Enhancing salt and moisture diffusion in beef by ultrasound-assisted tumbling: Insights from mathematical modeling, hyperspectral imaging, and finite element analysis.
Oct 2026· Food Research International· Vol 241, pp.
119712
· 0 citations· 41 references
Medicine
Abstract
This study aimed to explore the influence of ultrasound-assisted tumbling on mass transfer efficiency during beef brining. One-dimensional mathematical modeling for kinetic simulation, two-dimensional hyperspectral imaging for visualization, and three-dimensional finite element analysis for spatial diffusion simulation were respectively adopted to characterize the diffusion dynamics of salt and moisture in beef. Results indicated that ultrasound-assisted tumbling significantly increased the diffusion coefficients of salt and moisture (p < 0.05). Compared with diffusion, Peleg, Azuara, and Zugarramurdi-Lupín models, the Weibull model was identified as the most effective one in predicting the diffusion kinetics of salt and moisture (Rs2 ≥ 0.990, Rm2 ≥ 0.987). The visualization results of two-dimensional hyperspectral imaging and three-dimensional finite element simulation consistently indicated that the distribution of salt and moisture dynamically evolved during diffusion, exhibiting transient and irregular features, thereby reflecting the complex and nonlinear nature of mass transfer in meat. This study provides new insights and approaches for investigating the diffusion behavior of brine in meat products.
This study established a multiscale analytical framework to systematically investigate the mass transfer behavior of NaCl and moisture in chicken breast during ultrasonic-assisted low-temperature braising, as well as the regulatory mechanisms impacting quality evolution. Kinetic analysis demonstrated that ultrasound treatment significantly enhanced NaCl migration during processing, with the NaCl content reaching 1.83 g/100 g after treatment at 600 W for 150 min, representing a 29.8% increase compared with the control. The effective diffusion coefficient (Deff) calculated using Fick's second law increased to (5.69-6.37) × 10-9 m2/s under ultrasonic treatments. Low-field magnetic resonance imaging (LF-MRI) combined with image binarization revealed that ultrasound promoted the penetration of NaCl toward the sample center and improved moisture distribution. The proportion of immobilized water (P21) reached 96.39% at 450 W for 30 min. At the microscopic level, haematoxylin-eosin (HE) staining, and scanning electron microscope-energy dispersive spectroscopy (SEM-EDS) analyses revealed that ultrasound treatment generated microchannels, reducing mass transfer resistance. The resulting spongy structure enhanced moisture retention capacity. COMSOL Multiphysics simulations visualized the spatial and temporal evolution of NaCl and moisture migration, with strong agreement between predicted and experimental values (R2 > 0.97). Moderate ultrasonic treatment (300-450 W) achieved a favorable balance between enhanced salt uptake and reduced moisture loss, resulting in improved texture properties, including decreased shear force and hardness. The study established a correlation framework of "ultrasound transfer-structure response-quality improvement", providing insights into the precise control and quality improvement of novel thermally processed meat products using ultrasound treatment.
Yanzhao Zheng, Jinxue Hou, Jiacheng Chen et al.· Food Research International· 0 citations
Accurate prediction of moisture transfer during drying processes remains challenging. In the present study, a progressive numerical framework was developed to investigate moisture diffusion in ethanol-pretreated beetroot by systematically incorporating increasing levels of physical complexity into Fick’s second law of diffusion. Four one-dimensional formulations were examined, including constant moisture diffusivity, shrinkage under constant diffusivity, moisture-dependent effective diffusivity, and a fully coupled model combining moisture-dependent diffusivity with shrinkage. The methodology was further extended to two dimensions to evaluate the spatial evolution of moisture. The governing equations were solved using an implicit Crank–Nicolson finite difference scheme, while shrinkage was introduced through a time-dependent computational domain and moisture-dependent diffusivity was implemented as a variable transport property. The predicted moisture distributions demonstrated that incorporating shrinkage reduced the diffusion path length, whereas moisture-dependent diffusivity provided a more realistic representation of the transport resistance. The coupled formulation produced the most physically consistent description of moisture migration by simultaneously accounting for both mechanisms. Furthermore, the two-dimensional simulations provided additional insight into the spatial redistribution of moisture. The proposed framework establishes a physically based interpretation of the enhanced drying behavior observed after ethanol pretreatment and provides a flexible computational methodology for analyzing moisture transfer.
Christos Sarakinou, A. Goula· Applied Sciences· 0 citations
This study investigates the convective hot-air drying behavior of in-shell hazelnuts under controlled operating conditions, with emphasis on drying kinetics, thin-layer modelling, heat and mass transfer characteristics, and pressure drop behavior within the hazelnut bed. The experiment was performed in a laboratory dryer set to 50–60 °C and 1.5–2.1 m s⁻¹ airflow. The temporal evolution of moisture content, drying rate, and moisture ratio was experimentally determined, and the effective moisture diffusivity was evaluated using Fick’s second law of diffusion. The results showed that internal moisture diffusion governed the drying process. Higher drying air temperature and air velocity reduced the drying time and enhanced the drying rate. Effective moisture diffusivity increased with temperature. The two-term model provided the best agreement with the experimental data, efficient R² values between 0.9770 and 0.9953, RMSE values between 0.0178 and 0.0384, and X² values between 5.26 × 10− 4 and 2.90 × 10− 3. The coefficient of heat transfer was between 131 and 180 W m⁻² K⁻¹, governed by air velocity rather than temperature. The pressure drop values predicted by the Ergun equation showed good agreement with the experimental measurements, with deviations generally remaining below approximately 8% under the investigated airflow conditions.
Emel Çelik, N. Parlak, Z. Meral et al.· Heat and Mass Transfer· 0 citations
Accurate characterization of moisture migration within rough rice kernels during drying is essential for improving energy efficiency and mitigating fissure formation. This study presents a physics‐based investigation of moisture transport in rough rice subjected to combined hot‐air and far‐infrared (FIR) drying under different inlet air temperatures and FIR intensity levels. Spatiotemporal moisture distributions within the kernel were quantified by solving Fick's second law using the finite element method. For homogeneous kernels with uniform temperature and moisture, the effective moisture diffusivity (
D
eff
) ranged from 0.89 to 7.39 × 10
−11
m
2
s
−1
and followed a modified Arrhenius‐type relationship, incorporating both kernel temperature and FIR intensity. Introducing moisture‐dependent diffusivity, represented as a third‐degree function of moisture ratio, enhanced predictive accuracy and revealed strong temporal variability, with elevated diffusivities during early drying stages followed by asymptotic behavior at lower moisture levels. To account for kernel structural heterogeneity, an inhomogeneous three‐layer model representing the endosperm, bran, and husk was developed. Layer‐specific diffusivities exhibited distinct magnitudes and transport resistances (
D
1
= 0.31–2.73 × 10
−10
,
D
2
= 1.21–9.23 × 10
−12
, and
D
3
= 2.37–20.34 × 10
−11
m
2
s
−1
), each following modified Arrhenius‐type behavior. After decoupling thermal and FIR effects, remaining diffusivity variations were attributed solely to intrinsic layer properties, with diffusivity magnitudes decreasing sequentially from the endosperm to the husk and bran layers. These results provide a physically consistent framework for describing moisture transport in rough rice by coupling moisture‐dependent, temperature‐sensitive diffusivity with kernel structural heterogeneity under combined hot‐air and FIR drying.
Roh‐allah Motazedian, A. Rafati, Azharul Karim et al.· Journal of food process engi...· 0 citations
Thermal conductivity is a critical parameter that determines the thermal response, atomization efficiency, and release behavior of natural porous composites in heating-type aerosol generators. Although moisture and glycerol significantly affect the pore structure and heat transfer pathways of natural porous media, their coupling regulation mechanism at the molecular scale remains unclear. Based on the actual chemical components of natural porous composites (cellulose, hemicellulose, and lignin), a multi-component molecular model was established in this study. Molecular dynamics simulations were conducted under 36 working conditions with varying moisture content (0%–20%) and glycerol content (0%–20%). The results reveal that moisture serves as the dominant factor, which monotonically increases thermal conductivity by constructing continuous heat conduction pathways, with a maximum increment of 208.6%. Glycerol plays a secondary role: moderate addition reduces interfacial thermal resistance, while excessive addition induces molecular agglomeration and intensifies phonon scattering. Under dry conditions, the thermal conductivity presents a unimodal variation trend, and the optimal glycerol content ranges from 8% to 16%. A prominent synergistic enhancement effect exists between moisture and glycerol. When both contents reach 20%, the thermal conductivity peaks at 0.6185 W/(m·K). This study clarifies the heat transfer mechanism of natural porous composites applied in heating-type aerosol generators at the molecular scale, providing theoretical guidance for matrix formula design, aerosol additive optimization and thermal response performance regulation.
Quan Zhang, N. Gao· Journal of Physics, Conferen...· 0 citations
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