The drug patch shown in the figure in the next column releases a water-soluble epidermal growth factor

The €œdrug patch€ shown in the figure in the next column releases a water-soluble epidermal growth factor (species A) to repair a specific region of wounded tissue on the human body. A slow release of the drug is critical for regulating the rate of tissue repair. The drug layer (pure solute A) rests on top of a diffusion barrier. The diffusion barrier is essentially a micro porous polymer material consisting of tiny parallel pores filled with liquid water (species B). This diffusion barrier controls the rate of drug release. The thickness (L), pore size (d_pore), and porosity of the diffusion barrier are design parameters that determine the dosage rate of the drug to the tissue directly beneath it. The maximum solubility of the drug in water is 1.0 mole/m³at 25°C. The diffusion coefficient of the drug in water at infinite dilution is 1.0 × 10^-10m²/s at 25°C. The pore diameter (d_pore) is 100 Ã… (1Ã… = 10^-10m), and the equivalent molecular diameter of the drug is 25 Ã… The total surface area of the patch is 4.0 cm², but the cross-sectional area of the pore openings available for flux constitutes only 25% of this contact surface area. 

a. What is the effective diffusion coefficient of the drug in the diffusion barrier? Consider the Renkin equation for solute diffusion in solvent-filled pores A = drug, B = water
from Chapter 24. 

b. Estimate the thickness of the diffusion barrier (L) necessary to achieve a maximum possible dosage rate of 0.05 µmole per day, assuming that the drug is instantaneously consumed once it exits the diffusion barrier and enters the body tissue (1 µmole = 1.0 × 10^-6 mole).

Transcribed Image Text:

Drug patch (side view) Diffusion barrier (water-filled -micropores, dpore = 100 Å) Drug reservoir Impermeable barrier Skin surface Infected tissue (sink for drug); SIDE VIEW micropore array (not to scale)