Solute diffusion coefficient in the internal medium of a new gel based controlled release fertilizer

Abstract

The diffusion of solutes in a new controlled release device was investigated and in situ measurements of constant and variable diffusion coefficients were obtained. The new controlled release device consists of a dry mixture of fertilizer and gel forming thickener contained in a nonpermeable coating having at least one opening. Water penetrates into the device through the opening, forms a gel and dissolves the fertilizer, which is then released by Fickian or non-Fickian diffusion mechanisms. Based on measurements of the penetration of water and the dissolution of fertilizer, the pseudo-steady state transport equation was solved and the solute diffusion coefficient was calculated. The computation of the diffusion coefficient was possible solely because a dual boundary condition exists at the dissolution front. An analytical solution was developed assuming a constant diffusion coefficient. A numerical solution was obtained for the case where the diffusion coefficient is concentration dependent. Two thickeners were tested: sodium carboxymethylcellulose (Na-CMC) and sodium polyacrylamide (Na-PAM). It was found that the solute diffusion mechanism in Na-CMC gels is Fickian-like and can be approximated by a constant diffusion coefficient. The solute diffusion in Na-PAM gels showed non-Fickian behavior and was estimated numerically using the variable diffusion coefficient. For comparison with the theoretical solutions, a dialysis cell was used to simulate the conditions in the gel formed inside the device and to evaluate the effects of thickener concentration on the diffusion coefficient. Reasonable agreement was found between the pseudo-steady state solutions and the dialysis cell experimental results.