Introduction & Context
The production of Texturized Vegetable Protein (TVV) via co‑rotating twin‑screw extrusion is a critical process in food engineering for creating meat analogs, and it hinges on the thermomechanical transformation of globular proteins into a homogeneous, viscoelastic melt; therefore, performing a protein denaturation check is essential to verify that the proteins have been properly unfolded without excessive degradation.
Methodology & Formulas
The engineering logic follows a sequential approach: determining the mass balance for moisture conditioning, calculating the volumetric flow rate of the melt, and evaluating the rheological parameters within the die geometry, with all moisture fractions expressed on a wet basis (mass water per mass total); for detailed guidance on the optimal moisture content for puffing, see the dedicated page on optimal moisture content for puffing.
1. Moisture Conditioning: The required water injection rate is determined by the mass balance of the bone‑dry solids feed and the target moisture content, a factor that also influences the starch gelatinization degree; for a detailed methodology see our starch gelatinization degree estimation guide.
\[ \dot{m}_{\text{water}} = \frac{\dot{m}_{\text{dry}} \cdot M_{\text{target}}}{1 - M_{\text{target}}} - \frac{\dot{m}_{\text{dry}} \cdot M_{\text{initial}}}{1 - M_{\text{initial}}} \]
2. Volumetric Flow Rate: Assuming a constant melt density, the volumetric flow rate is derived from the total mass flow:
\[ Q = \frac{\dot{m}_{\text{total}}}{\rho_{\text{melt}}} \]
3. Die Rheology: The apparent shear rate (\(\dot{\gamma}\)) and shear stress (\(\tau\)) are calculated based on the slit die dimensions (width \(w\) and height \(h\)), assuming Newtonian, fully developed laminar flow:
\[ \dot{\gamma} = \frac{6 \cdot Q}{w \cdot h^{2}} \]
\[ \tau = \eta \cdot \dot{\gamma} \]
4. Pressure Drop: The pressure drop (\(\Delta P\)) across the die of length \(L\) is calculated to ensure the system operates within stable limits:
\[ \Delta P = \frac{12 \cdot \eta \cdot L \cdot Q}{w \cdot h^{3}} \]
| Parameter |
Regime / Threshold |
Engineering Significance |
| Moisture Content |
18% - 25% |
Required for lamellar structure; prevents burning or wet extrusion. |
| Barrel Temperature |
160°C - 180°C |
Ensures protein denaturation (>130°C) without thermal degradation. |
| Shear Rate |
> 100 s−¹ |
Minimum threshold for molecular alignment. |
| Shear Stress |
> 100,000 Pa |
Critical driver for lamellar orientation. |
| Pressure Drop |
30 - 100 bar |
Ensures flow stability; prevents surging or insufficient shear. |
The cooling die is essential for creating the fibrous, meat-like structure of TVP. If the temperature is not strictly controlled, the following issues may occur:
- Excessive heat prevents the formation of laminar flow, resulting in a porous or spongy texture rather than distinct fibers.
- Insufficient cooling leads to rapid expansion at the die exit, which compromises the structural integrity and bite quality of the extrudate.
Worked Example: Texturized Vegetable Protein (TVP) Extrusion
Scenario: A co-rotating twin-screw extruder processes defatted soy flour into a lamellar TVP analog. The system uses a cooling slit die to set the textured structure. The following calculations verify that the selected operating conditions produce a stable, high-shear flow capable of generating the required molecular orientation.
- Knowns:
- Bone-dry solids feed rate: \( \dot{m}_{\text{dry}} = 20.0\ \text{kg/hr} \)
- Initial moisture content of flour (wet basis): \( M_{\text{initial}} = 0.08\ (8\%) \)
- Target moisture content of dough (wet basis): \( M_{\text{target}} = 0.20\ (20\%) \)
- Barrel temperature: \( T_{\text{barrel}} = 170.0\ ^\circ\text{C} \)
- Melt density: \( \rho_{\text{melt}} = 1000.0\ \text{kg/m}^3 \)
- Apparent melt viscosity at die entry: \( \eta = 230.4\ \text{Pa·s} \)
- Die dimensions: width \( w = 0.02\ \text{m} \), height \( h = 0.002\ \text{m} \), length \( L = 0.05\ \text{m} \)
-
Moisture Conditioning (Water Injection)
The water already present in the flour (wet basis moisture balance):
\[
\dot{m}_{\text{water,initial}} = \frac{\dot{m}_{\text{dry}} \cdot M_{\text{initial}}}{1 - M_{\text{initial}}} = \frac{20.0 \cdot 0.08}{1 - 0.08} = \frac{1.6}{0.92} = 1.739\ \text{kg/hr}
\]
Total water required in the conditioned dough at the target moisture:
\[
\dot{m}_{\text{water,target}} = \frac{\dot{m}_{\text{dry}} \cdot M_{\text{target}}}{1 - M_{\text{target}}} = \frac{20.0 \cdot 0.20}{1 - 0.20} = \frac{4.0}{0.80} = 5.0\ \text{kg/hr}
\]
Thus, the water injection rate is:
\[
\dot{m}_{\text{water,inject}} = \dot{m}_{\text{water,target}} - \dot{m}_{\text{water,initial}} = 5.0 - 1.739 = 3.261\ \text{kg/hr} \approx 3.26\ \text{kg/hr}
\]
-
Total Mass Flow and Volumetric Flow
Total mass flow entering the die (dry solids + injected water):
\[
\dot{m}_{\text{total}} = \dot{m}_{\text{dry}} + \dot{m}_{\text{water,inject}} = 20.0 + 3.261 = 23.261\ \text{kg/hr}
\]
Volumetric flow rate (assuming incompressible melt):
\[
Q = \frac{\dot{m}_{\text{total}}}{\rho_{\text{melt}}} = \frac{23.261}{1000.0} = 0.02326\ \text{m}^3/\text{hr}
\]
Convert to SI units:
\[
Q = \frac{0.02326}{3600} = 6.461 \times 10^{-6}\ \text{m}^3/\text{s}
\]
-
Shear Rate in Slit Die
For a rectangular slit of width \( w \) and gap \( h \), the apparent shear rate is:
\[
\dot{\gamma} = \frac{6 \cdot Q}{w \cdot h^{2}} = \frac{6 \cdot (6.461 \times 10^{-6})}{0.02 \cdot (0.002)^2}
\]
\[
\dot{\gamma} = 484.6\ \text{s}^{-1}
\]
This exceeds the minimum threshold of \( 100\ \text{s}^{-1} \) for protein alignment.
-
Shear Stress – Driving Force for Orientation
Shear stress generated in the die:
\[
\tau = \eta \cdot \dot{\gamma} = 230.4\ \text{Pa·s} \cdot 484.6\ \text{s}^{-1} = 111{,}652\ \text{Pa}
\]
The value of \( 111{,}652\ \text{Pa} \) (about 1.12 bar) indicates that the stress is above the recommended minimum of \( 100{,}000\ \text{Pa} \) for lamellar texture development.
-
Die Pressure Drop
Pressure drop along the die length, assuming fully developed laminar flow:
\[
\Delta P = \frac{12 \cdot \eta \cdot L \cdot Q}{w \cdot h^{3}} = \frac{12 \cdot 230.4 \cdot 0.05 \cdot (6.461 \times 10^{-6})}{0.02 \cdot (0.002)^3}
\]
\[
\Delta P = 5.583 \times 10^{6}\ \text{Pa}
\]
Converting to bar:
\[
\Delta P_{\text{bar}} = \frac{5.583 \times 10^{6}}{100{,}000} = 55.83\ \text{bar}
\]
This value lies well within the stable operating range of 30–100 bar.
Final Answer
The die pressure drop is 55.83 bar, the shear rate is 484.6 s−¹, and the shear stress is 111,652 Pa. All parameters satisfy the empirical constraints for TVP texturization. The water injection rate is 3.26 kg/hr, and the total mass flow is 23.26 kg/hr.
