26.2 The spherical gel capsule shown in the figure at the top of the next column is used for long-term, sustained drug release. A saturated liquid solution containing the dissolved drug (solute A) is encapsulated within a rigid gel-like shell. The saturated solution contains a lump of solid A, which keeps the dissolved concentra- tion of A saturated within the liquid core of the capsule. Solute A then diffuses through the gel-like shell (the gel phase) to the surroundings. Eventually, the source for A is depleted, and the amount of solute A within the liquid core goes down with time. However, as long as the lump of solid A exists within the core to keep the source solution saturated in A, the concentration of A within the core is constant. The diffusion coefficient of solute A in the gel phase (B) is DAB = 1.5 × 10-5 cm²/s. The maximum solubility of the drug in the gel capsule material is C = 0.01 gmole A/cm³. a. Starting from the appropriately simplified differential forms of Fick's ux equation and the general differential equation for mass transfer relevant to the physical system of interest, develop the final, analytical, integrated equation to deter- mine the total rate of drug release (WA) from the capsule under conditions where the saturated concentration of A within the liquid core of the capsule remains constant. b. What is the maximum possible rate of drug release from the capsule, in units of gmole A per hour, when CAO~0? Saturated solution of drug (solute A) Surrounding liquid Lump of solid species A Gel capsule shell r = R₁ CA= CAS r = R₂ CA = CAO
26.2 The spherical gel capsule shown in the figure at the top of the next column is used for long-term, sustained drug release. A saturated liquid solution containing the dissolved drug (solute A) is encapsulated within a rigid gel-like shell. The saturated solution contains a lump of solid A, which keeps the dissolved concentra- tion of A saturated within the liquid core of the capsule. Solute A then diffuses through the gel-like shell (the gel phase) to the surroundings. Eventually, the source for A is depleted, and the amount of solute A within the liquid core goes down with time. However, as long as the lump of solid A exists within the core to keep the source solution saturated in A, the concentration of A within the core is constant. The diffusion coefficient of solute A in the gel phase (B) is DAB = 1.5 × 10-5 cm²/s. The maximum solubility of the drug in the gel capsule material is C = 0.01 gmole A/cm³. a. Starting from the appropriately simplified differential forms of Fick's ux equation and the general differential equation for mass transfer relevant to the physical system of interest, develop the final, analytical, integrated equation to deter- mine the total rate of drug release (WA) from the capsule under conditions where the saturated concentration of A within the liquid core of the capsule remains constant. b. What is the maximum possible rate of drug release from the capsule, in units of gmole A per hour, when CAO~0? Saturated solution of drug (solute A) Surrounding liquid Lump of solid species A Gel capsule shell r = R₁ CA= CAS r = R₂ CA = CAO
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
Ri = 0.20 cm, Ro = 0.35 cm
Please state any assumptions made for the process.
Transcribed Image Text:26.2 The spherical gel capsule shown in the figure at the top of the
next column is used for long-term, sustained drug release. A
saturated liquid solution containing the dissolved drug (solute A)
is encapsulated within a rigid gel-like shell. The saturated solution
contains a lump of solid A, which keeps the dissolved concentra-
tion of A saturated within the liquid core of the capsule. Solute A
then diffuses through the gel-like shell (the gel phase) to the
surroundings. Eventually, the source for A is depleted, and the
amount of solute A within the liquid core goes down with time.
However, as long as the lump of solid A exists within the core to
keep the source solution saturated in A, the concentration of A
within the core is constant. The diffusion coefficient of solute A in
the gel phase (B) is DAB = 1.5 × 10-5 cm²/s. The maximum
solubility of the drug in the gel capsule material is
c = 0.01 gmole A/cm³.
a.
Starting from the appropriately simplified differential forms
of Fick's ux equation and the general differential equation
for mass transfer relevant to the physical system of interest,
develop the final, analytical, integrated equation to deter-
mine the total rate of drug release (WA) from the capsule
under conditions where the saturated concentration of A
within the liquid core of the capsule remains constant.
b. What is the maximum possible rate of drug release from the
capsule, in units of gmole A per hour, when CAO~0?
Saturated
solution of
drug (solute A)
Surrounding
liquid
Lump of
solid species A
Gel capsule
shell
r = R₁
CA= CAS
r = R₂
CA CAO
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