Couette streaming

The first mode may occur when a droplet is subjected to aerodynamic pressures or viscous stresses in a parallel or rotating flow. A droplet may experience the second type of breakup when exposed to a plane hyperbolic or Couette flow. The third type of breakup may occur when a droplet is in irregular flow patterns. In addition, the actual breakup modes also depend on whether a droplet is subjected to steady acceleration, or suddenly exposed to a high-velocity gas stream.[2701[2751... 

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. 

It is also possible to calculate the shear viscosities and the twist viscosities by applying the SLLOD equations of motion for planar Couette flow, Eq. (3.9). If we have a velocity field in the x-direction that varies linearly in the z-direction the velocity gradient becomes Vu=ye ej, see Fig. 3. Introducing a director based coordinate system (Cj, C2, 63) where the director points in the e3-direction and the angle between the director and the stream lines is equal to 0, gives the following expression for the strain rate in the director based coordinate system. 

Uniform free stream flow velocity Uniform speed of plate in Couette flow Uniform velocity of fluid at channel inlet, equal to average longitudinal velocity in channel with no fluid removal or addition... 

For definiteness let us assume that the experiment is carried out in a cylindrical CouETTE apparatus. This may be represented by Fig. 10 a, Fig. 10 a. Cylindrical Fig. 10 b. Ellipsoidof polarisability where the outer cylinder is CouETTE apparatus. in the streaming liquid. assumed to rotate with respect... 

In employing the B.E.M. to the problem in hand, a dimensionless stream function-vortic-ity formulation has been used. Results are presented for constant stream function values in the vicinity of the inlet to a thrust pad enabling a visualisation of the flow pattern. A determination of the pressure variation on the moving surface (or runner) of the bearing in the inlet region is also undertaken. The non-zero value of pressure at the nominal inlet to the pad is detailed with consideration of both Poiseuille and Couette dominated flows. 

With the problem as stated there are three types of flow, a pressure driven flow, a plate driven flow and a mixture of the two. A pressure driven flow is taken to be a flow dominated by Poiseuille flow in the channel ODEF but which is not a pure Poiseuille flow. Conversely a plate driven flow is a flow dominated by Couette flow in the channel. Using these definitions, results are presented for both a plate driven and a pressure driven flow. In addition the pressure generated on the moving plate is also presented for a fixed flow rate Q and for various speeds U. The results for a flow rate of 3.0 and a plate speed of 1.0 are shown in Figure (5). The upper diagram shows lines of constant stream function, calculated at equal intervals between 0 and Q (3.0 in this example). The velocity profiles beneath are calculated at the stations (a) to (e) in the x-direction and to a normalised height of 1,0 (the film thickness) in the y-direction. 

Couette flow can be used as a prototype flow to model shear-driven flows such as micromotor, microbearing, and so on. As the flow is shear driven, the pressure does not change in the stream-wise direction. The compressibility effects may be important for large temperature fluctuations or at high speed. Let us consider an incompressible Couette flow with slip (Figure 3.12). 

Rotational Couette flow (RCF) is analyzed in the next example. Because the flow is confined inside the Couette flow cell and there is no exit stream, we use the nomenclature G(y) and g(y)dy instead of F(y) mdj y)dy. 

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