Fractional calculus-based anomalous diffusion modeling and statistical optimization of microwave drying of ultrasound pretreated potatoes

Potato (Solanum tuberosum L.) is a staple food widely consumed worldwide. Drying is an effective technique to extend its shelf life and create various products. This study optimizes the microwave drying of ultrasound-pretreated potatoes using response surface methodology. An anomalous diffusion model based on fractional calculus was utilized to analyze the drying kinetics. The model fitted the experimental data well (R2 > 0.99, RMSE < 0.0276, and χ2 < 0.0138), revealing super-diffusive behavior with fractional order (α) values ranging from 1.30 to 1.71. This study optimizes the microwave drying process in terms of maximizing the effective diffusivity (Deff) of ultrasound-pretreated potatoes. The effective diffusivity (Deff) coefficients varied between 2.93 × 10−10 and 12.59 × 10−10 m2/s. Optimization results identified the conditions maximizing Deff as 2 mm slice thickness, 90% microwave power, and 5.86% salt concentration. Under these optimum conditions, the dried potatoes exhibited a rehydration ratio (RR) of 4.41 ± 0.22, color values of L*= 54.33, a*= 5.32, b*= 30.62, and a salt content of 3.39%. The results demonstrate that ultrasound pretreatment in salt solution effectively enhances the microwave drying efficiency of potatoes.