On the Pressure Dependency of the Bagley Correction

Abstract

The effect of pressure on the viscosity of polymer melts is an often forgotten parameter due to the inherent difficulty to measure this quantity. Different experimental approaches have already been undertaken in literature in the past. Apopular methodology to measure the pressure dependence of the viscosity is to use ac apillary rheometer equipped with a counter pressure chamber in which the exit pressure can be controlled. In order to process the data, one of the key elements is the Bagley correction that is required to determine the correct entrance pressure at as pecific shear rate. In all analysis approaches presented in literature on data at controlled exit pressure, the Bagley correction was always determined at atmospheric exit pressure, disgarding possible effects of an enhanced exit pressure. In this paper, an ew analytical approach is presented that for the first time allows for ad irect assessment of the entrance pressures obtained when capillary measurements are performed with controlled counter pressures. It is demonstrated, using polycarbonate, that the entrance pressure correction needed to obtain correct viscosity values under pressure is significantly different than the one needed to correct measurements performed at atmospheric exit pressure. 1I ntroductionAlready in 1957, Maxwell and Jung demonstrated that the apparent viscosity of abranched polyethylene melt increased exponentially with pressure (Maxwell and Jung, 1957). This dependency has important consequences for polymer processing operations. For instance, under typical injection molding conditions, at pressures of the order of several tens of MPa, neglecting the increase of viscosity with pressure can lead to incomplete cavity filling and/or longer processing times. With a growing demand on product performance and accuracy, in combination with the availability of sophisticated numerical simulations, an accurate incorporation of pressure effects is more and more required. Nevertheless, the pressure effect on viscosity is often ignored and the amount of experimental data is still relatively limited. The latter is due to the inherent difficulty in performing accurate measurements of the pressure effect as was reviewed by for instance Goubert et al. (2001) and more recently by Cardinaels et al. (2007).Since the pioneering work of Maxwell and Jung, arange of analysis procedures and experimental devices has been discussed in literature, which can be categorized into indirect and direct methods. Indirect methods to determine the pressure dependence of the viscosity are typically based on the principle of free volume and use the temperature dependency of viscosity and an equation of state for the polymer (the pressure-volume-temperature behavior) to determine the pressure sensitivity of the viscosity (e. g. Utracki, 1983Utracki, , 1985Utracki and Sedlacek, 2007). Regarding the direct methods, two approaches exist. The first one requires no special instruments but is based on the non-linearities in the Bagley plots, obtained either with capillary...

The influence of recycling on the viscosity of polyamide 6 and a general modeling approach

“…The measurement procedure for the viscosity determination of polymers using such device is standardized in ISO 11443:2004 . 13,14 In the following measurements, a capillary rheometer of the type Rheograph 2002, Göttfert Werkstoff-Prüfmaschinen GmbH, Buchen, Germany, was used for the determination of the viscosity behavior.…”

Steady State and Dynamic Oscillatory Shear Properties of Carbon Black Filled Elastomers

“…Nonlinearity can also occur due to the pressure dependence of viscosity. 67,82,83 This would manifest itself as a convex shape in the Bagley plot and would result in an overestimation of the polymer viscosity. Pantani et al and Laun have offered methods for dealing with nonlinear Bagley plots affected by high pressure.…”

“…Pantani et al and Laun have offered methods for dealing with nonlinear Bagley plots affected by high pressure. 82,84,85 High pressure can also reduce wall slip which would also lead to an overestimation of the polymer viscosity. 71 On the other hand, high shear can sometimes induce higher wall slip, particularly if it causes migration of compound ingredients to the wall.…”

Enhancing High-Pressure Capillary Rheometer Viscosity Data Calculation with the Propagation of Uncertainties for Subsequent Cross-Williams, Landel, and Ferry (WLF) Parameter Fitting

“…The wall shear stress in the capillary is where is the (linear) pressure drop within the capillary, and is the ratio of the capillary of length and diameter [ 14 , 15 ]. Due to the narrow capillary diameter (typically ), it is impossible to directly mount a pressure sensor.…”

“…However, in contrast, BC plots with an upwards curvature, can occur if the pressure dependency of the melt is non-neglectable. In such cases, BC polynomials of second degree are more suitable to estimate the pressure losses [ 15 , 24 , 25 ].…”