Rheology-Guided and CFD-Integrated Analysis of Non-Isothermal Gelation Kinetics in a Three-Stage Cooling Die for Soy Protein Concentrate Extrusion

Soy protein concentrate (SPC) undergoes continuous thermal and structural changes during passage through a cooling die, yet these changes are often interpreted using viscosity-based descriptions that do not explicitly account for structural development rate (SDR). This study developed a rheology-guided framework to analyze SPC behavior in a three-stage cooling die by integrating isothermal and non-isothermal rheological characterization with computational fluid dynamics (CFD). SPC samples containing 76, 78, and 80% moisture were evaluated using strain sweep, frequency sweep, viscosity, time sweep, and temperature sweep tests. Lower moisture promoted stronger structure development, higher viscosity, and faster gelation. For the 76% moisture sample, peak SDR increased from 6.66 Pa/s at 50 °C to 22.46 Pa/s at 100 °C, while the time to peak decreased from 937 to 360 s. During non-isothermal cooling, the major structure development occurred in the 80-50 °C interval, where ΔG' reached 4902.54 Pa at 76% moisture. CFD analysis showed that the gelation-kinetics-based model predicted both pressure and extrudate temperature more accurately than the viscosity-based model. Pressure RMSE ranged from 8.57 to 14.43 kPa for the kinetic model, compared with 11.31 to 22.39 kPa for the viscosity model. These results demonstrate that the three-stage cooling die should be interpreted as a coupled thermal, flow, and structure-development domain.