will increase the required time in part (b) by a factor of 2.0.

Transcribed Image Text:

Detail for one pore Bulk stomach fluid (essentially water) CAc.0 0.4 mm Initially NA Cross-section view of pill L = 2.0 mm 0.36 cm Lo = at a later time 1.2 mm Solid A