THE SIMPLE PROCEDURE OF THE CALCULATION OF DIFFUSION COEFFICIENT FOR ADSORPTION ON SPHERICAL AND CYLINDRICAL ADSORBENT PARTICLES

Abstract

The simple method of the calculation of the diffusion coefficient of an adsorbed phase (De ), based on the analytical solution of Fick's law of diffusion, for adsorption process is presented. Two shapes of the sorbent granules, i.e., spherical and cylindrical ones, are considered, and the adsorption process is assumed to take place in the Henry's region of the isotherm. Adopting the method proposed by Korta on the solution of Fick's law of diffusion, mathematically simple equations are developed to correlate the constant K of the analytical solution with the value of the relative adsorption as well as with the values of the geometrical parameters of the adsorbent granules. Using these simple equations, one can calculate the values of De and avoid, at the same time, mathematically advanced and time-consuming minimization procedure. Moreover, the procedure is likely to become complicated because of difficult mathematical functions and operations occurring in the equations that describe the process, for example, Bessel function or the summation from unity to infinity. The presented simplified procedure is adopted for the results of paracetamol adsorption from water solution on two carbons with different shapes of granules, and it is shown that the obtained values of diffusion coefficients are practically the same as those calculated by means of the exact numerical procedure from the analytical solution.