Film-surface diffusion during the adsorption of acid dyes onto activated carbon

A mass transport model has been developed and applied to the adsorption of three acid dyes onto activated carbon in three single component systems. The mass transfer model is based on two rate controlling mass transfer steps, namely external film mass transfer and homogeneous solid-phase surface diffusion (HSD). Almost all previous film-HSD models have been based on numerical solutions to the diffusion equation using orthogonal collocation or Crank-Nicolson finite difference solutions. However, in the present model a semi-analytical solution to the solid surface diffusion equation is presented, yielding a sophisticated solution of the differential equations. The solutions provide a good correlation between the experimental concentration-time decay curves by incorporating the Langmuir equilibrium isotherm to describe the solid phase surface dye concentrations. However, the surface diffusivities show a dependence on the carbon particle surface coverage and these diffusivities have been correlated using a Darken relationship.