Non-Linear Melt Viscosity Calibration in Polymer Processing Operations
Non-linear viscosity calibration requires multi-point shear rheometry and Cross model fitting to prevent extreme die sizing and molding pressure errors.
Carreau Yasuda
Meaning
Mathematical constitutive equation for non-Newtonian fluids describes the dependence of viscosity on the shear rate across a wide range of flow conditions. The carreau yasuda model incorporates parameters that capture both the low-shear and high-shear plateau regions, along with the transition between them. It is particularly useful for polymer melts and complex fluids that exhibit shear-thinning behaviour.
Rheological Range
Traditional power-law models fail at extreme shear rates because they predict infinite viscosity at rest and zero viscosity at infinite shear. Utilising the carreau yasuda formulation corrects this error by defining physical limits for both extremes. This enables engineers to simulate manufacturing processes like injection moulding or extrusion where the fluid experiences widely varying shear stresses.
Transition Parameter
A distinguishing feature of this model is the introduction of a dimensionless parameter that adjusts the width of the transition region between the Newtonian plateau and the power-law region. Adjusting this exponent allows a precise fit to experimental rheological data for polymers with different molecular weight distributions. It represents the structural sensitivity of the fluid to the onset of shear orientation, capturing how quickly the polymer chains untangle and align under flow.
Numerical Simulation
Applying the equation in computational fluid dynamics ensures that pressure drops and flow rates in complex geometries are calculated with high accuracy. The computational cost increases slightly due to the non-linear nature of the equation, but it prevents the underestimation of flow resistance.