Hagenbach Correction

The acceleration of a sample at the entrance zone of a capillary die due to a change in cross section from sample reservoir (barrel) leads to an additional pressure drop that has to be corrected.

For high-pressure capillary applications, the pressure drop from this acceleration effect is ignored as it is small compared to the elastic stringing and viscous elongation of these viscoelastic materials in the entrance zone (Bagley correction) that normally leads to higher-pressure drops.

For mainly low-viscosity samples like paper coatings and printing inks, the pressure drop from the acceleration (kinetic energy) is higher than the Bagley entrance pressure drop. For those samples, the Hagenbach correction is applied to get the correct viscosity data from the corrected shear pressure drop along the capillary die. The density of the sample at the test temperature is required to apply the correction.

Where

η: Viscosity
R: die diameter
Q: volumetric flow rate
L: die length
∆p: pressure drop over the capillary
ρ: density