Bagley End Correction Methods for Polymer Capillary Rheometry Data Analysis
Bagley end corrections isolate true wall shear stress from entry pressure losses, preventing viscosity overestimation that distorts mold tooling and cash flow.
Barus Equation
Meaning
Mathematical functions for fluid behavior describe the exponential increase of viscosity when a liquid is subjected to high pressure. The barus equation provides the specific formula for calculating this change using a pressure-viscosity coefficient. High pressure environments such as injection molding or gear lubrication require this correction but the formula stops being accurate at pressures where the fluid reaches a glass transition.
Pressure Sensitivity
Viscous resistance is not constant when the internal forces of a system change. Through the barus equation, engineers predict how much power is needed as the pressure in a mold cavity rises.
Calculation Method
Base viscosity at atmospheric pressure and an exponent containing the pressure term form the basis of the math. Applying the barus equation involves measuring the fluid at multiple points to find the unique coefficient for that material. Because the relationship is exponential, even small increases in pressure lead to large jumps in flow resistance.
Changes in the molecular weight of the polymer can shift this coefficient.
Modeling Application
Simulation software uses these relationships to prevent the flashing of tools and ensure complete part filling. Without the barus equation, a model might suggest a machine has the capability to fill a part that its actual pump capacity cannot handle. The cost of calling a tool ready early is high when the real-world pressure requirements exceed the equipment limits.
A demonstrated rate of production often falls short of a forecast because this sensitivity was ignored during the design phase.