A drug at a concentration C, is encapsulated in a permeable polymeric membrane of thickness L...

 

Transcribed Image Text:

A drug at a concentration C, is encapsulated in a permeable polymeric membrane of thickness L and area A. The spherical capsule of volume V1₁ is placed in well-stirred water of volume V₂. The drug diffuses through the polymeric membrane and is released into the water which is free from the drug at the beginning. The diffusivity of the drug in the polymer membrane is D and its distribution coefficients may be expressed as Cmim₁ C₁ and Cine = m₂ C; where Cs and C₂ are the drug concentrations in the internal and external liquids, C and Cme are the corresponding solubilities of the drug in the membrane, and m₁ and m₂ are the distribution coefficients. Develop a simple mathematical model for evolution of drug concentration in the liquid. "Pseudo-steady state' transport of the drug through the membrane may be assumed. Diffusional resistance of the membrane is controlling; surface mass transfer resistances may be neglected. Determine the drug concentrations within the capsule and in the external liquid after five hours for the following values of different quantities: Diameter of the capsule, d = 8 cm; initial drug concentration within the capsule, C= 80 g/L; volume of water, V₂ = 1 liter; distribution coefficients, m₁ = 0.2 and m₂=0.1; thickness of the membrane, L= 0.2 mm; and diffusivity of the drug in the polymer, D = 8 x 101 m²/s. Liquid 2 Volume=V₂ Concentration-C-(1) Membrane Liquid 1 Volume V Concentration G() A drug at a concentration C, is encapsulated in a permeable polymeric membrane of thickness L and area A. The spherical capsule of volume V1₁ is placed in well-stirred water of volume V₂. The drug diffuses through the polymeric membrane and is released into the water which is free from the drug at the beginning. The diffusivity of the drug in the polymer membrane is D and its distribution coefficients may be expressed as Cmim₁ C₁ and Cine = m₂ C; where Cs and C₂ are the drug concentrations in the internal and external liquids, C and Cme are the corresponding solubilities of the drug in the membrane, and m₁ and m₂ are the distribution coefficients. Develop a simple mathematical model for evolution of drug concentration in the liquid. "Pseudo-steady state' transport of the drug through the membrane may be assumed. Diffusional resistance of the membrane is controlling; surface mass transfer resistances may be neglected. Determine the drug concentrations within the capsule and in the external liquid after five hours for the following values of different quantities: Diameter of the capsule, d = 8 cm; initial drug concentration within the capsule, C= 80 g/L; volume of water, V₂ = 1 liter; distribution coefficients, m₁ = 0.2 and m₂=0.1; thickness of the membrane, L= 0.2 mm; and diffusivity of the drug in the polymer, D = 8 x 101 m²/s. Liquid 2 Volume=V₂ Concentration-C-(1) Membrane Liquid 1 Volume V Concentration G()

Answer rating: 100% (QA)

The diffusion of a drug through a permeable polymeric membrane can be modeled using Ficks law of dif... View the full answer