Many bio catalytic reactions are carried out with living cells as the bio catalyst. In some processes,

Question:

Many bio catalytic reactions are carried out with living cells as the bio catalyst. In some processes, the cells are immobilized within an agarose gel. However, living cells uniformly distributed within an agarose gel require glucose to survive, and the glucose must diffuse through the gel material to reach the cells. An important aspect of the biochemical system design is the effective diffusion coefficient of glucose (species A) into the cell-immobilized gel. Consider the experiment shown in the figure on page 531, where a slab of the cell-immobilized gel of 1.0 cm thickness is placed within a well-mixed aqueous solution of glucose maintained at a concentration of 50 mmole/L. The glucose consumption within the cell-immobilized gel proceeds by a zero-order process given by R_A= -m = -0.05 mmole/L-min. The solubility of the glucose in both water and the gel are the same€“i.e., the concentration of glucose on the water side of the water-gel interface is equal to the concentration of glucose on the gel side of the water-gel interface. A syringe mounted in the center of the gel carefully excises a tiny sample of the gel for glucose analysis. The measured steady-state glucose concentration at the center of the gel is 4.50 mmole/L.

a. Develop a model, in final integrated form, to predict the concentration profile of glucose within the gel. Specify the boundary conditions, so that the model is truly predictive and is based only on process input parameters, not measured parameters. As part of the model development, state at least three relevant assumptions.

b. Using the model developed in part (a), the known process parameters, and the measured concentration of glucose at the center of the gel, estimate the effective diffusion coefficient of glucose within the cell-immobilized gel.

Living cells in agarose gel RA = m = -0.05 mmol/L-min (1.0 cm thick) Well-mixed Well-mixed glucose solution glucose solu