Modeling the Kinetics of Potassium Diffusion in Estima Potato under Different Leaching Conditions

Abstract

The diffusion of potassium in potato (Solanum tuberosum) at different leaching conditions was investigated. Two modes of pretreatment of potato samples (cubes and spheres) by preheating to 80°C and leaching at temperatures of 20-80°C were performed using a temperature- and agitation-controlled batch extractor. A Fickian model incorporating the effective diffusion coefficient ( $D_{\text{eff}}$ ), partition coefficient ( $K$ ) between the solute concentration in the potato and medium, and mass transfer coefficient ( $\text{kl}$ ) was developed to simulate and predict the fraction of potassium leached from the potato at any temperature. Results showed significant reduction in activation energies from 92 to 25.02 kJ/mol for cubes and from 75.02 to 13.40 kJ/mol for spheres culminating in higher extraction rates when samples were preheated to 80°C. The $D_{\text{eff}}$ , $K$ , and $\text{kl}$ values obtained were in the range of $0.02-7.33\times {10}^{-9}\hspace{0.17em}\hspace{0.17em}{\text{m}}^2/\text{s}$ , $0.63-8.00\times {10}^{-2}$ , and $\mathrm{0.01333.00}\times {10}^{-4}\hspace{0.17em}\hspace{0.17em}\text{m}/\text{s}$ , respectively. The kinetic parameters showed a change in slope or discontinuity in the gelatinization temperature range as a function of temperature, an indication of a change in the diffusional matrix. The optimum operating conditions were 80°C preheating and leaching at temperatures up to 50°C. The proposed mathematical model offered a satisfactory description of both dynamic and equilibrium mass transfers of potassium by adequately predicting the fraction of potassium from potato cubes and spheres. The present findings could be useful in the pretreatment of potato for renal patients.