Consider a spherical gel bead containing a bio catalyst uniformly distributed within the gel. Within the gel bead, a homogeneous, first-order reaction A †’_k1D is promoted by the bio catalyst. The gel bead is suspended within water containing a known, constant, dilute concentration of solute A (c_Aˆž).
a. Define the system, and identify the source and the sink for the mass-transfer process with respect to reactant A. List three reasonable assumptions for this process. Then, using the €œshell balance€ approach, develop the differential material balance model for the process in terms of concentration profile c_A. State all boundary conditions necessary to completely specify this differential equation.
b. The analytical solution for the concentration profile is given by 

What is the total consumption rate of solute A by one single bead in units of µmol A per hour? The bead is 6.0 mm in diameter. The diffusion coefficient of solute A within the gel is 2 · l0^-6 cm²/s, k₁ is 0.019 s^-1, and C_Aˆž is 0.02 µmole/cm³. Differentiate the relationship for c_A(r) with respect to r, then estimate the flux N_A at r = R.

Transcribed Image Text:

R sinh(r/k1/DAB) СА(r) 3 САю r sinh(R/k1/DA