Compute polymer viscosity curves in real time with the Carreau-Yasuda model and the power law. Estimates the gate pressure drop and cooling time to support the first stage of injection-moulding CAE.
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 Design 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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Design-point viscosity (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)
Arrhenius dependence (approximate) of the zero-shear viscosity over melt temperature ±40°C
Power law: $\eta = m\,\dot{\gamma}^{n-1}$, $m=\eta_0\lambda^{\,n-1}$ (the high-shear asymptote of Carreau-Yasuda). Gate pressure drop: $\Delta P = 2L\,\tau_w/R$, $\tau_w=\eta(\dot{\gamma}_w)\,\dot{\gamma}_w$, $\dot{\gamma}_w=\frac{3n+1}{n}\frac{Q}{\pi R^3}$ (wall shear rate; approximate for Carreau-Yasuda)
What Is Polymer Viscosity and Flow Analysis?
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Isn't the "viscosity of a polymer" constant once the temperature is fixed? This tool talks about a "viscosity curve".
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Roughly speaking, the viscosity of a molten plastic changes a lot with the "shear rate". Stir it slowly (low shear) and it is thick; inject it fast (high shear) and it becomes runny. The upper chart of this tool computes that change with a model. First pick HDPE or PC under "Polymer preset" and see how the chart changes.
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Really? Switching to PC did change the curve... So which should I use, "Carreau-Yasuda" or the "power law"?
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In practice the Carreau-Yasuda model is used when a wide range has to be captured accurately. The power law is simpler to compute and is used mainly as an approximation in the high-shear region. Switch between them under "Viscosity model" and compare the behaviour at low shear rates (left end of the chart): Carreau-Yasuda flattens at the left end (the first Newtonian plateau).
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I see! And how are the "gate pressure drop" and "cooling time" below related to this viscosity?
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Good observation. In the "gate" that feeds resin into the mould the shear rate becomes very high. From the viscosity curve you chose, the tool computes in real time the pressure drop for the gate dimensions you design (radius R and length L) and the flow rate Q. Move the parameters and narrow the gate (smaller R) to see how the pressure drop shoots up. The clogging trouble you meet on the shop floor is exactly this miscalculation.
Frequently Asked Questions
The power law is a simplified model that covers only the high-shear region, with poor accuracy at low shear. The Carreau-Yasuda model computes viscosity continuously from low to high shear, so it is recommended for injection-moulding analysis, which spans the high shear in the gate and the low shear inside the cavity.
η₀ is often given on the data sheet of the polymer in the molten state. A guide for λ is the reciprocal (1/γ̇) of the shear rate at which the viscosity starts to fall. If unknown, start from a measured η₀ and λ in the range 0.01–1 s and adjust until the flow length or pressure drop matches the real machine.
The main causes are differences between the measured and assumed resin and mould temperatures, or the simplification of the channel cross-section. In particular, if the viscosity drop due to shear heating in the gate is not considered, the pressure drop is overestimated. Also, too small a Yasuda parameter a makes the transition abrupt and may diverge from real behaviour.
The cooling time depends mainly on the thermal diffusivity of the resin, the mould temperature and the part thickness. This tool uses the melt temperature Tm and thermal diffusivity α of the selected preset with a mould temperature of 50°C and an ejection temperature of 100°C (fixed), and computes the one-dimensional plate heat-conduction approximation t_c≈t²/(π²α)·ln(4/π·(Tm−Tw)/(Te−Tw)). Because the cooling time grows with the square of the thickness, uniform wall thickness at the design stage is important.
Real-World Applications
Injection-mould design: When deciding gate sizes and cavity layout, the pressure drop is predicted with calculations like this tool's. Too large a pressure drop causes short shots (incomplete filling) because the machine cannot deliver it, and too small a drop causes jetting, so the calculation is essential for an optimal design.
Selection and evaluation of moulding materials: Even the same material (say PP) from different manufacturers has a different viscosity curve because of additives and molecular-weight distribution. When a new material is to be run in an existing mould, the viscosity curve and pressure drop are simulated to verify mouldability in advance.
Optimisation of moulding conditions: The change in viscosity and heat generation in the gate when the injection speed (equivalent to the flow rate Q) is changed can be estimated. This helps set conditions that minimise fill time while avoiding burning and degradation.
Pre-processing and verification for CAE software: Before a full 3-D filling analysis, the pressure drop at a representative gate is computed quickly to check that the material data entered (Carreau-Yasuda parameters) and the boundary conditions are reasonable.
Common Misconceptions and Points to Note
There are several pitfalls that beginners in CAE in particular tend to fall into when they start using this tool. The first is that "the parameters of the preset materials are not absolute constants". Even "PC" varies greatly in viscosity between manufacturers and grades (high-flow, flame-retardant and so on). The preset values are only representative. Compare them with the viscosity curve on the data sheet of the actual material and fine-tune λ and n where necessary.
The second is overlooking the assumptions behind the gate pressure-drop calculation. The formula assumes "fully developed laminar flow in a circular channel". It therefore excludes the contraction loss at the real gate entrance and the effect of the frozen skin at the wall caused by the mould temperature. Treat the result as the theoretical minimum pressure drop; shop-floor practice is to allow a safety margin of 1.5 to 2 times.
The third is not to over-trust the cooling-time calculation. The tool's cooling time is a theoretical value based only on heat conduction to a mould wall at constant temperature. In real moulding, complex factors such as the layout and flow of the cooling channels and the heat released by crystallisation come into play. Treat the value as a guide to "the order of magnitude of cooling": if the calculation says 10 s, the actual cycle time is often around 12–15 s.
Choose HDPE, PP, PA6, PC or PET from "Polymer preset" to load representative values of the four Carreau-Yasuda parameters (zero-shear viscosity η₀, relaxation time λ, flow index n, Yasuda parameter a). Use "Custom" or the sliders and numeric fields to change them freely
Switch between Carreau-Yasuda and the power law under "Viscosity model". Both models are drawn on the viscosity curve (10⁻²–10³ s⁻¹) and the design point is computed with the selected model
Set the gate radius R (0.2–5 mm), gate length L and flow rate Q (1–200 cm³/s); the design-point viscosity (green marker) at the wall shear rate γ̇_w=(3n+1)/n·Q/(πR³) and the gate pressure drop ΔP=2Lτ_w/R update immediately
Set the part thickness t (0.5–10 mm) to display the one-dimensional cooling time, using the preset's melt temperature and thermal diffusivity with a mould temperature of 50°C and an ejection temperature of 100°C. The lower chart shows the temperature dependence (Arrhenius approximation) of the zero-shear viscosity of three polymers
Worked Example
Select the PA6 preset (η₀=1500 Pa·s, λ=0.005 s, n=0.60, a=1.5) with gate radius R=1.3 mm (2.6 mm diameter), gate length L=3 mm, flow rate Q=10 cm³/s and thickness t=2 mm. The viscosity curve falls gently, about 1,380 Pa·s at γ̇=100 s⁻¹ and about 770 Pa·s at 1,000 s⁻¹, and at the gate wall shear rate γ̇_w≈6,800 s⁻¹ the tool shows a design-point viscosity of ≈366 Pa·s, a gate pressure drop ΔP≈11.4 MPa and a cooling time ≈6.7 s. Doubling the flow rate to Q=20 cm³/s gives γ̇_w≈13,500 s⁻¹, viscosity ≈278 Pa·s and ΔP≈17.3 MPa: doubling the flow raises ΔP by only about 1.5× (2^n with n=0.6).
Practical Notes
The preset parameters are representative values. Even the same PA6 varies greatly with grade, fillers and moisture (nylon moulded wet hydrolyses, its molecular weight drops and the viscosity falls). Adjust η₀, λ and n to the viscosity curve on the data sheet of the actual material
The larger ΔP, the larger the shear heating in the gate. A guide to the adiabatic temperature rise is ΔT≈ΔP/(ρc_p): about 10°C for ΔP=20 MPa and ρc_p≈2×10⁶ J/(m³·K). Because the heating lowers the viscosity, the ΔP of this tool is an estimate on the high side
λ corresponds to the reciprocal (1/λ) of the shear rate at which viscosity starts to fall; increasing λ lowers the design-point viscosity and ΔP. The power law η=η₀(λγ̇)^(n−1) coincides with the high-shear asymptote of Carreau-Yasuda and overestimates the viscosity at low shear (left end of the chart)
ΔP assumes fully developed, isothermal laminar flow in a circular channel and excludes entrance losses and the frozen layer at the wall. The cooling time uses a one-dimensional plate model with the preset's melt temperature Tm and thermal diffusivity α, a mould temperature of 50°C and an ejection temperature of 100°C (fixed), and scales with the square of the thickness (about 12.6 s for HDPE at t=3 mm)
🎬 Watch it in motion
Pipe Flow | a parabolic profile, and radius rules everything #Shorts
