Solvent impregnated resins (SIR) as extractants evenly dispersed in a solid polymeric medium are used to separate spiramycin

a macrolide antibiotic. In this paper a particle-diffusion control mathematical model based on linear adsorption isotherm on the inner surface of SIR is developed and its analytical solution under the condition of finite fluid volume can be expressed as follows: where u(t) is referred to as equilibrium fraction of spiramycin

sn are the roots of the equation: snctg sn = 1 + sn2/(3ω)

τ is dimensionless time

and ω is a characteristic constant depending on the properties of both SIR itself and the bulk solution of spiramycin. Freundlich adsorption isotherm is also used for the differential equation of diffusion in order to modify the linear type isotherm and its numerical solution is calculated by using finite difference scheme in steps of time and radius. Batch experimental results showed good agreement of the theoretical bulk spiramycin concentration history calculated from the analytical solution with the real values measured. The effective diffusion coefficients of spiramycin were estimated in the range of 3.7× 10-12-29.4 × 10-12 m/s for Amberlite XAD-4 resin impregnated with amyl acetate. The differences between analytical solutions with respect to linear isotherm and the relevant numerical solutions with respect to nonlinear isotherm were within the range of experimental errors indicating that the assumption of linear isotherm is a good approach to the practical process.