Combined ANFIS and numerical methods to reveal the mass transfer mechanism of ultrasound-enhanced extraction of proteins from millet

Millet protein, as a promising plant-based protein substitute source, is an excellent basis for essential amino acids compared to commonly consumed staple grains. Compared with the traditional extraction process, ultrasound has been used to enhance the extraction efficiency of various plant-based proteins. To reveal the mechanism of ultrasound-enhanced extraction of proteins, adaptive neuro-fuzzy inference system (ANFIS) algorithm and numerical simulation based on Fick’s law were applied to illustrate the mass transfer behavior of millet proteins under different ultrasonic conditions including solid–liquid ratios (S/L ratios), pH and acoustic energy density levels (AED). The results showed that AED dominated the changes in effective diffusion coefficient ($D_e$), showing a positive correlation relationship (p < 0.05). Specifically, when the AED was 47.07 W/cm², the $D_e$ value increased by 95% compared to that of 23.47 W/cm². Meanwhile, the ANFIS model successfully predicted protein yields across all investigated parameters, achieving a coefficient of determination (R²) greater than 0.97. This model also elucidated the interactions among four critical factors, among which pH and S/L ratios were the main factors affecting protein yield. Concerning the ultrasonic cavitation bubble dynamics, the bubble collapse efficiency enhanced with an increase in AED, and therefore high AED ultrasound can significantly enhance the cavitation effect. Additionally, the results of the yields and physical properties of millet protein also indicated that in contrast with the traditional extraction methods, the ultrasound impactfully improved extraction yield (by 165%), and combined with pH condition, it decreased the protein particle size (from 813.55 nm to 299.30 nm) without altering the molecular weight distribution. This study offers a novel perspective on the mechanism underlying ultrasound-enhanced protein extraction, drawing upon principles of ultrasonics and extraction processes. The insights gained can serve as a foundation for the food industry to upscale the extraction process, potentially enhancing efficiency and yield.