Glossary
Bagley Correction
The Rosand high-pressure capillary rheometer systems enables controlled extrusion (by volumetric flow) of a sample through a high-precision die of known dimensions. This allows for characterizing material flow properties, typically under conditions of high force (or pressure) and/or high shear rate.
Why the Bagley Correction?
During the high-pressure capillary rheometer measurement, the material typically flows from a 15-mm diameter barrel into a 1-mm diameter die. The pressure required to accelerate the material into the die is measured at the die inlet. Thus, the measured value contains not only the pressure needed to shear the material through the die, but also the pressure required to accelerate melting from the low flow velocity in the feed channel to much higher flow velocity in the round die or capillary. This velocity change causes pressure changes which may be considered under the following equation, see figure 1).
ΔPmeasured = ΔPentry + ΔPshear + ΔPoutlet
Consequently, the pressure transducer measures a pressure drop that exceeds the pressure drop within the die.
In order to obtain the true wall shear StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress necessary for the calculation of true shear viscosity, it is essential to correct these described effect. This process is referred to as the Bagley correction.
How to Perform the Bagley Correction?
- Historical Bagley Correction
One solution is to use the method described in standard DIN 11443. In this standard, the pressure drop is measured on a series of dies of the same diameter, but decreasing length (different L/D ratio). A linear fit is carried out on the measured points, enabling an extrapolation to the L/D ratio of 0 length (Figure 2).
However, the result of the extrapolation for L/D = 0 often provides an incorrect, negative pressure because the extrapolation may not be linear at low L/D ratios (Figure 3).
- Bagley Correction in One Measurement: The Twin-Bore Barrel
An alternative method to correct the entrance and exit effects is to work with an orifice die (typically 250 µm long) together with the long capillary die on a twin-bore instrument. With this approach, the entrance pressure drop can be directly measured,). A notable benefit of this approach is that measurement and correction occur in a single test run using the twin-bore capillary rheometer, thereby obviating the need for the minimum of three tests required by the historical Bagley correction.
Automatic Calculations in Flowmaster: One Click away from Bagley Correction
The NETZSCH FlowMaster software facilitates the automated execution of extrapolation procedures necessary for implementing the Historical Bagley correction. By using the twin-bore barrel option and zero-length die, this configuration allows for simultaneous measurements on capillary and orifice die.
The inlet pressure drop at the die is determined in this way, and absolute shear StressStress is defined as a level of force applied on a sample with a well-defined cross section. (Stress = force/area). Samples having a circular or rectangular cross section can be compressed or stretched. Elastic materials like rubber can be stretched up to 5 to 10 times their original length.stress and absolute shear viscosity are calculated using the Bagley method. This correction takes place by just one click in the NETZSCH FlowMaster software.
