Rheological measurements normal stress

Polyolefin melts have a high degree of viscoelastic memory or elasticity. First normal stress differences of polyolefins, a rheological measure of melt elasticity, are shown in Figure 9 (30). At a fixed molecular weight and shear rate, the first normal stress difference increases as MJM increases. The high shear rate obtained in fine capillaries, typically on the order of 10 , coupled with the viscoelastic memory, causes the filament to swell (die swell or... 

The theoretical basis for spatially resolved rheological measurements rests with the traditional theory of viscometric flows [2, 5, 6]. Such flows are kinematically equivalent to unidirectional steady simple shearing flow between two parallel plates. For a general complex liquid, three functions are necessary to describe the properties of the material fully two normal stress functions, Nj and N2 and one shear stress function, a. All three of these depend upon the shear rate. In general, the functional form of this dependency is not known a priori. However, there are many accepted models that can be used to approximate the behavior, one of which is the power-law model described above. 

Here are the components of the stress tensor as defined in rheology Tn—T22 is the first normal stress difference and T21 the shear stress, equal to Nt and rxsh, respectively. Hence, from dynamic mechanical measurements it is possible to determine the zero shear first normal stress coefficient Fq0 and zero shear viscosity y0. 

It is well known in polymer rheology that a torsional parallel-plate flow cell develops certain secondary flow and meniscus distortion beyond some stress level [ 14]. For viscoelastic melts, this can happen at an embarrassingly low stress. The critical condition for these instabilities has not been clearly identified in terms of the shear stress, normal stress, and surface tension. It is very plausible that the boundary discontinuity and stress intensification discussed in Sect. 4 is the primary source for the meniscus instability. On the other hand, it is well documented that the first indication of an unstable flow in parallel plates is not a visually observable meniscus distortion or edge fracture, but a measurable decay of stress at a given shear rate [40]. The decay of the average stress can occur in both steady shear and frequency-dependent dynamic shear. 

The rheological behaviour of the two polymers was determined using classical techniques of rheometry, already described in Chapter II. 1 (rotational and capillary rheometers for shear viscosity and first normal stress difference measurements CogsweU method for the elongational viscosity). 

Chapter 3. In-plant measurement of flow behavior of fluid Foods. Using a vane-in-a-cup as a concentric cylinder system. The vane yield stress test can be used to obtain data at small- and large-deformations. Critical stress/strain from the non-linear range of a dynamic test. Relationships among rheological parameters. First normal stress difference and its prediction. 

Steady shear flow measnrements, however, can measure only viscosity and the first normal stress difference, and it is difficult to derive information abont fluid structure from such measurements. Instead, dynamic oscillatory rheological measurements are nsed to characterize both enhanced oil recovery polymer solutions and polymer crosslinker gel systems (Prud Homme et al., 1983 Knoll and Pmd Homme, 1987). Dynamic oscillatory measurements differ from steady shear viscosity measnrements in that a sinusoidal movement is imposed on the fluid system rather than a continnons, nnidirectional movement. In other words, the following displacement is imposed ... 

Steady-state shear rheology typically involves characterizing the polymer s response to steady shearing flows in terms of the steady shear viscosity (tj), which is defined by the ratio of shear stress (a) to shearing rate y ). The steady shear viscosity is thus a measure of resistance to steady shearing deformation. Other characteristics such as normal stresses (Ai and N2) and yield stresses (ffy) are discussed in further detail in Chapter 3. 

Shear-Sensitive Systems. In addition to hydrodynamic effects and simple viscous behavior, the act of pigmentation creates a certain amount of complex behavior (13). If the particles are fine. Brownian movement (14-17) and rotational diffusion (14. 18. 19) are among the phenomena that cause dispersed systems to display complex rheology. The role of van der Waals forces in inducing flocculation (20) and the countervailing role of two electroviscous effects (17. 21. 22) in imparting stability, particularly in aqueous systems, have been noted. Steric repulsions appear to be the responsible factor in nonaqueous systems (23. 24). The adsorbed layer can be quite large (25-28). as detected by diffusion and density measurements of filled systems or by viscometry and normal stress differences (29). 

A systematic study of the basic rheological properties for a wide variety of polypropylene melts has been made by Minoshima et al. [89]. These authors measured shear viscosities at low shear rates in a Rheomatrics mechanical spectrophotometer and at high rates in an Instron capillary rheometer. The principal normal stress difference, Ni, was measured in the mechanical spectrophotometer with a cone and plate device. The elongational viscosity, of special importance to fiber formation, was measured in an apparatus built by Ide and White [90],... 

The steady-state shear flow properties in the low shear rate region and the dynamic functions were measured using a rotational viscometer (cone-plate type, RGM151-S, Nippen Rheology Kiki Co., Ltd., Japan). The cone radius R was 21.5mm, the gap between the central area of the cone and plate H was kept at 175p.m, and the cone angle 0 was 4°. The measurements were carried out at 200°C Steady state shear properties (shear viscosity //, and the first normal stress difference Ni) as well as dynamic functions (storage and loss moduli G, G", respectively. 

A number of mathematical expressions have been proposed to calculate die swell in relation to some measurable rheological variable. Most of these expressions relate to the maximum swell or equilibrium swell (BJ, assuming fully developed laminar flow in long dies. One of the first simple expressions, relating die swell as an elastic recoil mechanism to the first normal stress difference - T22 and the shear stress X21, can be expressed as follows [3] ... 

Cone-and-plate rheology represents one of the most ideal means of measuring viscosity of molten plastics. The melt is placed between a plate and a cone that are located a precise distance apart. The torque required to impose a constant rate of angular rotation is measured. Cone angles of 3° or less are used, which result in a geometry where the shear rate is constant with radius so that no assumptions about the flow kinematics are needed. The main drawback of the technique is that it is limited to very low shear rates. It remains an ideal method for the determination of the zero shear viscosity, a number that is found to correlate well to the molecular weight of the plastic. The first and second normal stresses can also be measured using this apparatus. 

The rheological responses measured at low values of strain better reflect the effects of the blend structure. For multiphase systems, there are serious disagreements between the predictions of continuum-based theories and experiments, that is, between the small and large deformation behavior. For example, the identity of zero-deformation rate dynamic and steady state viscosity is seldom found, and so is the Trouton rule. Similarly, the derived by Cogswell, relationship between the extensional viscosity and the capillary entrance pressure drop, and derived by Tanner equation for calculating the first normal stress difference from the extrudate swell, are rarely valid. 

---