Couette shear rate

The viscous dissipation is determined by the product of shear stress and shear rate. The average shear rate in the screw channel can be approximated by the Couette shear rate ... 

The polymer melt viscosity ri will depend on the local shear rate in the screw channel. If it is assumed that the representative shear rate in the channel is the Couette shear rate and that the polymer melt behaves as a power law fluid, which melt viscosity can be represented by ... 

The situation in the screw clearance is substantially different from the screw channel. The strain rates in the screw channel are relatively low, but the melt temperature variations can be high [84]. In the screw clearance, however, the strain rates are very high, and the stock temperature increase can also be very high. This can be verified by the following simple analysis. The shear rate in the clearance is approximately the Couette shear rate ... 

The Haake ProFlow on-line rheometer, which was designed for measuring the melt viscosity and flow index, was side-mounted at the end of a single screw extruder with a diameter of 20 mm and the melt shear viscosity of each resin was measured online at 250°C. The values of the shear rates inside the channel of conventional screw element and in the barrier clearance of the fluted mixing element used in this work, whieh are approximated by the Couette shear rate, are calculated to be about 10 s and 100 s, respectively. The viscosity ratios of the dispersed phase to the continuous phase for used PP/PA6 blend at these two shear rates are about 2.6 and 4.2, respectively. 

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

Figure 3 illustrates some additional capability of the flow code. Here no pressure gradient is Imposed (this is then drag or "Couette flow only), but we also compute the temperatures resulting from Internal viscous dissipation. The shear rate in this case is just 7 — 3u/3y — U/H. The associated stress is.r — 177 = i/CU/H), and the thermal dissipation is then Q - r7 - i/CU/H). Figure 3 also shows the temperature profile which is obtained if the upper boundary exhibits a convective rather than fixed condition. The convective heat transfer coefficient h was set to unity this corresponds to a "Nusselt Number" Nu - (hH/k) - 1. 

Although only one density profile Is shown In each of Figures 7 and 8 the density profiles of the two systems both at equilibrium and In the presence of flow that have been determined. A conclusion of great importance that is suggested by the Couette flow simulations is that the density profiles of the two systems in the presence of flow coincide with the equilibrium density profiles, even at the extremely high shear rates employed in our simulation. A detailed statistical analysis that Justifies this point was presented In Reference ( ). 

MHz, from 20% w/w CTAB-D20 (41 °C) at observed, consistent with an ordered phase, different positions across the annular gap of a while near the outer wall the single peak of an cylindrical Couette cell and at an apparent isotropic phase is seen. In between, a mixed shear rate of 20 s 1. Near the inner wall, where phase region exists (adapted from Ref. [38]). 

One characteristic of shear banded flow is the presence of fluctuations in the flow field. Such fluctuations also occur in some glassy colloidal materials at colloid volume fractions close to the glass transition. One such system is the soft gel formed by crowded monodisperse multiarm (122) star 1,4-polybutadienes in decane. Using NMR velocimetry Holmes et al. [23] found evidence for fluctuations in the flow behavior across the gap of a wide gap concentric cylindrical Couette device, in association with a degree of apparent slip at the inner wall. The timescale of these fluctuations appeared to be rapid (with respect to the measurement time per shear rate in the flow curve), in the order of tens to hundreds of milliseconds. As a result, the velocity distributions, measured at different points across the cell, exhibited bimodal behavior, as apparent in Figure 2.8.13. These workers interpreted their data... 

Fig. 2.8.13 Velocity probability distributions at different positions across the gap in a 5 mm-9 mm Couette cell at a shear of 0.101 s-1 and following long pre-shearing at high shear rate.

Common geometries used to make viscosity measurements over a range of shear rates are Couette, concentric cylinder, or cup and bob systems. The gap between the two cylinders is usually small so that a constant shear rate can be assumed at all points in the gap. When the liquid is in laminar flow, any small element of the liquid moves along lines of constant velocity known as streamlines. The translational velocity of the element is the same as that of the streamline at its centre. There is of course a velocity difference across the element equal to the shear rate and this shearing action means that there is a rotational or vorticity component to the flow field which is numerically equal to the shear rate/2. The geometry is shown in Figure 1.7. 

When the shear rate reaches a critical value, secondary flows occur. In the concentric cylinder, a stable secondary flow is set up with a rotational axis perpendicular to both the shear gradient direction and the vorticity axis, i.e. a rotation occurs around a streamline. Thus a series of rolling toroidal flow patterns occur in the annulus of the Couette. This of course enhances the energy dissipation and we see an increase in the stress over what we might expect. The critical value of the angular velocity of the moving cylinder, Qc, gives the Taylor number ... 

The Taylor vortices described above are an example of stable secondary flows. At high shear rates the secondary flows become chaotic and turbulent flow occurs. This happens when the inertial forces exceed the viscous forces in the liquid. The Reynolds number gives the value of this ratio and in general is written in terms of the linear liquid velocity, u, the dimension of the shear gradient direction (the gap in a Couette or the radius of a pipe), the liquid density and the viscosity. For a Couette we have ... 

Couette flow is shear-driven flow, as opposed to pressure-driven. In this instance, two parallel plates, separated by a distances h, are sheared relative to one another. The motion induces shear in the interstitial fluid, generating a linear velocity profile that depends on the motion of the moving surface. If we assume a linear shear rate, the shear stress is given simply by... 

The monodisperse materials described hereafter were obtained with the Couette type cell designed by Bibette et al. [ 150,159]. It consists of two concentric cylinders (rotor and stator) separated by a very narrow gap (100 pm), allowing application of spatially homogeneous shear rates over a very wide range (from 0 to 14280 s ), with shearing durations of the order of 10 s. 

Inverted W/O emulsion. The premixed emulsion was composed of aqueous droplets dispersed in an oil phase containing a lipophilic surfactant. The droplet mass fraction (/>, was set to 80%. This crude emulsion was sheared into the Couette-type cell [159] at constant shear rate V = 10000 s and a... 

Two main types of viscometers are suitable for the determination of the viscosity of a polymer melt The rotation viscometer (Couette viscometer, cone-plate viscometer) and the capillary viscometer or capillary extrusiometer. The latter are especially suitable for laboratory use since they are relatively easy to handle and are also applicable in the case of high shear rates. With the capillary extrusiometer the measure of fluidity is not expressed in terms of the melt viscosity q but as the amount of material extruded in a given time (10 min). The amount of ex-trudate per unit of time is called the melt index or melt flow index i (MFI). It is also necessary to specify the temperature and the shearing stress or load. Thus MFI/2 (190 °C)=9.2 g/10 min means that at 190 °C and 2 kg load, 9.2 g of poly-... 

The main characteristics of Newtonian liquids is that simple shear flow (e.g., Couette flow) generates shear stress t, which is proportional to the shear rate... 

Fig. 4.25 Experimentally measured SANS patterns for an FCC micellar phase in a dPS-PI diblock (A/ = 55kgmor, 60wt% PS) in core contrast-matched decane/ d-decane mixtures (15wt% polymer) subject to steady shear in a Couette cell at different shear rates (McConnell et al. 1995) (a) y — 0.01 s aligned by inserting the stator (b) y=0.06s 1 (c) y = 0.66s 1 (d) y = 6.60s (e) y = 66.0 s (f) y = 200.0s-1. The wavevectors qv (horizontal) and qe (vertical) for these patterns range from —0.028 to 0.028 A. ...

A graphic example of the consequences of the existence of in stress in simple steady shear flows is demonstrated by the well-known Weissenberg rod-climbing effect (5). As shown in Fig. 3.3, it involves another simple shear flow, the Couette (6) torsional concentric cylinder flow,3 where x = 6, x2 = r, x3 = z. The flow creates a shear rate y12 y, which in Newtonian fluids generates only one stress component 112-Polyisobutelene molecules in solution used in Fig. 3.3(b) become oriented in the 1 direction, giving rise to the shear stress component in addition to the normal stress component in. 

Figure 3.19 Profiles of shear stress, shear rate and speed through the cross-section in the case of an isothermal, simple shear flow (Couette flow) with Newtonian, shear thinning, and shearthickening fluids...

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