Couette geometry

Figure 7.8. (a) Photomicrograph of a premix silica-in-octane-in-water emulsion. The octane contains 17% vol of silica particles. Compositions are given in the text, (b) Same sample after being sheared at 3750 s in a Couette geometry device. The scale bar corresponds to 10 pm. 

Experimentally, the dynamic shear moduli are usually measured by applying sinusoidal oscillatory shear in constant stress or constant strain rheometers. This can be in parallel plate, cone-and-plate or concentric cylinder (Couette) geometries. An excellent monograph on rheology, including its application to polymers, is provided by Macosko (1994). 

Rofe, C. J., Lambert, R. K., and Callaghan, P. T. (1994). Nuclear magnetic resonance imaging of flow for a shear-thinning polymer in cylindrical Couette geometry. J. Rheology 38, 875-887. 

Problem 1.1 Compute the shear rate profile in the Taylor-Couette (or circular Couette) geometry (see Fig. Al-1) for a Newtonian fluid with negligible inertia and negligible gravity and for... 

In the last decade of the nineteenth century, Maurice Couette invented the concentric cylinder viscometer. This instrument was probably the first rotating device used to measure viscosities. Besides the coaxial cylinders (Couette geometry), other rotating viscometers with cone-plate and plate-plate geometries are used. Most of the viscometers used nowadays to determine apparent viscosities and other important rheological functions as a function of the shear rate are rotating devices. 

Equation [213] can be equivalently obtained using the Mori-Zwanzig formalism. " It is also seen that, in contrast to LRT developed for shear flow in bulk fluids, the one presented here has two coefficients, (which is similar to the shear viscosity q) and, which has no parallel in bulk fluids. should be interpreted as an average location at which hydrodynamics is found to be nominally invalid. Note that although the surface may have corrugations in the X as well as the y direction, the corrugation in the x direction alone matters to the frictional force in the planar Couette geometry. 

For dynamic mechanical and steady shear measurements, the Rheometric Scientific RFSII rheometer was used equipped with the sensitive range force rebalance transducer and couette geometry or parallel plate tooling. 

Figure 3-5. Typical rheometer geometries (a) parallel disk, (b) concentric cylinder (Couette) geometry, (c) cone-and-plate. Either the angular velocity is set and one measures the torque required to produce this rotation rate, or the torque is set and one measures the angular velocity. We analyze the Couette device in this section.

Couette geometry. Couette geometry, in which a piston is rotated... 

The excellent reproducibility of HPG-titanate gel viscosities is shown in Figure 12 in which data from two experiments are superimposed (29). The stress vs. time data are nearly indistinguishable. These data were taken in a narrow-gap Couette geometry (the ratio of the cup radius to bob radius was 1.1) that was loaded as it was rotating by using the impingement-mixing device (27). 

Figure 12. Reproducibility of viscosity data. Two sets of data are superimposed and show excellent reproducibility. Data were taken at ambient temperature in an RSIV rheometer with a Couette geometry and by using impingement mixing. Reproduced with permission from ref. 27. Copyright 1987 American...

If one needs to investigate the dependence of r] on shear rate, y, one must have access to a rheometer, an instrument that can characterize the dependence of viscosity on shear rate, thus enabling an extrapolation to the Newtonian limit. Typically, such measurements are conducted in Couette (concentric cylinder) or cone and plate geometry. In the Newtonian limit, for Couette geometry, when the inner cylinder is rotated, and provided that the gap between the inner and outer cylinder is small (i.e., RilRo < 0.99, where Ri and Ro are the radii of the inner and outer cylinders), the shear stress on the wall of the outer (resting) cylinder is... 

XX, YY, ZZ component of quadrupolar tensor q universal gas constant 8.31432 J/mol K radius of a curvature (Ch. 3) of a spherical particle or an atom (Ch. 15) of a capillary mid-point radius in Couette geometry Bjerrum radius... 

Mason et al. (136) determined the yield stresses and yield strains of a series of monodisperse emulsions, using either a cone-and-plate or double-wall Couette geometry in oscillatory mode. Wall-induced coales-cence and wall slip were claimed to be absent, but no mention is made of attempts to reduce end or edge effects. Estimated film thicknesses were used to arrive at the effective volume fractions. Their data for the yield stress could be fit to... 

The angular bracket indicates the time average. Notice that the friction coefiicient C, has disappeared from this relation although its existence was of crucial importance for the derivation of (2). The angular velocity uj is defined as the ratio of (L) and of the relevant component of the (time averaged) moment of inertia tensor. To be more specific, a plane Couette geometry is considered with the flow in -direction and the gradient of the velocity in y-direction, viz. Vx = jy, Vy = = 0, where... 

Figure 11 Schemes of the different geometries that can be used for flow or viscoelastic rheological measurements. From left to right double cylinders or Couette geometry, cone and plate geometry, and parallel plates geometry.

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