Analytical solution for a linear adsorption isotherm

A simple equation derived by Sutherland (1952) can be used as a first approximation but its range of application is very limited (Miller 1990). The derivation of Sutherland is based on a linear adsorption equation of the form 

The parameter r denotes the interfacial concentration in the equilibrium state of adsorption. The determination of the function exp( )erfc( ) is very complicated and values are obtained either from tables or from calculations via special numerical procedures (described in Appendix 4B). 

As mentioned before, this relation is valid only at very small coverages of the interface. Therefore, either T(t) [and consequently y(t)], has to be calculated numerically from Eq. 

Collocation Solution FOR a Langmuir-Type Adsorption Isotherm 

Recently, the model of diffusion controlled adsorption was solved by a so-called collocation method using the Langmuir isotherm (2.37) (Ziller Miller 1986). If we define a 

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