Rotating velocity pattern

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. 

Acceleration of rotation speed is, roughly speaking, wave pattern (phase) speed (20-100km/s), which is enough to enforce the equatorial rotation velocity to reach its break-up velocity. 

Fig. 1. The velocity pattern for a rotating-disc electrode. The functions F, G, and H describe the radial, angular, and normal components, respectively. The distance normal to the electrode, z, is normalised with the thickness of the hydrodynamic layer, ZH, where ZH is given by vft2itW) and v/cm2s-1 and W/Hz are the kinematic viscosity and rotation speed, respectively.

Since PCA filters out the vibrational motions with frequencies higher than 2n/t Equation 5.14 means that the rotational velocity of the moving normal mode coordinates is determined entirely by the fastest motions recorded in the trajectory. In other words, the rotation is so quick that the same pattern of motion never appears after one cycle of vibration, or the protein continuously changes its pattern of motion by rotating the mode space. 

Fig. 7.21 (a) Scattering curves of 2D SAXS patterns of PCL filaments drawn at different screw rotation velocities and (b) correlation function obtained ifom the scattering curves... 

Fig. 2.3 The HH 30 system ([27]). The background image, taken with the Hubble Space Telescope (HST [28]), shows an edge-tm disk traced by the dark bar, a jet perpendicular to the disk and scattered light from the embedded proto-star. The left panel presents the CO(/ = 2 — 1) emission at large positive and negative velocities relative to the dense core narrow emission. This high velocity CO emission follows the narrow jet. The middle panel presents the CO (7 = 2 — 1) emission in two velocity intervals indicated with blue and red contours the emission approaching us/ieceding from us. This velocity pattern is consistent with Keplerian rotation around a solar mass star. The right panel presents the continuum emission due to dust grains in the circumstellar disk. The spatial resolution of the millimetre observations is 1" [27]...

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. 

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. 

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 ... 

---