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 enables characterizing material flow properties, typically under conditions of high force (or pressure) and/or high shear rate.

### Why the Bagley Correction?

During a measurement with the high-pressure capillary rheometer, 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 entrance. Thus, the measured value contains not only the pressure needed to shear the material through the die, but also the pressure required for the material to go in and out of the die (entrance and exit pressures, see Figure 1). Thus, the pressure transducer measures a pressure drop that is higher than the pressure drop in the die.

ΔPmeasured = ΔPentry + ΔPshear + ΔPoutlet

These two effects need to be corrected in order to obtain the true 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 required for the calculation of true shear viscosity. This is 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 (decreasing L/D ratios). A linear fit is carried out on the measured points, enabling an extrapolation to the L/D ratio of 0 mm (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

Another 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. This way, the entrance pressure drop is directly measured so that no extrapolation is needed (Figure 4). Another advantage of this method is that measurement and correction run simultaneously in one test (with the twin-bore capillary rheometer) instead of the minimum 3 tests required for the historical Bagley correction.

### Automatic Calculations in Flowmaster: One Click away from Bagley Corrections

The NETZSCH FlowMaster software offers the possibility to automatically perform extrapolation required for the historical Bagley correction.

Using the twin-bore barrel option and a zero-length die, this configuration allows for simultaneous measurements on both long (capillary) and short (orifice) dies. This way, the inlet pressure drop at the die is determined and, therefore, 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, using the Bagley method. This correction takes place autonomously by one click in the NETZSCH FlowMaster software.