A time-release drug capsule is ingested and settles in the gastrointestinal system. Once inside the body, the capsule slowly released to the body through a diffusion-limited process. Assume the drug carrier is a spherical bead of gelatinous material that can pass through the body without disintegrating. A water soluble drug (species A) is uniformly dissolved within the gel, and has an initial concentration of 50 mg/cm’. Consider a limiting case where the drug is immediately consumed once it reaches the surface of the capsule. a) Define a coordinate system and simplify the differential equation for mass transfer of the drug in terms of concentration c,. State all simplifying assumptions. b) Write the boundary conditions and initial conditions necessary to solve the differential equation. Note: the differential equation does not need to be solved.

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Heat and Mass Transport

A time-release drug capsule is ingested and settles in the
gastrointestinal system. Once inside the body, the capsule
slowly released to the body through a diffusion-limited process.
Assume the drug carrier is a spherical bead of gelatinous
material that can pass through the body without disintegrating.
A water soluble drug (species A) is uniformly dissolved within
the gel, and has an initial concentration of 50 mg/cm'. Consider
a limiting case where the drug is immediately consumed once it
reaches the surface of the capsule.
a) Define a coordinate system and simplify the
differential equation for mass transfer of the drug in
terms of concentration c,. State all simplifying
assumptions.
b) Write the boundary conditions and initial conditions
necessary to solve the differential equation. Note: the
differential equation does not need to be solved.
Transcribed Image Text:A time-release drug capsule is ingested and settles in the gastrointestinal system. Once inside the body, the capsule slowly released to the body through a diffusion-limited process. Assume the drug carrier is a spherical bead of gelatinous material that can pass through the body without disintegrating. A water soluble drug (species A) is uniformly dissolved within the gel, and has an initial concentration of 50 mg/cm'. Consider a limiting case where the drug is immediately consumed once it reaches the surface of the capsule. a) Define a coordinate system and simplify the differential equation for mass transfer of the drug in terms of concentration c,. State all simplifying assumptions. b) Write the boundary conditions and initial conditions necessary to solve the differential equation. Note: the differential equation does not need to be solved.
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