Determination of kinetic parameters for the adsorption of a protein on porous beads using symbolic computation and numerical Laplace inversion

The work deals with the determination of the kinetic parameters for the adsorption of human serum albumin (HSA) onto spherical resin beads (Blue Sepharose CL-6B) in a batch stirred tank. By noting the practically linear equilibrium adsorption isotherm during experimental conditions and assuming that the adsorption rate is very rapid compared with the diffusion in the adsorbent particles, the differential equations describing the process with the appropriate boundary conditions are solved in the Laplace domain thus facilitating the expression of the bulk concentration of protein in the tank in terms of the unknown kinetic parameters and the Laplace variable. In order to cheaply and accurately invert the Laplace transform (which cannot be done analytically), we employ IMN approximants using . This gives an explicit expression of the bulk concentration as a function of time and the unknown parameters. Subsequent nonlinear regression facilitates rapid determination of the desired kinetic parameters, viz., the film transfer coefficient, kf; the effective diffusion coefficient, De, and the modified diffusion coefficient D. The values obtained are in agreement with those in the literature.