A biosensor is a device that uses a biological mechanism to aid in the detection of a solute (A) within a mixture. Consider the hemispherical-shaped biosensor tip shown in the figure on page 529. The biosensor consists of two sections. In the first section, an enzyme that recognizes only solute A within the mixture will convert it to product B (i.e., A †’ B) according to a zero-order reaction that is independent on the concentration of A or B (i.e., R_A= €“k, R_B= +k). In the second section, an electrode that recognizes only solute B immediately consumes B at the nonporous electrode surface. The system for analysis is the hemispherical biosensor tip, and the source for A in surround fluid is constant. The gel layer is dilute with respect to reactant A and product B. 

a. Develop the integrated algebraic models for c_A(r), N_A(r) and c_B(r), N_B(r). As part of this analysis, state all assumptions, show development of the differential equations for mass transfer, and state boundary conditions. 

b. Plot out the fluxes N_B at r = R₁ and r = R₂ for various values of zero-order rate constant k (you pick the range for k), using the given values of D_A-gel = D_B-gel = 1.0 · 10^-6 cm²/s, R₁ = 0.2 cm, R₂ = 0.5 cm. Perform the calculations on a spreadsheet.

Transcribed Image Text:

Gel containing enzyme that catalyzes Surrounding well-mixed fluid mixture containing solute A (CAo) but negligible product B Biosensor electrode surface (immediately consumes B) Inert r = R2 nonpermeable barrier r = 0 r = R, Biosensor housing (not part of the system)