Brandani has derived a solution for Nonlinear Equilibrium on a homogeneous surface using the Langmuir isotherm for micrpore controlled particles. In this paper a family of solutions for heterogeneous surfaces is derived using the Toth isotherm which has a heterogeneity parameter t in it. The solution of Brandani when t = 1 is a particular member of the family of solutions

The project novelty is the extension of the literature work of Brandani which covered homogeneous surfaces to all surfaces which basically are heterogeneous in nature. Brandani showed that ZLC experiments for homogeneous surfaces provide satisfactory diffusivities in the long time region of the experiment but that the equilibrium parameters are difficult to determine accurately. In this paper, in determining both the diffusivity and equilibrium parameters for heterogeneous surfaces due caution should be observed. In fact for the heterogeneity parameter t less than 0.5, it is very difficult to determine either diffusivity or equilibrium parameters just using the long time region of the experimental curve.