Couette flow apparatus

Canedo et al. (36) confirmed these predictions for bubbles in a Couette flow apparatus. 

The breakup or bursting of liquid droplets suspended in liquids undergoing shear flow has been studied and observed by many researchers beginning with the classic work of G. I. Taylor in the 1930s. For low viscosity drops, two mechanisms of breakup were identified at critical capillary number values. In the first one, the pointed droplet ends release a stream of smaller droplets termed tip streaming whereas, in the second mechanism the drop breaks into two main fragments and one or more satellite droplets. Strictly inviscid droplets such as gas bubbles were found to be stable at all conditions. It must be recalled, however, that gas bubbles are compressible and soluble, and this may play a role in the relief of hydrodynamic instabilities. The relative stability of gas bubbles in shear flow was confirmed experimentally by Canedo et al. (36). They could stretch a bubble all around the cylinder in a Couette flow apparatus without any signs of breakup. Of course, in a real devolatilizer, the flow is not a steady simple shear flow and bubble breakup is more likely to take place. 

Figure 14.5 Comparison of predicted (solid lines) and experimental (symbols) time evolution of the mass mean aggregate diameter in a Couette flow apparatus at different global average shear rates Mean primary particle diameter 0.81 pm solids volume fraction 3.76 x 10 pH 9.15 ...

U, V cm/s Speed of moving plane in planar Couette flow apparatus 7.2... 

Among the different possible ways to measure viscosities in rotating viscometers, the coaxial cylinder apparatus is the most commonly used in practice. The measured liquid intersperses the annular gap between the stationary inner cylinder (bob) and the rotating outer cylinder (cup). Therefore a velocity gradient builds between the inner and outer cylinders (Couette flow). The momentum, which is transferred by this downward gradient to the inner cylinder, is directly proportional to the viscosity. Deflection is compensated by a torsion bar and the equilibrium deflection is measured electrically. The measurement of the angular velocity of the cup and the angular deflection of the bob makes it possible to determine the viscosity [4, 11]. 

The apparatus was heated in an oven at 175° and the inner cylinder rotated to give an amount of shear strain (i.e., similar to Couette flow in Figure 2.8). 

Figure 20-8 Torque versus impeller speed for water and a Cm = 0.10 bleached kraft suspension measured in the Couette test apparatus described in the caption to Figure 20-7. The insert diagrams show the observed pulp suspension motion at points along the flow curve.

Flow birefringence of polymer solutions is, in general, measured with the aid of an apparatus of the Couette type, containing two coaxial cylinders. One of these cylinders is rotated at constant speed, the other is kept in a fixed position. The light beam for the birefringence measurement is directed through the annular gap between these cylinders, in a direction parallel with the axis of the apparatus. In this way, the difference of principal refractive indices An is measured just in the above defined plane of flow (1—2 plane). 

It is also possible to calculate the flow path in a Couette apparatus for non-Newtonian liquids (flowing between rotating cylinders Fig. 31) (see page 56). If an inner cylinder rotates at an angular velocity co and a shear deformation takes place in the gap between the internal and external cylinder (R — i a) we observe a torque M ... 

Several designs have evolved, many with horizontal axes (i.e. both ends closed) with the outer cylinder rotating and the inner cylinder fixed, which provides best hydrodynamic stability. Some horizontal-axis Couette flocculators are flow-through designs, even with a tapered gap to provide taper flocculation However, horizontal-axis apparatuses suffer from end effects which cause secondary circulation, so only a limited central zone (about one quarter of the length) is in defined laminar flow. 

Although Newton had the right physical insight, it was not until 1845 that Stokes finally was able to write out this concept in three-dimensional mathematical form. Only in 1856 were Poiseuille s capillary flow data analyzed to prove Newton s relation experimentally. Couette tested the relation carefully, using the concentric cylinder apparatus shown in Chapter 5 (Figure 5.1.1), and found that his results agreed with the viscosities he measured in capillary flow experiments (Couette, 1890 Markovitz, 1968). 

A continuous highly oriented fiber may be grown from dilute polyethylene solution subjected to shear flow in a Couette apparatus [70,74]. This device consists of a pair of coaxial cylinders, the inner one of which can be rotated rapidly. A dilute polyethylene solution introduced into the gap between the cylinders is subjected to shear flow. When the appropriate conditions of shear, temperature, and concentration are met, the polymer will crystallize on to a seed fiber held in the flow field. As the extended polyethylene fiber grows, it is wound up at a rate equal to its extensional growth rate, the tip of the growing fiber thus remaining at a fixed position. The resulting fiber consists of a bundle of shish... 

For quantitative measurements an apparatus is used which resembles the CoUette viscosimeter. It consists of two coaxial cylinders inside one another the outer or the inner of which can rotate, so that in the liquid between the cylinders a laminar flow is produced for a not too great velocity of the rotating cylinder ... 

---