Torsional flow

With the supposition that the slip layer is thin and the slip velocity is constant, various analyses have been developed in the search for the ideal experimental method to define slip. The Mooney analysis (20) for both tube flow and concentric cylinder flow has been applied to a wide range of materials including polymer solutions (21), filled suspensions (22), semisolid foods (23), fruit purees (24), and ketchups (25). Alternate estimates of slip velocity have been determined experimentally from, parallel plate torsion flow (26), from flow data in channels and inclined planes, and from porous medium geometries (8). 

B.K. Aral and D.M. Kalyon, Effects of Temperature and Surface Roughness on Time-Dependent Development of Wall Slip in Steady Torsional Flow of Concentrated Suspensions, J. Rheol., 38(4) 957-972 (1994). 

Non-Newtonian Viscosity In the cone-and-plate and parallel-disk torsional flow rheometer shown in Fig. 3.1, parts la and 2a, the experimentally obtained torque, and thus the % 2 component of the shear stress, are related to the shear rate y = y12 as follows for Newtonian fluids T12 oc y, implying a constant viscosity, and in fact we know from Newton s law that T12 = —/ . For polymer melts, however, T12 oc yn, where n < 1, which implies a decreasing shear viscosity with increasing shear rate. Such materials are called pseudoplastic, or more descriptively, shear thinning Defining a non-Newtonian viscosity,2 t],... 

The velocity field between the cone and the plate is visualized as that of liquid cones described by 0-constant planes, rotating rigidly about the cone axis with an angular velocity that increases from zero at the stationary plate to 0 at the rotating cone surface (23). The resulting flow is a unidirectional shear flow. Moreover, because of the very small i//0 (about 1°—4°), locally (at fixed r) the flow can be considered to be like a torsional flow between parallel plates (i.e., the liquid cones become disks). Thus... 

Torsional Flow of a CEF Fluid Two parallel disks rotate relative to each other, as shown in the following figure, (a) Show that the only nonvanishing velocity component is vg = flr(z/H), where ft is the angular velocity, (b) Derive the stress and rate of deformation tensor components and the primary and secondary normal difference functions, (c) Write the full CEF equation and the primary normal stress difference functions. 

FIG. 15.2 Types of simple shear flow. (A) Couette flow between two coaxial cylinders (B) torsional flow between parallel plates (C) torsional flow between a cone and a plate and (D) Poisseuille flow in a cylindrical tube. After Te Nijenhuis (2007). 

In Couette flow and in torsional flow between a cone and a plate the shear rate may be considered constant, provided the slit Ar between the two cylinders and the angle A between cone and plate, respectively, are small. On the other hand, the shear rates in... 

F. Torsional Flow between Two Disks the Upper One of Which is Rotating and Attached to a Vertical Tube h = Height of rise of fluid in tube R, = Radius of tube R2 = Radius of disks Wq = Angular velocity of tube-disk assembly H = Gap between disks g = Gravitational acceleration... 

There is also a variety of wall-slip techniques used in rheological analysis (Gupta, 2000). The methods described here are flow visualization, capillary flow and torsional flow. 

Aral, B.K. and D.M. Kalyon, Ejfects of temperature arul surface roughness on time-dependent development of wall slip in torsional flow of concentrated suspensions. Journal of Rheology, 1994. 38 p. 957-972... 

In torsional flows between two parallel disks, the apparent shear rate, ya. (not corrected for slip effects) is a linear function of the radius, r, and is given by t Q r... 

In Hgure 1 the shear stress at the edge, calculated from Equation 3, is shown versus the apparent shear rate, YaR, in parallel disk torsional flow of suspension I. 

The variation of Qs/Q with the shear stress can be rationalized by observing the variation of viscosity with the shear stress in both suspensions. The true viscosity of the suspensions can be obtained by using Equations 3,4 and 6 in parallel disk torsional flows and nations 8-12 in capillary flows. 

The combined shear stress versus the true shear rate data in double logarithmic form are shown in Hgure 11 and indicate the presence of a viscous Newtonian region at the low shear rates employed in the torsional flow experiments. 

Figure 11. Shear stress versus the true shear rate at the wall from capillary and parallel disk torsional flow experiments on suspension 1.

Yilmazer, U. and Kalyon D.M. (1989), "Slip Effects in Capillaiy and Parallel Disk Torsional Flows of Highly Hlled Suspensions", J.Rheol., 33(8), 1197-1212. Yilmazer, U. and Kalyon D.M. (1991), "Dilatancy of Concentrated Suspensions with Newtonian Matrices", Polym.Comp., 12, 6-232. 

Figure 5.50. DMA sample geometries for solids and liquids for solids—dual cantilever, tension, single cantilever, three-point bending or flexure, compression for liquids— cone-plate flow, torsional flow the rheometers that measure liquid-state properties also measure the properties of solid samples in torsional shear (courtesy of TA Instruments).

The measured viscosities and first normal stress differences for Tsang and Dealy s two polyethylenes are shown in Figure 9.7. The data at shear rates up to 1 s were obtained in a torsional flow between a cone and plate, while the data at higher shear rates were obtained from the pressure drop in a capillary. The high- and low-shear rate data appear to be consistent, but it is difficult to obtain overlap with a commercial piston-driven capillary viscometer because of the importance of frictional losses at very low rates. These data are typical of many commercial polymers. 

Experiments on torsional flow and an overview of the onset and properties of elastic turbulence, as these low Reynolds number instabilities are sometimes known, is in... 

In the assumptions for flow between concentric cylinders, we ignored any end effects. It is not too difficult to estimate their importance. At the bottom of the cylinder in Figure 5.3.1 there will also be a shear flow. This can be approximated as torsional flow between parallel disks, to be discussed in Section 5.5. From that section we can use eq. 5.5.8 and the power law, eq. 2.4.12, for to calculate the extra torque contributed by the end... 

Parallel disks (S.S) (torsional flow) Easy to load viscous samples Best for C and C" of melts, curing Vary yhyh and 12. (Vi - N2)(y) Nonhomogeneous not good for (Kf.y) OK for G t) and tKy) Edge failure Evaporation... 

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