Manipulation of the Model Equations

Due to the simplicity of this illustrative problem and of the linear equilibrium isotherm Y = aX+b we can reduce the two coupled two point boundary value differential equations (6.127) to one differential equation as follows. 

Thus by the product rule of differentiation, used in reverse, we have 

Using this initial condition in equation (6.128) we find the value of C as 

Substituting the value of Y in equation (6.129) into equation (6.126) we finally get 

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A schematic diagram showing the details of the proposed model for the equivalent sphere representing the microbial floe is presented in Figure 6.34. A number of simplifying assumptions are implicit in the lengthy manipulation of the model equations. 

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