Modeling Super-Diffusive Drying Behavior of Laser-Perforated Grapes Using Fractional Calculus: A Comparative Study with Alkaline Dipping

Abstract Drying large grape varieties is limited by low mass transfer rates, resulting in long drying times. This study evaluated blue laser micro-perforation as a chemical-free pretreatment alternative to alkaline dipping for drying large Kavacık grapes ( Vitis vinifera L. cv. Alphonse Lavallée), focusing on mass transfer behavior. Drying was conducted at 60, 70, and 80 °C with an air velocity of 2.5 m/s. The effects of pretreatment on drying behavior, drying mechanism, and selected physicochemical properties were examined. Moisture diffusion was modeled using both Fick’s second law and an anomalous (non-Fickian) diffusion model based on fractional calculus. The non-Fickian model provided a superior fit to the experimental data ( R 2 > 0.99; χ 2 < 0.008; RMSE < 0.01) under all drying conditions. The effective moisture diffusivity ( D eff ) of laser-treated samples ranged between 1.42 × 10 −10 and 7.79 × 10 −10 m 2 /s and was lower than that of untreated samples (3.22 × 10 −10 –12.80 × 10 −10 m 2 /s), indicating super-diffusive mass transport behavior ( α > 1), where α represents the anomalous diffusion exponent. Drying temperature significantly enhanced D eff in both pretreatments, such that higher drying temperatures resulted in increased effective moisture diffusivity due to enhanced molecular diffusion and reduced internal resistance. Physicochemical properties, including water activity, rehydration ratio, pH, titratable acidity, color (ΔE), and shrinkage ratio, were not significantly affected by the type of pretreatment or drying conditions. Laser micro-perforation achieved drying efficiency and quality retention comparable to alkaline dipping without chemical additives, demonstrating strong potential as a sustainable pretreatment for industrial-scale fruit drying. Graphical Abstract