4.3.1. Amperometric Biosensor

Glucose Biosensor. Glucose biosensor using glucose oxidase is used as an example. The reaction and the transducer used are:

Model geometry

Assumptions. To write mass balance equations for the reaction and to set up boundary conditions, simplifying assumptions are necessary. Here, we will consider a very simple case for illustration purpose.

1. The outer membrane offer no mass transfer resistance to the substrate (glucose) or the product (H2O2).
2. No oxygen limitation in the enzyme layer.
3. The substrate concentration at x=d is the same as that of bulk (no mass transfer resistance of the liquid film)
4. The enzymes are homogeneously distributed in the immobilized layer.
5. The inner membrane is extremely thin and offers no mass transfer resistance to the product or the substrate.
6. The pores of the outer membrane is sufficiently large that it offers no mass transfer resistance to the substrate.
7. One dimensional transport.

Differential Mass Balance. Unsteady state, differential mass balance is written for both the substrate glucose and the product (H2O2).

For the substrate (glucose):

For the product (H2O2):

Boundary Conditions. To solve these equations, boundary conditions are necessary.

For the substrate:

For the product.

* When liquid film resistance is considered, replace Eqs. (6c) and (7c) by:

Steady State Case When[S] << KM. Since the solution process is complicated for the full unsteady state case, we will only solve the steady case when [S] << KM

For the substrate (glucose):

where

For the product (H2O2):

Solution of Eq. (5) with BCs (7a) and (7b):

Substituting Eq. (13) in Eq. (11), and solving with BCs (12a) and (12b):

Sensor signal output will become: