Rheological normal stress

These normal stresses are more pronounced for polymers with a very broad molecular weight distribution. Viscosities and viscoelastic behavior decrease with increasing temperature. In some cases a marked viscosity decrease with time is observed in solutions stored at constant temperature and 2ero shear. The decrease may be due to changes in polymer conformation. The rheological behavior of pure polyacrylamides over wide concentration ranges has been reviewed (5). 

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. 

De Witt T., Mezner. W. A rheological equation of state which predicts non-Newtonian viscosity, normal stresses and dynamics module. J. Appl.Phys., 1985, v. 26, p. 889-892. 

Various investigations have considered the effects of titanate treatments on melt rheology of filled thermoplastics [17,41]. Figure 10, for example, shows that with polypropylene filled with 50% by weight of calcium carbonate, the inclusion of isopropyl triisostearoyl titanate dispersion aid decreases melt viscosity but increases first normal stress difference. This suggests that the shear flow of the polymer is promoted by the presence of titanate treatment, and is consistent with the view that these additives provide ineffective coupling between filler particles and polymer matrix [42]. 

The Entanglement Concept in Polymer Rheology 8.4. Second Normal Stress Function... 

Mieras,H.J.M.A. Elastic or normal-stress behavior of monodisperse polystyrene melts or solutions. Paper presented at the conference Advances in Rheology, Glasgow, September 1969. 

HupplerJ.D., MacDonald,I.F., Ashare,E., Spriggs,T.W., Bird,R.B., Holmes,L.A. Rheological properties of three solutions. Part II. Relaxation and growth of shear and normal stresses. Trans. Soc. Rheol. 11,181-204 (1967). 

With the aid of these relaxation times other rheological properties like normal stresses, flow birefringence and dynamic shear moduli can be calculated. A more detailed discussion of this procedure wiE be given in Chapter 4. 

Concentrated emulsions can exhibit viscoelasticity, as can gelled foams and some suspensions. Compared with the previous equations presented, additional coefficients (including primary and secondary normal stress coefficients) are needed to characterize the rheology of viscoelastic fluids [376,382]. 

In a complex, polymeric liquid, normal stresses as well as the shear stress can be present, and these contributions will influence the shape of the structure factor. The simplest rheological constitutive model that can account for normal stresses is the second-order fluid model [64], where the first and second normal stress differences are quadratic functions of the shear rate. Calculations using this model [92,93,94,90,60], indicate that the appearance of normal stresses can rotate the structure factor towards the direction of flow in the case of simple shear flow and can induce a four-fold symmetry in the case of exten-sional flow. 

In the normal stress extruder we first want to evaluate the pressure at the center as a function of disk outer radius, frequency of rotation, and rheological properties. We do this in the absence of radial flow (i.e., for a closed discharge condition), which will give us the... 

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. 

The principal quantities determining the rheological behaviour of polymer melts are the viscosity and normal stress coefficients in shear and extensional... 

The reality, however, is not as simple as that. There are several possibilities to describe viscosity, 77, and first normal stress difference coefficient, P1. The first one originates from Lodge s rheological constitutive equation (Lodge 1964) for polymer melts and the second one from substitution of a sum of N Maxwell elements, the so-called Maxwell-Wiechert model (see Chap. 13), in this equation (see General references Te Nijenhuis, 2005). 

FIG. 15.46 Viscosity, 77, and first normal stress difference, Nh of Vectra 900 at 310 °C as functions of shear rate, according to Langelaan and Gotsis (1996). The first normal stress coefficient, Yi, is estimated from N, by the present author. ( ) Capillary rheometer ( ) and ( ) cone and plate rheometer ( ) complex viscosity rj (A) non-steady state values of the cone and plate rheometer. Courtesy Society of Rheology. 

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. 

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