Effective elongational viscosity

Figure 29. Maximum value of effective elongational viscosity vs. solution con-centration. The extrapolated value o/C 0.064% is indicated by an arrow a-PS-decahydronaphthalene, Mw4 x JO ).

Mitsoulis, E., Valchopoulos, J. and Mirza, F. A., 1985. A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell. Poly. Eng. Sci. 25, 677 -669. 

Han, C. D. and Lamonte, R. R. Studies on melt spinning I. Effect of molecular structure and molecular weight distribution on elongational viscosity, Trans. Soc. Rheol., 16, 447 (1972). 

As Hashemzadeh s measurements in porous media flows have shown, the co-acrylates have a smaller elongational viscosity portion than the polyacrylamides, i.e., they are more easily deformed and their drag-increasing mechanism first comes into effect at smaller Reynolds numbers, although the value of the drag increase at this point is far smaller than for the polyacrylamides. 

The shear viscosity can be used for relating the polymer flow properties to the processing behavior, extruder design, and many other high shear rate applications. Elongational viscosity, die swell measurements as well as residence time effects can be estimated. Typical data are shown in Figure 6. 

Particle asymmetry has a marked effect on viscosity and a number of complex expressions relating intrinsic viscosity (usually extrapolated to zero velocity gradient to eliminate the effect of orientation) to axial ratio for rods, ellipsoids, flexible chains, etc., have been proposed. For randomly orientated, rigid, elongated particles, the intrinsic viscosity is approximately proportional to the square of the axial ratio. 

D. Sarkar and M. Gupta, Further investigation of the effect of elongational viscosity on entrance flow, J. Reinf. Plast. Comp., 20, 1473-1484 (2001). 

Godunov SK, Romenskii El (1972) Non-steady state equation of non-linear theory of elasticity in Euler co-ordinates. Zh Prikl Mech Technich Phys 6 124-144 (in Russian) Golovicheva IE, Sinovich SA, Pyshnograi GV (2000) Effect of molecular weight on shear and elongational viscosity of linear polymers. Prikl Mech Tekhnich Fiz 41(2) 154-160 (in Russian)... 

Both effects have important consequences for processing of polymers. The thickening of the elongational viscosity stabilizes filaments and films of polymers. The thinning of the shear viscosity causes many problems in mixing and dispersion in polymer products, because flow then mainly occurs in high shear regions and not elsewhere. 

It shoiild be noted that this is the exact derivation of equation (3). These models are usually referred to quasi-linear models and display qualitatively correct predictions of typical phenomena of elongational flows such as the occurrence of the strain-hardening effect in transient extension. Nevertheless the predicted elongational viscosity is never boimded in the long time range and a steady state value can only be expected for small elongation rates. Moreover, the shear behaviour remains unrealistic as compared to the experiment, especially because of constant predicted viscosity and first normal... 

Another source of error in the determination of the apparent viscosity in capillary flow lies in the fact that as the polymer liquid converges from the barrel to the capillary, the convergence of the flow requires a sharp pressure drop due to the elongational viscosity flow. This effect is illustrated in Figure 13,12. The drop in pressure is not P2 — P )/L but rather (P2 — P )/L, in which L is related to L by... 

The second Interesting observation based on ICR and RMS results Is related to the need for pressure correction In capillary flow. Already In Fig. 19 an agreement between the dynamic viscosity, n, and corrected for pressure effect capillary shear viscosity, n, was shown. In Fig. 22 five different measures of viscosity are shown for LLDPE-A (four for the other samples) steady state elongational viscosity, nE/3 conqplex and dynamic viscosity, n and n > as well as the steady state capillary viscosity corrected and uncorrected for the pressure effects, hcorr n(lCR), respectively. There Is a... 

Bagley (1992a) measured the apparent biaxial elongational viscosity of wheat flour dough. The upper convected Maxwell model was considered to be adequate in explaining both the effect of crosshead speed and sample... 

Applications in which dynamic uniaxial elongational viscosities (DUEVs) have been important to the performance of water-borne formulations are discussed. The achievement of high viscosities at low shear rates with minimum mechanical degradation of the water-soluble polymer and with minimum viscoelastic effects in applications that involved converging flows are discussed. These two factors serve as driving forces for the acceptance of hydrophobically modified water-soluble polymers. Complexities arising from the combined contribution of shear and elongational deformations in applications and in their measurement are discussed in the final section. 

---