Meaning
Rheological equations fitting non-Newtonian flow curves represent how polymer melt viscosity transitions from a zero-shear plateau to power-law shear thinning. Applying the cross model allows mould filling simulation software to calculate pressure drop through injection runners and narrow gate geometries. Polymer engineers rely on this formulation during mold design to predict cavity packing behavior.
The equation ceases to hold at extreme shear rates where viscous dissipation causes severe local thermal degradation.
Viscosity Prediction
Flow calculations use four specific material constants to map pseudoplastic behavior across commercial processing ranges. Curve fitting with the cross model captures both the zero-shear viscosity region and high-shear thinning trends in molten polyolefins. Accurately modeling this transition prevents underestimating required injection pressures during fast injection cycles.
Virgin resin exhibits distinct curve parameters compared to shear-degraded regrind material.
Parameter Fitting
Capillary rheometer test data collected across multiple temperatures provides the empirical foundation for mathematical fitting routines. Extracting parameters for the cross model requires measuring shear stress across four orders of magnitude in velocity gradient. Capillary end corrections eliminate entrance pressure losses from raw experimental data sets.
Datasheet values fitted from limited test points fail to capture low-shear sagging in heavy extrusion profiles.
Simulation Accuracy
Mould filling analysis depends heavily on accurate viscosity inputs when predicting gate freeze times and volumetric shrinkage patterns. Integrating the cross model into finite element solvers improves cavity pressure predictions by matching physical flow resistance across variable wall thicknesses. Incorrect zero-shear viscosity parameters cause artificial pressure spikes during the packing phase.
Real-time cavity transducers confirm theoretical calculations during production verification runs.