Living cells immobilized within an agarose gel requires glucose to survive. An important aspect of the biochemical system design is the effective diffusion coefficient of glucose into the agarose gel itself, which you may consider as a homogeneous material that is mostly liquid water. Consider the experiment that is shown below, where a slab of the agarose gel of 1.0 cm thickness is placed within a well-mixed aqueous
solution of glucose maintained at a concentration of 50 mmol/L, which is relatively dilute. The solubility of the glucose in water is equal to the solubility of glucose in the gel.
A syringe mounted at the center of the gel carefully excises a tiny sample of the gel for glucose analysis. Initially, there is no glucose in the gel. However, after 42 h, the measured concentration of glucose in the gel at the sampling point is 48.5 mmol/L.
a. What is the general differential equation for mass transfer for this process in terms of concentration cA? Propose reasonable boundary/initial conditions for this equation. List three assumptions made in obtaining this equation.
b. Based on the measurements provided above, what is the effective diffusion coefficient of glucose into the gel?
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