Extensional flow viscosity measurements

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. 

By contrast, quite different results have been obtained with dilute polymer solutions. Here the extensional viscosity may be as much as thousand times the shear viscosity. Measurement of extensional viscosity of such mobile liquids is far more difficult than shear viscosity, or even impossible. According to Barnes et al. (General references, 1993) "The most that one can hope for is to generate flow which is dominated by extension and then to address the problem of how best to interpret the data in terms of material functions that are Theologically meaningful". An example of the difficulties that arise with the measurement of extensional viscosity is shown In Fig. 16.21 for a Round Robin test... 

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. 

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... 

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. 

The evidence which points to the role of extensional viscosity is partly direct and partly circumstantial. In the case of laminar flows, the role is obvious in flows through porous media or around small bodies, regions of high extensional deformation are easily identified and strain rates in these zones are consistent with the rates necessary for high extensional viscosity. In turbulent flows altered by polymer addition, principally boundary layers and jets, the regions most affected by the polymer are zones which are dominated by shear but periodically subjected to significant extensional motion hence extensional viscosity is linked with the effect. However, in these turbulent flows, simultaneous measurements of the hydro-dynamic effect and the fluid property have not yet been made and thus a direct relationship has not been established. 

Extensiometer n. A rheometer for measuring the extensional flow properties of molten polymers. In one early form, the Cogswell rheometer, useful at tensile viscosities over lO Pa/s, unidirectional tensile force was exerted on a polymer rod by a dead-weight acting through a cam and pulley. As the cam rotated, the moment arm exerted... 

At low shear rates, polymeric liquid properties are characterized by two constitutive parameters zero shear rate viscosity t]o and recoverable shear compliance Jq, which indicates fluid elasticity. At higher shear strain rates, rheological behavior is measured with a viscometer. Extensional strain viscosity, associated with extensional flow, occurs with film extrusion. 

In extensional flow, the morphological rearrangements lead to high extensional-to-shear viscosity ratios (both measured at the same < ) and the deformation rate), and to yield stresses that are larger than in shear. The effects increase with concentration and anisometry of suspended particles [10]. 

A. E. Everage and R. L. Ballman, The extensional flow capillary as a new method for extensional viscosity measurement. Nature 273, 213-215 (1978). 

The material function of prime importance in extensional flow is the extensional viscosity whidi is basically a measure of the resistance of the material to flow when stress is applied to extend it. 

In extensional flow, the diagonal components of are non-zero (i.e. T,y = 0 for i j). In the case of uniaxial extension, Th is the primary stress that can be measured, while T22 and T33 are generally equal to the pressiure of the environment. Thus, the uniaxial extensional viscosity rj is defined by. 

The rotational viscometers and the capillary rheometers described in sections 3.1 and 3.2 are those applicable for shear flows. However, there are processing operations that involve extensional flows. These flows have to be treated differently for making mecisurements of extensional viscosity. The extensional viscosity of a material is a measure of its resistance to flow when stress is applied to extend it. In general, measurement of steady-state extensional viscosity has proven to be extremely difficult. Steady extensional rate would be achieved by pulling Ihe ends of the sample apart such that I = Zq exp(ef) or in other words, at a rate that increases exponentially with time. Steady-state is reached when the force is constant. However, often d e sample breaks before steady-state is achieved or the limits of the equipment are exceeded or at the other extreme, die forces become too small for the transducer to differentiate between noise etnd response signal. Nevertheless, there have been various methods attempted for the measurement of extensional viscosity. 

The important rheological properties which need to be studied and measured in order to be able to characterize suspensions are the same as those which have already been indicated in Chapter 2. However, only the viscous flow behavior in shear and extensional flow will be discussed in this chapter. In particular, shear viscosity will be dealt with in sufficient detail because of the wealth of information that exists on it. 

Fig. 13.26. Uniaxial extensional flow generated between a fixed plate and a plate moving at desired velocity (v), while the entire geometry is held in a constant-temperature bath. Measurement of the sample dimension and the required tension force allows calculation of the elongational viscosity.

---