Analysis of the General Situation

We now return to the master differential equation, Eqn. 107. We require an analytical solution to this nonlinear problem to derive an expression for the flux and hence an expression for the current. Much of the previous work described in the literature employed a numerical finite-difference approach to this problem, although Albery and coworkers and Lyons et presented an approximate analytical 

We return to Eqn. 107 and multiply both sides of the expression by du/dx , note the identity 

Integrating this expression and noting that when = 0, dujdx = 0, we obtain 

We also note that m = 1 when X Hence from Eqn. 130 we obtain 

This is a rather complex expression for the flux, and it is valid for thick films and all values of the substrate concentration. When a 1, 

---

Many of the corresponding numerical results are presented here. These values are used as a basis for a comparison of the merits of the different methods. An analysis of the general situation regarding the quantum mechanical approach to biochemical problems is discussed in section D. 

---