Rotation flow pattern

Fig. 15. Flow pattern in rotating Couette flow where and Q2 represent the outer and inner rotational speeds.

These simple velocity profiles do not indicate directly any dependence of the flow pattern efficiency upon the rotational speed of the centrifuge. A dependence on speed is to be expected on the basis of the argument that at high speeds the gas in the centrifuge is crowded toward the periphery of the rotor and that the effective distance between the countercurrent streams is thereby reduced. It can be seen from the two-sheU model that, as the position of upflowing stream approaches the periphery, the flow pattern efficiency drops off from its maximum value. 

When the flow pattern in a mixed tank is primarily tangential, the fluid discharge from the impeller to the surroundings and its entrainment into the impeller are small. Also, fluid transfer in the vertical direction is at a minimum. The mixing effect is lowest when the rotational velocity of the liquid approaches that of the mixer. 

If the room has a certain amount ol heat surplus, this will lead to thermal stratification. Ihe thermal stratification will attenuate the rotation, and eventually lead to a flow pattern as showm in Fig. 8.22,... 

The flow pattern in Fig. 10.55 has a violent turbulent region, characterized by a vortex street and two free vortices rotating in opposite directions... 

The propeller agitator with three blades rotates at relatively high speeds of 60-300 ips high efficient mixing is obtained. The generated flow pattern is axial flow since the fluid moves axially down to the centre and up the side of the tank. 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

The next most importtmt parameters in Czochralski growth of crystals are the heat flow and heat losses in the system. Actually, aU of the parameters (with the possible exception of 2 and 9) are strongly ciffected by the heat flow within the crystal-pulling system. A tj pical heat-flow pattern in a Czochralski sjretem involves both the crucible and the melt. The pattern of heat-flow is important but we will not expemd upon this topic here. Let it suffice to point out that heat-flow is set up in the melt by the direction of rotation of the cr5rstal being pulled. It is also ctffected by the upper surface of the melt and how well it is thermally insulated from its surroundings. The circular heat flow pattern causes the surface to radiate heat. The crystal also absorbs heat and re-radiates it... 

We can rotate the crucible by itself, or in conjunction with the crystal. But another complexity arises, namely what direction of rotation and what relative speed of rotation should we use for both, or either If we rotate the crystal clockwise and the crucible counter-clockwise, then the heat flow patterns become complex indeed. These complexities have been studied in detail but will not be enumerated here. 

As mentioned earlier, in curved channels a secondary flow pattern of two counter-rotating vortices is formed. Similarly to the situation depicted in Figrue 2.43, these vortices redistribute fluid volumes in a plane perpendicular to the main flow direction. Such a transversal mass transfer reduces the dispersion, a fact reflected in the dependence in Eq. (108) at large Dean numbers. For small Dean numbers, the secondary flow is negligible, and the dispersion in curved ducts equals the Taylor-Aris dispersion of straight ducts. 

Fig. 1. Flow near a rotating hemisphere electrode. (a) Dye movement at Re = 1300. (b, c) Spiral flow patterns etched on a copper hemisphere.

The lack of hydrodynamic definition was recognized by Eucken (E7), who considered convective diffusion transverse to a parallel flow, and obtained an expression analogous to the Leveque equation of heat transfer (L5b, B4c, p. 404). Experiments with Couette flow between a rotating inner cylinder and a stationary outer cylinder did not confirm his predictions (see also Section VI,D). At very low rotation rates laminar flow is stable, and does not contribute to the diffusion process since there is no velocity component in the radial direction. At higher rotation rates, secondary flow patterns form (Taylor vortices), and finally the flow becomes turbulent. Neither of the two flow regimes satisfies the conditions of the Leveque equation. 

Centrifugal force can also be used to separate solid particles from fluids by inducing the fluid to undergo a rotating or spiraling flow pattern in a stationary vessel (e.g., a cyclone) that has no moving parts. Cyclones are widely used to remove small particles from gas streams ( aerocyclones ) and suspended solids from liquid streams ( hydrocyclones ). 

M at 25°C [114]. Equation (51) or (52) enables the diffusivity of a solute to be measured. For example, from the slope of the line in Fig. 17 under sink conditions, D is calculated to be 6.1 X 10-6 cm2/sec for 2-naphthoic acid. At low rotational speeds, the dissolved solute may not be uniformly distributed throughout the volume of the dissolution medium, and/or natural convection may become significant. The former effect may complicate the analytical procedure, while the latter effect will cause positive deviations of J values from Eqs. (51) and (52). At high rotational speeds, turbulence may disturb the flow pattern in Fig. 16, causing other deviations [101,104],... 

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... 

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 ... 

In the paddle method, bulk Reynolds numbers range from Re = 2292 (25 rpm, 900 mL) up to Re = 31025 (200 rpm, 500 mL). In contrast, Reynolds numbers employing the basket apparatus range from Re = 231 to Re = 4541. These Reynolds numbers are derived from dissolution experiments in which oxygen was the solute [(10), Chapter 13.4.8] and illustrate that turbulent flow patterns may occur within the bulk medium, namely for flow close to the liquid surface of the dissolution medium. The numbers are valid provided that the whole liquid surface rotates. According to Levich (9), the onset of turbulent bulk flow under these conditions can then be assumed at Re 1500. 

None of the set-ups discussed so far provides stirring of the electrolyte for bubble removal or for enhancement of the reaction rates. A standard set-up developed to study kinetic electrode processes is the rotating disc electrode [11]. The electrode is a small flat disc set in a vertical axle. The hydrodynamic flow pattern at the disc depends on rotation speed and can be calculated. An additional ring electrode set at a different potential provides information about reaction products such as, for example, hydrogen. However, because this set-up is designed to study kinetic processes and is usually equipped with a platinum disc, it becomes inconvenient if silicon samples of different geometries have to be mounted. 

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