A patch is designed to release a drug for motion sickness. The patch is applied

Question

A patch is designed to release a drug for motion sickness. The patch is applied one hour before the flight and is worn until the flight is over. The patch is a cylindrical disk with a thickness of 3mm and a radius of 1 cm. The starting drug concentration is 50 mM. Assume the drug concentration in the adjacent skin is much less than the concentration in the patch. The diffusion coefficient of the drug in the patch is 1x10-8 cm2 /s. The drug release rate must be above 0.5x10-10 mol/s to ensure enough drug in the bloodstream for the drug to be effective. Can the release rate be achieved for a 14-hour flight? If not, what would you propose to achieve the target release rate?

Explanation / Answer

For 1 second the release rate is 0.5*10-10 mol,
for 14 hr release rate will be 0.5*10-10 *14*3600 = 2.52*10-6 mol
c = 50*10-6 - 2.52*10-6 = 4.748*10-5 mol
D = 1*10-8 cm2 /sec ; x = 3 mm = 0.3 cm
J = D * c / x = 1*10-8 cm2 / sec * ( 4.748*10-5 mol / 0.3 cm)
J = 1.58267*10-12 mol /cm sec
Release rate = 1.58*10-12 mol / cm sec * 1 cm = 1.58*10-12 mol / sec
8.4*10-12 < 0.5*10-10 , therefore the release rate cannot be achieved for a 14-hour flight
To achieve the target release rate the concentration gradient should be decreased

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