PAT-driven dairy processing: a rheo-Raman-based kinetic model for in-line prediction of milk coagulation dynamics

Area of Science:

• Food Science
• Biophysics
• Chemical Engineering

Background:

• Rennet-induced milk coagulation is crucial in dairy processing.
• Understanding the dynamic behavior of milk constituents during coagulation is essential for process optimization.
• Existing models may not fully capture the complex kinetics and real-time changes.

Purpose of the Study:

• To develop a mathematical model for describing the dynamic behavior of milk constituents during rennet-induced coagulation.
• To predict the temporal evolution of the elastic modulus, a key parameter in industrial applications.
• To enable real-time monitoring of milk coagulation using Raman spectra and rheological data.

Main Methods:

• Analysis of Raman spectra coupled with rheological measurements.
• Multivariate statistical analysis (Principal Component Analysis) to interpret spectral data.
• Development and analytical integration of a system of ordinary differential equations (ODEs).
• Validation using a test sample and coupling with a Kalman filter for real-time estimation.

Main Results:

• A mathematical model was developed predicting the evolution of Raman spectral principal components and elastic modulus.
• The model incorporates an activation function to account for gelation delay.
• Pseudo-kinetic constants and lag times were found to depend on temperature and rennet concentration.
• High prediction performance (R² = 0.9992) was achieved, demonstrating model accuracy.

Conclusions:

• The developed mathematical model accurately describes rennet-induced milk coagulation dynamics.
• The model enables reliable prediction of elastic modulus, crucial for industrial cheese making.
• Integration with a Kalman filter allows for real-time, in-line monitoring of milk coagulation.