Extensional flow measurements

In marked contrast to measurements of shear rheological properties, such as apparent viscosity in steady shear, or of complex viscosity in small amplitude oscillatory shear, extensional viscosity measurements are far from straightforward. This is particularly so in the case of mobile elastic liquids whose rheology can mitigate against the generation of well-defined extensional flow fields. 

Techniques for measming the extensional properties of fluids can be divided (broadly) into those of the flow-through and stagnation-point types [Hermansky and Boger, 1995]. The former usually involve spinnable fluids, a feature exploited in instruments such as the Carri-Med (now TA Instruments) EV rheometer [Ferguson and Hudson, 1990]. 

In spin-line experiments, flmd is delivered through a nozzle and subsequently stretched by an applied force. Procedmes are available for obtaining 

Where a fluid is not spinnable the various orifice flow techniques, which involve pressure drop measinements across a contraction [Binding, 1988, 1993], can provide a means of estimating the extensional-viscosity behaviour of shear-thinning polymer solutions. 

For low viscosity fluids such as dilute polymer solutions, the various stagnation-point devices can prove useful. In this category is the coiiunercially available Rheometrics RFX opposing jet device, a development of earlier instruments [Cathey and Fuller, 1988], which has the potential to produce a wide range of strain rates, and which has been used to study fluids with a viscosity approaching that of water [Hermansky and Boger, 1995]. 

---

Figure 9.18 refers to two other standard experiments. It depicts the results of stress growth experiments, conducted again on a polyethylene melt. The figure includes both measurements probing shear and tensile properties, thus facilitating a direct comparison. Curves show the building-up of shear stress upon inception of a steady state shear flow at zero time and the development of tensile stress upon inception of a steady state extensional flow. Measurements were carried out for various values of the shear rate 7 or the Hencky rate of extension ch ... 

Flow is generally classified as shear flow and extensional flow [2]. Simple shear flow is further divided into two categories Steady and unsteady shear flow. Extensional flow also could be steady and unsteady however, it is very difficult to measure steady extensional flow. Unsteady flow conditions are quite often measured. Extensional flow differs from both steady and unsteady simple shear flows in that it is a shear free flow. In extensional flow, the volume of a fluid element must remain constant. Extensional flow can be visualized as occurring when a material is longitudinally stretched as, for example, in fibre spinning. When extension occurs in a single direction, the related flow is termed uniaxial extensional flow. Extension of polymers or fibers can occur in two directions simultaneously, and hence the flow is referred as biaxial extensional or planar extensional flow. 

It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase elasticity and the shear rate sensitivity of the melt viscosity ( ). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the ability to measure long chain branching and its molecular weight distribution is critical in order to tailor product performance. 

In the opposed jets design fluid is sucked or pumped into a beaker. The profile which develops is dominantly extensional. In the profiled slot design a rectangular channel is designed such that in the total slip condition an extensional flow develops with a constant rate. The pressure is measured at the stagnation point. Other designs include the open syphon, where fluid is sucked from a beaker through a nozzle which is... 

A second device that is also able to generate truly extensional flow field has been developed by Meissner (41) utilizing the concept of rotary clamps. At a constant strain rate this instrument can measure stress growth and thus allow the steady state flow measurements. 

Patzold (1980) compared the viscosities of suspensions of spheres in simple shear and extensional flows and obtained significant differences, which were qualitatively explained by invoking various flow-dependent sphere arrangements. Goto and Kuno (1982) measured the apparent relative viscosities of carefully controlled bidisperse particle mixtures. The larger particles, however, possessed a diameter nearly one-fourth that of the tube through which they flowed, suggesting the inadvertant intrusion of unwanted wall effects. 

The maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

A few rheometers are available for measurement of equi-biaxial and planar extensional properties polymer melts [62,65,66]. The additional experimental challenges associated with these more complicated flows often preclude their use. In practice, these melt rheological properties are often first estimated from decomposing a shear flow curve into a relaxation spectrum and predicting the properties with a constitutive model appropriate for the extensional flow [54-57]. Predictions may be improved at higher strains with damping factors estimated from either a simple shear or uniaxial extensional flow. The limiting tensile strain or stress at the melt break point are not well predicted by this simple approach. 

M.Takahashi, T.Isaki, T.Takigawa, T.Masuda, Measurement of biaxial and uniaxial extensional flow of polymer melts at constant strain rates, J. Rheol. 31 (1993), 827-846. 

One technique for measurement of extensional flow that has been used to study various doughs is that of Cogswell (1972, 1978) for entrance flows. The analysis is based on several assumptions (Padmanabhan and Bhattacharya, 1993) (1) The flow is isothermal and creeping (negligible inertial effects), (2) the fluid is incompressible and has a pressure-independent viscosity, (3) the shear viscosity follows the power law model, t]a = Ky" (4) there is no slip at the edge of the converging profile, and (5) that the entrance pressure drop (Ape) in converging flow from a circular barrel in to a circular die can be considered to be made up of that due to shear (Ape,s) and extensional flow (Ape,E) ... 

The melt viscosity of LCPs is sensitive to thermal and mechanical histories. Quite often, instrumental influences are important in the value of viscosity measured. For example, the viscosity of HBA/HNA copolyesters are dependent on the die diameter in capillary flow (59). LCP melts or solutions are very efficiently oriented in extensional flows, and as a result, the influence of the extensional stresses at the entrance to a capillary influence the shear flow in the capillary to a much greater extent than is usually found with non-LC polymers. 

A commercial instrument for extensional viscosity measurements is currently offered by the Thermo Electron Corporation [40], The device uses capillary breakup techniques and is called the Haake CaBER . Vilastic Scientific, Inc. also offers an orifice attachment to their oscillatory rheometer for extensional viscosity determinations [41,42], The principle of operation of the rheometer is oscillatory tube flow [43,44], Dynamic mechanical properties can be determined... 

However, rheological measurements are also performed with other types of flow or stress fields. If a uniaxial extensional flow field is applied to a material, the stress distribution can be described by... 

---