Relations between rheological properties of molten starches and their expansion behaviour in extrusion

Shear viscosity (η), first normal stress difference (N1), and extensional viscosity (ηE) of polymer melts measured under processing conditions are important in process modeling, quality control, and process control. A slit rheometer that could simultaneously measure η, N1, and the planar extensional viscosity (ηp) was designed and tested by attaching it in-line to a laboratory model single-screw extruder. A tube (circular cross-section) rheometer to measure η and the uniaxial extensional viscosity (ηu) simultaneously was also designed and tested. Two commercial grades of LDPE (low density polyethylene) with melt index values of 6 and 12 were used as test materials for the study. Exit and hole pressure methods were used to estimate N1, and the entrance pressure drop method using the analyses of Cogswell, Binding, and Gibson (the last analysis used with the axisymmetric case only) was used to estimate ηE.

In-line measurement of rheological properties of polymer melts

Kinematics and dynamics of the viscoelastic flow in an axisymmetric 4 : 1 sudden contraction geometry are studied for a highly elastic polyisobutylene (PIB) based polymer solution (referred to as PIB-Boger fluid). The critical conditions for the onset of the elastic instabilities and the dynamics of the resulting secondary flows are measured for various flow rates. The spatio-temporal characteristics of the flow are determined by instantaneous pressure measurements and streakline photography. The nonlinear dynamics of the global flow field both upstream and downstream of the contraction plane are systematically examined. New dynamic flow behavior and elastic instabilities downstream of the contraction plane are reported. It is shown that the instantaneous pressure measurements along with flow visualization can be used as an effective tool to characterize viscoelastic flows in complex geometries.

Instabilities in viscoelastic flow through an axisymmetric sudden contraction

Shear flow is ubiquitous. Not only is it arguably the most widely-used deformation type to characterise complex fluids in rheological studies but also, in practice, the deformation most likely to occur in the great majority of flows, e.g. involving fluid transport through pipes or conduits. In steady simple shear flow the rheological properties of a complex fluid are completely characterised in just three material functions; the variation with shear rate of the shear viscosity and the so-called first and second normal-stress differences. Despite requiring only three material functions to be completely characterised, most shear-flow rheological characterisations are usually restricted simply to the shear viscosity and, at best, the variation of the first normal-stress difference N1 with shear rate. The second normal-stress difference N2 remains very much neglected. For dilute polymer solutions where this quantity may be negligibly small in comparison to the first normal-stress difference, such neglect is justified but for a whole range of complex fluids – indeed even polymer solutions outside of the dilute regime and especially melts – it is not clear that N2 may be safely disregarded. Indeed, in this review article we spotlight a number of flows where second normal-stress differences are of importance and potentially major consequence. Following this attention, we review the many experimental techniques which have been proposed for its measurement and survey the available literature for measurements of this quantity for various complex fluids including the aforementioned polymeric solutions, melts, liquid crystals, dense non-Brownian suspensions (both with Newtonian and complex fluid bases), semi-dilute wormlike micellar fluids and magnetorheological fluids. Theoretical predictions for N2 from various commonly-used continuum constitutive equations – primarily from the polymer literature – are also given and their asymptotic predictions at low and high shear rates compared. Finally, we end with a brief summary and outlook.

A review of the second normal-stress difference; its importance in various flows, measurement techniques, results for various complex fluids and theoretical predictions

A study of the first and second normal stress differences was made in order to determine the properties for an LDPE melt at high shear rates. Time dependent measurements of N 1 and N 2 were carried out using cone/plate and plate/plate rheometry, in order to extend the shear rate for rotational rheometry up to 120 s−1. Measurements utilizing the pressure hole method extended the shear rate range to approximately 1000 s−1. For N 1 there is an overlap in the data, that is within the experimental error, for N 2 the data is inconsistent in behaviour. Both N 1 and N 2 initially demonstrated a power law behaviour, but converged to a plateau at high shear rates. This behaviour is believed to be a true response of an oriented polymer network and not slip.

Measurements of first and second normal stress differences in a polymer melt

This paper provides an assessment of our current understanding of the hole-pressure effect and the role it plays in the field of viscometry. The discovery in 1968 by Broadbent, Kaye, Lodge and Vale that the use of pressure taps to measure the normal stress exerted on a boundary by a non-Newtonian material can lead to significant errors has opened up interesting new avenues for making viscometric measurements. The kinematical theory developed by Higashitani and Pritchard (1972) to estimate the hole pressure, to which a deeper understanding has recently been supplied by Yao and Malkus (1990), has formed the basis of many new developments in viscometry. It is interesting that such a simplistic theory for the hole pressure apparently has a rather wide range of applicability.

M. Yao

Papers

The hole-pressure effect and viscometry