3. (15 points) Living cells homogeneously distributed (immobilized) with an agarose gel require glucose to survive. An important aspect of the biochemical system design is the effective diffusion coefficient of glucose (A) into the cell- immobilized gel. Consider the experiment shows below where a slab of the cell-immobilized gel of 1.0cm thickness is placed within a well-mixed aqueous solution of glucose maintained at a concentration of 50 mmol/L. The glucose consumption within the cell-immobilized gel proceeds by a zero-order process given by R₁ = -0.05 mmol/(L min). The solubilities of glucose in both the water and the gel are the same; that is, the concentration of the glucose on the water side of the water-gel interface is equal to the concentration of the glucose on the gel side of the water gel interface. A syringe is mounted at the center of the gel carefully excises a tiny sample of the gel for glucose analysis. A Well mixed solution Constant concentration 50nmol/L Living cells in agarose gel R = -0.05mmol/cm³min 1.0cm thick Well mixed solution Constant concentration 50nmol/L =--= Center of gel a) Develop a model for the steady state concentration profile in the slab. Assume that the diffusion coefficient of A in the gel is the same as the diffusion coefficient of A in water. b) Plot the concentration as a function of position in the slab. c) What is the concentration at the centerline (measured by the syringe)?

Curren'S Math For Meds: Dosages & Sol

11th Edition

ISBN:9781305143531

Author:CURREN

Publisher:CURREN

Chapter13: Dimensional Analysis/units Conversion

Section: Chapter Questions

Problem 1.3P

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Transcribed Image Text:3. (15 points) Living cells homogeneously distributed (immobilized) with an agarose gel require glucose to survive. An important aspect of the biochemical system design is the effective diffusion coefficient of glucose (A) into the cell- immobilized gel. Consider the experiment shows below where a slab of the cell-immobilized gel of 1.0cm thickness is placed within a well-mixed aqueous solution of glucose maintained at a concentration of 50 mmol/L. The glucose consumption within the cell-immobilized gel proceeds by a zero-order process given by R₁ = -0.05 mmol/(L min). The solubilities of glucose in both the water and the gel are the same; that is, the concentration of the glucose on the water side of the water-gel interface is equal to the concentration of the glucose on the gel side of the water gel interface. A syringe is mounted at the center of the gel carefully excises a tiny sample of the gel for glucose analysis. A Well mixed solution Constant concentration 50nmol/L Living cells in agarose gel R = -0.05mmol/cm³min 1.0cm thick Well mixed solution Constant concentration 50nmol/L =--= Center of gel a) Develop a model for the steady state concentration profile in the slab. Assume that the diffusion coefficient of A in the gel is the same as the diffusion coefficient of A in water. b) Plot the concentration as a function of position in the slab. c) What is the concentration at the centerline (measured by the syringe)?

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