A spherical gel bead (d = 0.7 cm diameter) is loaded with the anti-nausea drug Dramamine to a uniform initial mass concentration of 70 mg/cm³. The forces inside the stomach generate a fluid velocity of 0.5 cm/s around the bead. The concentration of Dramamine in the bulk stomach liquid (CA) is essentially zero, but the concentration at the surface of the bead (CAs) may be greater than zero, because of the convective mass transfer resistance. Assume that the concentration of Dramamine at the surface of the bead is the same as in the surrounding fluid phase. The fluid in the stomach approximates the properties of water. The diffusivity of Dramamine in water, DẠB, is 4.6 x 10-6 cm²/s at 37°C, whereas the diffusivity of Dramamine in the gel, DA,gel is 3.0 x 10-7 cm²/s at 37°C. The external mass transfer coefficient, kɩ, can be estimated by adapting the heat transfer correlation discussed in class: Sh = k d D -= 2.0+0.6 Re¹/2 Sc¹/3 AB Where d is the diameter of the bead. The viscosity and density of water at 37°C are available online. (a) Is the transport of Dramamine from the interior of the bead to the fluid in the stomach limited by diffusion inside the bead or the external mass transfer resistance? (b) How long will it take for a 50% change in the concentration of the Dramamine at the center of the bead?
A spherical gel bead (d = 0.7 cm diameter) is loaded with the anti-nausea drug Dramamine to a uniform initial mass concentration of 70 mg/cm³. The forces inside the stomach generate a fluid velocity of 0.5 cm/s around the bead. The concentration of Dramamine in the bulk stomach liquid (CA) is essentially zero, but the concentration at the surface of the bead (CAs) may be greater than zero, because of the convective mass transfer resistance. Assume that the concentration of Dramamine at the surface of the bead is the same as in the surrounding fluid phase. The fluid in the stomach approximates the properties of water. The diffusivity of Dramamine in water, DẠB, is 4.6 x 10-6 cm²/s at 37°C, whereas the diffusivity of Dramamine in the gel, DA,gel is 3.0 x 10-7 cm²/s at 37°C. The external mass transfer coefficient, kɩ, can be estimated by adapting the heat transfer correlation discussed in class: Sh = k d D -= 2.0+0.6 Re¹/2 Sc¹/3 AB Where d is the diameter of the bead. The viscosity and density of water at 37°C are available online. (a) Is the transport of Dramamine from the interior of the bead to the fluid in the stomach limited by diffusion inside the bead or the external mass transfer resistance? (b) How long will it take for a 50% change in the concentration of the Dramamine at the center of the bead?
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
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this is a chemical engineering transport problem
Transcribed Image Text:A spherical gel bead (d = 0.7 cm diameter) is loaded with the anti-nausea drug Dramamine to a uniform
initial mass concentration of 70 mg/cm³. The forces inside the stomach generate a fluid velocity of 0.5 cm/s
around the bead. The concentration of Dramamine in the bulk stomach liquid (CA) is essentially zero, but
the concentration at the surface of the bead (CAS) may be greater than zero, because of the convective mass
transfer resistance. Assume that the concentration of Dramamine at the surface of the bead is the same as in
the surrounding fluid phase. The fluid in the stomach approximates the properties of water. The diffusivity
of Dramamine in water, DẠb, is 4.6 x 10-6 cm²/s at 37°C, whereas the diffusivity of Dramamine in the gel,
DA,gel is 3.0 x 10-7 cm²/s at 37°C. The external mass transfer coefficient, kī, can be estimated by adapting
the heat transfer correlation discussed in class:
k_d
D AB
Where d is the diameter of the bead. The viscosity and density of water at 37°C are available online.
Sh =
= 2.0+0.6 Re¹/2 Sc¹/3
=
(a) Is the transport of Dramamine from the interior of the bead to the fluid in the stomach limited by
diffusion inside the bead or the external mass transfer resistance?
(b) How long will it take for a 50% change in the concentration of the Dramamine at the center of the bead?
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