Introduction
Milk, one of the most nutritious food sources, is rich in protein, fat, vitamins, and minerals, making it an essential component of human diets. However, raw milk provides an ideal environment for microbial growth due to its high moisture and nutrient content, leading to rapid spoilage and potential health risks if not properly processed. Traditional thermal pasteurization, the standard method for ensuring microbial safety and extending shelf life, often results in uneven heat distribution, causing degradation of heat-sensitive compounds and compromising sensory and nutritional quality. These limitations have driven the search for non-thermal alternatives. Hydrodynamic cavitation emerges as a promising, innovative approach, generating localized bubble formation and collapse that produce pressure shocks capable of disrupting microbial structures without causing an overall temperature increase, thereby preserving desirable food properties. Oscillatory flow reactors, particularly single-orifice designs, excel at creating controlled cavitation and enhanced mixing, even at low Reynolds numbers, through reciprocating fluid motion and specialized baffle geometry. Turbulent kinetic energy (TKE) is a key parameter that determines cavitation intensity, mixing efficiency, and microbial inactivation efficacy. Computational Fluid Dynamics (CFD) combined with Response Surface Methodology (RSM) provides a powerful tool for modeling flow dynamics and optimizing reactor geometry to maximize TKE. This study aims to optimize a single-orifice oscillatory flow reactor using CFD-RSM for non-thermal pasteurization of milk. The primary objectives are to achieve maximum TKE through geometric and operational parameter optimization, enhance hydrodynamic cavitation for microbial inactivation, and maintain milk's nutritional and sensory qualities, offering a sustainable alternative to thermal methods.

Material and Methods
This study employed a computational approach integrating CFD and RSM for reactor optimization. A single-orifice oscillatory-flow reactor with annular baffles was modeled in COMSOL. Turbulence was simulated with the standard k-ε model under time-dependent conditions. Milk was treated as the working fluid (density: 1030 kg/m³; viscosity: 0.002 Pa·s). Key independent variables included baffle-to-reactor diameter ratio (d₀/D: 0.4–0.8), oscillation frequency (5–15 Hz), baffle spacing (10–20 mm), and baffle orifice diameter (3–7 mm). Box-Behnken design in Design-Expert software generated experimental runs to optimize maximum and average TKE. For microbial validation, fresh milk samples were sterilized, inoculated with E. coli, and processed through the reactor under optimized conditions derived from simulations. Bacterial reduction was assessed via plate counting on MacConkey agar. Milk samples were sourced locally and processed in a controlled laboratory setting. Inoculation and plating were performed in triplicate for accuracy. Optimization relied on 29 RSM runs.
Results and Discussion
CFD-RSM optimization revealed that oscillation frequency exerted the strongest influence on TKE, with significant positive linear and quadratic effects. A higher frequency (15 Hz) markedly increased both the maximum and average TKE by enhancing vortex formation, increasing shear rates, and intensifying oscillatory motion. In contrast, increasing baffle-to-reactor diameter ratio (d₀/D from 0.4 to 0.8) and baffle orifice diameter (3–7 mm) generally reduced TKE by diminishing flow constriction and weakening cavitation intensity at orifice regions. Baffle spacing exerted a mixed influence: closer spacing (10 mm) substantially increased maximum TKE via localized turbulence intensification, whereas wider spacing (up to 20 mm) slightly improved average TKE through enhanced axial dispersion and a more uniform energy distribution. The optimal configuration was determined as d₀/D = 0.4, oscillation frequency = 15 Hz, baffle spacing = 10 mm, and baffle orifice diameter = 3 mm. Under these conditions, CFD simulations predicted a maximum TKE of 0.36683 m²/s², concentrated primarily at the baffle orifices where rapid acceleration triggers bubble collapse, and an average TKE of 0.071449 m²/s², representing a substantial improvement over non-optimized geometries. Contour visualizations confirmed peak TKE localization in orifice zones, validating effective cavitation generation. Microbial validation experiments demonstrated strong inactivation efficacy. Milk samples processed under optimized conditions showed a significant logarithmic reduction in Escherichia coli counts, which was directly correlated with elevated TKE levels. Cavitation-induced mechanisms, including high-pressure shocks (megapascal range), high-velocity microjets (>100 m/s), extreme shear stresses, and localized production of reactive oxygen species (•OH radicals) disrupted bacterial cell membranes, caused cell lysis, and induced DNA damage without bulk temperature rise. Quality analyses confirmed preservation of key milk attributes. Contents of fat, protein, lactose, and solids-non-fat remained statistically comparable to untreated controls, with negligible changes in pH and overall acidity. No significant degradation of heat-sensitive components was observed, addressing critical limitations of conventional thermal pasteurization such as whey protein denaturation, Maillard reactions, and partial vitamin loss. Regression models exhibited excellent predictive performance (R² > 0.95), underscoring methodological robustness. The optimized single-orifice oscillatory flow reactor thus generates intense hydrodynamic cavitation sufficient for effective non-thermal pasteurization, with TKE established as a reliable indicator of microbial inactivation potential and process efficiency.
Conclusions
This study successfully optimized a single-orifice oscillatory flow reactor using computational fluid dynamics and response surface methods (CFD-RSM), maximizing turbulent kinetic energy to drive hydrodynamic cavitation for non-thermal milk pasteurization. The identified optimal parameters (d₀/D = 0.4, 15 Hz frequency, 10 mm baffle spacing, 3 mm orifice diameter) yield high TKE, enabling effective inactivation of Escherichia coli through turbulent flow, mechanical shear, pressure shocks, and reactive species generation, without compromising milk's compositional quality. The approach offers a sustainable, energy-efficient alternative to thermal methods, preserving heat-sensitive nutrients and sensory properties while ensuring microbial safety. By linking TKE directly to cavitation intensity and inactivation efficacy, this work provides a scalable framework for industrial adoption in dairy processing. Future research should focus on pilot-scale validation, energy consumption analysis, and extension to other liquid foods with varying viscosities and microbial loads. Ultimately, this technology advances non-thermal processing paradigms, contributing to higher-quality, safer dairy products.