Compute viscosity curves using Carreau-Yasuda and power-law models for common polymers. Calculate gate pressure drop and cooling time to support early-stage injection molding CAE studies.
Material & Model
Polymer Preset
Viscosity Model
Model Parameters
Zero-Shear Viscosity η₀ (Pa·s)
Pa·s
Relaxation Time λ (s)
s
Flow Index n
Yasuda Parameter a
Gate & Part Parameters
Gate Radius R (mm)
Gate Length L (mm)
Flow Rate Q (cm³/s)
cm³/s
Part Thickness t (mm)
Results
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η at Design Point (Pa·s)
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Gate ΔP (MPa)
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Cooling Time (s)
Viscosity Curve (log η vs log γ̇)
Temperature Dependence (3 Polymers)
Zero-shear viscosity vs melt temperature ±40°C (Arrhenius approximation)
What exactly is a viscosity curve, and why does it matter for something like a plastic bottle?
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Basically, a viscosity curve shows how "thick" or "runny" a polymer melt is under different processing forces. In practice, when you inject plastic into a mold, the force (shear rate) changes dramatically. For instance, in the thin neck of a bottle, the plastic gets stretched fast and its viscosity drops—it thins out. That's why we need models like Carreau-Yasuda. Try selecting the "Polypropylene" preset above and watch how the curve changes with shear rate.
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Wait, really? So the "Flow Index n" in the simulator controls how much it thins? What does a value of 0.3 versus 0.7 actually mean?
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Exactly! The flow index n is the power-law exponent. A value of 0.3 means the polymer is very "shear-thinning"—its viscosity plummets even at low shear rates, which is great for filling intricate molds. A value of 0.7 means it's less sensitive to shear, behaving more like a simple fluid. A common case is PVC (n ~ 0.3) vs. some polycarbonates (n ~ 0.7). Move the "Flow Index n" slider in the simulator and see how the slope of the curve changes dramatically.
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Okay, I see the curve. But how do we use this to design a real mold? What's the connection to "Gate Pressure Drop"?
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Great question! The pressure drop tells you how much pump pressure you need to push the melt through the narrow gate into the mold cavity. If the pressure is too high, you might get flash or need an overly expensive machine. The simulator calculates this using the viscosity at the shear rate in your gate. For example, try increasing the "Gate Radius R". You'll see the pressure drop decrease because there's less resistance in a wider channel. This is critical for balancing mold filling.
Physical Model & Key Equations
The Carreau-Yasuda model describes how polymer viscosity changes over a wide range of shear rates, capturing the zero-shear plateau, the shear-thinning region, and the transition between them.
η: Viscosity (Pa·s) η₀: Zero-shear viscosity – the viscosity at very low flow rates. λ: Relaxation time – dictates when shear-thinning begins. ṙ: Shear rate (1/s) – the speed gradient within the flow. n: Flow index – power-law exponent; lower n means more shear-thinning. a: Yasuda parameter – controls the sharpness of the transition zone.
For pressure drop in a cylindrical gate (a common simplification in injection molding), the power-law form is often used for calculation, where the consistency coefficient (m) is derived from the Carreau-Yasuda model at the relevant shear rate.
$$\Delta P = \frac{2(3n+1)}{n \pi}\left( \frac{Q}{R^3} \right)^n m L$$
ΔP: Pressure drop across the gate (Pa). Q: Volumetric flow rate (m³/s). R: Gate radius (m). L: Gate length (m). m: Consistency coefficient (Pa·sⁿ).
This equation shows how pressure is highly sensitive to gate radius (R³ in the denominator) and the non-Newtonian nature of the polymer (through n and m).
Frequently Asked Questions
The power-law model is a simplified model that only handles high shear rate regions, and its accuracy in low shear rate regions is poor. The Carreau-Yasuda model can continuously calculate viscosity from low to high shear rates, so for injection molding analysis that covers high shear rates at the gate to low shear rates inside the cavity, the Carreau-Yasuda model is recommended.
η₀ is often listed in the data sheet of the polymer in its molten state. A guideline for λ is the reciprocal of the shear rate (1/γ̇) at which viscosity begins to decrease. If unknown, start with η₀ as a measured value and λ around 0.01 to 1 second, then adjust to match the actual flow length and pressure loss of the machine.
The main causes are discrepancies between the measured and set values of resin temperature or mold temperature, or simplification of the flow channel cross-sectional shape. In particular, if the viscosity reduction due to shear heating at the gate is not considered, the pressure loss will be overestimated. Additionally, setting the Yasuda exponent a too small can make the transition too steep, potentially deviating from actual behavior.
Cooling time mainly depends on the thermal diffusivity of the resin, mold temperature, and product wall thickness. This tool performs a simple one-dimensional heat conduction calculation based on the set difference between melt temperature and mold temperature, as well as the thermal diffusivity (material constant). Since cooling time increases in proportion to the square of the wall thickness, uniform wall thickness is important during the design stage.
Real-World Applications
Injection Molding Process Window Definition: Engineers use these curves to define the allowable injection speeds and pressures for a given material and part. Setting the injection speed too low can cause the melt to freeze prematurely; too high can cause degradation from excessive shear heat.
Gate and Runner System Design: The calculated pressure drop is critical for designing balanced runner systems in multi-cavity molds. It ensures all cavities fill at the same time and pressure, preventing defects like short shots or overpacking in specific cavities.
Material Selection and Substitution: When switching polymer grades or suppliers, engineers overlay viscosity curves to ensure the new material will behave similarly in the existing mold. A significant shift in the curve could require retooling the mold.
Predicting Wear on Machine Components: High viscosity at processing shear rates leads to higher pressure and stress on injection screws, check rings, and mold gates. This analysis helps predict maintenance schedules and component life.
Common Misconceptions and Points to Note
When starting with this tool, there are several pitfalls that newcomers to CAE often encounter. The first is understanding that "the parameters for preset materials are not absolute constants." For example, even a material like "PC" can have vastly different viscosity characteristics depending on the manufacturer and grade (high-flow, flame-retardant, etc.). The tool's preset values are merely representative. It's crucial to compare them with the viscosity curve from your actual molding material's datasheet and be prepared to fine-tune λ and n if necessary.
The second point is overlooking the assumptions behind the gate pressure loss calculation. The formula assumes "fully developed laminar flow in a circular channel." This means it does not account for entrance effects at the actual gate constriction or the influence of a frozen layer (frozen skin) at the wall due to mold temperature. You should consider the calculated value as a theoretical minimum pressure loss; practical wisdom suggests applying a safety margin of 1.5 to 2 times this value.
The third point is not over-relying on the cooling time calculation. The tool's cooling time is a theoretical calculation based solely on heat conduction to a mold wall at constant temperature. However, in actual molding, complex factors like cooling channel layout and flow rate, or resin crystallization heat, come into play. Use this calculated value as a reference "to grasp the order of magnitude for cooling." For instance, if the calculation yields 10 seconds, the actual cycle time will often be around 12-15 seconds—understand it in terms of such correlations.
Enter zero-shear viscosity (η₀) in Pa·s using valEta0Num or sliderEta0—typical range 10–10,000 Pa·s for thermoplastics like PET or PP.
Set the natural time constant (λ) in seconds via valLamNum or sliderLam; for injection molding, use 0.001–1 s depending on molecular weight.
Define power-law index (n) between 0.2–1.0 using valNNum or sliderN; lower values indicate stronger shear-thinning behavior.
Adjust Carreau-Yasuda exponent (a) via valANum or sliderA, typically 0.5–2.0, to control transition smoothness from Newtonian to power-law regimes.
Simulator calculates viscosity at your design shear rate, gate pressure drop across a 2 mm diameter orifice, and cavity cooling time assuming 3 mm wall thickness and mold temperature 60°C.
Worked Example
For ABS resin at 220°C: set η₀=850 Pa·s, λ=0.08 s, n=0.65, a=1.2. At a typical injection shear rate of 500 s⁻¹, the simulator returns η=28.4 Pa·s. With melt supply pressure 80 MPa, gate ΔP≈6.2 MPa through a 2 mm gate. For a 120 cm³ cavity with specific heat 1.8 kJ/kg·K and thermal diffusivity 0.11×10⁻⁶ m²/s, cooling time to 70°C≈42 s. Adjust λ upward to 0.15 s to reduce gate pressure to 5.1 MPa and extend cooling to 51 s for thicker sections.
Practical Notes
For thin-wall injection molding (wall <1.5 mm), increase shear rate assumption to 1000+ s⁻¹ to capture viscosity drop; most polymers show n=0.5–0.8.
Use Carreau-Yasuda model (a≠1) when flow transitions are gradual; set a=1 to revert to standard Carreau behavior for quick estimates.
Gate pressure ΔP scales with (η×Q)/A; reducing gate diameter from 3 mm to 2 mm increases ΔP by ~2.25× for constant flow rate.
Cooling time dominates cycle time; validate mold temperature and wall thickness independently—simulator assumes uniform cooling boundary condition.