A spherical tissue engineered device is being explored. It would be a pellet of radius L containing insulin-producing cells for use as an implant to treat diabetes. This implant would be cultured in a bath with a constant oxygen concentration of co. Fick's 2nd law in spherical coordinates is: Dij d ar + R; dt When integrated at steady state, it yields the following equation, with A and B designating the unknown integration constants. (You don't have to integrate this yourself!) c (r) : -R;r + 4 + B 6D¡j Using symmetry and the known concentration where the device is in contact with the bath, solve for A and B and show that: = 1 + (1 - (4)') c(r) R; L² CO Using the solution above, if a spherical tumor is not vascularized, how large can it grow (radius, in mm, two significant digits) before the oxygen concentration in the center of the tumor falls to zero? (This is the maximum size that the tumor can grow without vascularization.) The concentration of oxygen in the fluid surrounding it is constant at 0.15 mol/m3, the diffusivity of oxygen in the tumor is 6.9 E-9 m²/s, and the reaction rate of oxygen in the tumor is -0.28 mol/(m³os).
A spherical tissue engineered device is being explored. It would be a pellet of radius L containing insulin-producing cells for use as an implant to treat diabetes. This implant would be cultured in a bath with a constant oxygen concentration of co. Fick's 2nd law in spherical coordinates is: Dij d ar + R; dt When integrated at steady state, it yields the following equation, with A and B designating the unknown integration constants. (You don't have to integrate this yourself!) c (r) : -R;r + 4 + B 6D¡j Using symmetry and the known concentration where the device is in contact with the bath, solve for A and B and show that: = 1 + (1 - (4)') c(r) R; L² CO Using the solution above, if a spherical tumor is not vascularized, how large can it grow (radius, in mm, two significant digits) before the oxygen concentration in the center of the tumor falls to zero? (This is the maximum size that the tumor can grow without vascularization.) The concentration of oxygen in the fluid surrounding it is constant at 0.15 mol/m3, the diffusivity of oxygen in the tumor is 6.9 E-9 m²/s, and the reaction rate of oxygen in the tumor is -0.28 mol/(m³os).
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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![A spherical tissue engineered device is being explored. It would be a pellet of radius L containing
insulin-producing cells for use as an implant to treat diabetes. This implant would be cultured in a
bath with a constant oxygen concentration of co.
Fick's 2nd law in spherical coordinates is:
Dij a
dc
dt
r2 ] + R;
„2 dr
When integrated at steady state, it yields the following equation, with A and B designating the
unknown integration constants. (You don't have to integrate this yourself!)
c (r)
-R;r?
+ 4 + B
Using symmetry and the known concentration where the device is in contact with the bath, solve for
A and B and show that:
E(1-(5)
c(r)
= 1 +
бсо Dij
CO
Using the solution above, if a spherical tumor is not vascularized, how large can it grow (radius, in
mm, two significant digits) before the oxygen concentration in the center of the tumor falls to zero?
(This is the maximum size that the tumor can grow without vascularization.)
The concentration of oxygen in the fluid surrounding it is constant at 0.15 mol/m³, the diffusivity of
oxygen in the tumor is 6.9 E-9 m²/s, and the reaction rate of oxygen in the tumor is -0.28
mol/(m3os).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cb97671-2ce0-48ec-9c65-dcf985c16d5e%2F46efef46-8a8d-416c-abd6-13d8cc2ae143%2F2tjdzu1_processed.png&w=3840&q=75)
Transcribed Image Text:A spherical tissue engineered device is being explored. It would be a pellet of radius L containing
insulin-producing cells for use as an implant to treat diabetes. This implant would be cultured in a
bath with a constant oxygen concentration of co.
Fick's 2nd law in spherical coordinates is:
Dij a
dc
dt
r2 ] + R;
„2 dr
When integrated at steady state, it yields the following equation, with A and B designating the
unknown integration constants. (You don't have to integrate this yourself!)
c (r)
-R;r?
+ 4 + B
Using symmetry and the known concentration where the device is in contact with the bath, solve for
A and B and show that:
E(1-(5)
c(r)
= 1 +
бсо Dij
CO
Using the solution above, if a spherical tumor is not vascularized, how large can it grow (radius, in
mm, two significant digits) before the oxygen concentration in the center of the tumor falls to zero?
(This is the maximum size that the tumor can grow without vascularization.)
The concentration of oxygen in the fluid surrounding it is constant at 0.15 mol/m³, the diffusivity of
oxygen in the tumor is 6.9 E-9 m²/s, and the reaction rate of oxygen in the tumor is -0.28
mol/(m3os).
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