What is the Bagley Correction and Why do I Need to Perform One?

When testing using a capillary rheometer, it is desirable to know the pressure drop along the capillary. Realistically, it is not possible to test for this inside the die itself, and pressure transducers are typically located just above the die. While this makes the machine design much simpler and more budget-friendly, it does introduce a very particular kind of error that affects readings of pressure drop, shear stress, and viscosity.

When the melt is pushed through the die, there are two drops in pressure that it experiences. First of all, the pressure drop due to the ‘entrance’ effects experienced at and around the die-mouth. This is related to the shape and size of the die and the compaction of the melt from a large to a small geometry. Additionally, there is a second pressure drop experienced between the start and end of the capillary. It is this second quantity that we are really interested in, and the separation of the two quantities is the product of the Bagley correction. The Bagley correction is unique for each configuration and set of parameters; it is only changed in die length that does not require a new correction to be performed.

Performing a Bagley correction might seem daunting, but it’s actually rather simple involving two basic rheology tests. Each test should be set up with identical parameters (a simulation of the anticipated testing conditions) and dies of the same geometry, but differing lengths. The analysis then consists of a mere pinch of high school algebra. Essentially, the two tests (ideally performed simultaneously on a dual bore machine) produce data that can be expressed as simultaneous equations:

E + A = x   (1)

E + B = y   (2)

Where E is the pressure drop due to entrance effects; A and B the drop in pressure in each barrel due to the lengths of the dies; x and y the pressure drop recorded by the transducers in each barrel. 

Then:

B = cA   (3)

Because:
1. The ratio of the length of one die to the other is known (c).
2.  The drop in pressure across the die is proportional to the shape, size and length of the die.
3.  The dies have the same shape and size.
4.  Thus the ratio of the die lengths is also the ratio of the pressure drops between the two dies.

Then taking equation 2 from equation 1:

A – B = x – y   (4)

A – cA = x – y   (5)

As c, x and y are known, you can now work back through the equations and calculate A, B and E. Software can be used to automatically perform the necessary calculations and execute a Bagley correction on all data collected following the procedure.

Having said this, if the data is purely for Quality Control purposes, then you won't need to perform the Bagley correction. As long as each test is executed using strictly the same equipment in the same configuration, then the results are comparable.