Quantitative models of diffusion-controlled adsorption

The quantitative description of adsorption kinetics processes is much more complicated than the use of the simplified models mentioned above. An introduction into the variety of theoretical models and appropriate boundary conditions is given in a recent review (Miller et al. 1994a). The diffusion-controlled model assumes that the step of transfer from the subsurface 

If any flow in the bulk phase is neglected the diffusion equation (4.8) reads 

The transport problem can be solved only after definition of the corresponding initial and boundary conditions. Pick s first law is used as the boimdary condition at the surface located at x=0. It has the following general form 

This condition describes the surfactant flux from the bulk to the interface during adsorption. If the surface concentration T is higher than the equilibrium value Fq a desorption process creates a surfactant flux in the opposite direction. Neglecting again any flow and fluxes other than bulk diffusion, for example surface diffusion, the boundary condition becomes very simple. 

The diffusion problem of a surfactant mixture can be described in an analogous way. The generalised diffusion equation reads 

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