An ophthalmic drug is dissolved in a polymer and cast in the form of tiny spheres for delivery to the eye with a dropper. Once in the eye, the drug diffuses out providing longer-term delivery. Under physiological conditions (37°C), once out of the spheres and into the lacrimal fluid, the drug is quickly absorbed into the eye. The initial drug content of the spheres is 1.0 wt%. The diffusion coefficient of the drug in water at 37°C is 6.0 ×

10⁻⁶ cm²/s and the diffusivity in the polymer is 1.1 × 10⁻¹² cm²/s. The distribution coefficient describing partitioning between the polymer and the lacrimal fluid is  = 5.0 × 10⁶.

(a) Determine the radius of the spheres needed if it is desired to deliver 50% of the drug over a 7-day period (168 h) and the external mass transfer resistance is neglected.

(b) Determine the radius of the spheres needed if it is desired to deliver 50% of the drug over a 7-day period (168 h) and the external mass transfer resistance is considered assuming that the Sherwood number is equal to 2 as suggested by Eq. (11.56).

Eq. (11.56):

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