Hydrodynamics free falling velocity

In the narrow tubes used by Beek and van Heuven, the bubbles assumed the shape of Dumitrescu (or Taylor) bubbles. Using the hydrodynamics of bubble rise and the penetration theory of absorption, an expression was developed for the total absorption rate from one bubble. The liquid surface velocity was assumed to be that of free fall, and the bubble surface area was approximated by a spherical section and a hyperbola of revolution. Values calculated from this model were 30% above the measured absorption rates. Further experiments indicated that velocities are reduced at the rear of the bubble, and are certainly much less than free fall velocities. A reduction in surface tension was also indicated by extreme curvature at the rear of the bubble. 

In gas-liquid spray towers the liquid is atomized and enters as a fine spray at the top and the gas is introduced at the bottom. The gas flow rate has to be kept sufficiently low to permit the liquid to fall. It is generally chosen in such way that the liquid drops of mean diameter fall at 20 percent of their free-fall velocity, as calculated from Stokes law. An efficient dispersion of the liquid requires the openings of the distributor to be small and the pressure high. Thereby a fraction of the drops hits the wall and flows down the wall as a film. Furthermore, a certain degree of coalescence of the drops is inevitable, so that the drop size, velocity, and therefore residence time vary strongly with position. A rigorous hydrodynamic analysis of such a situation is extremely complicated so that only the overall behavior has been studied. 

Hydrodynamics of free fall or rise of a spherical crystal The following is the method to calculate the free fall or rise velocity of a spherical crystal (Clift et al., 1978). For a small particle (see below) or viscous fluid, the ascent or descent velocity U can be calculated using Stokes law ... 

Figure 2.10 Cylindrically symmetric hydrodynamical model of accretion flow with rotation during the early collapse phase, showing the inflow of matter in the meridional plane and the build-up of a flat rotating disk structure after about 1.05 free-fall times. Arrows indicate matter flow direction and velocity, gray lines indicate cuts of isodensity surfaces with meridional plane. Dark crosses outline locations of supersonic to subsonic transition of inflow velocity this corresponds to the position of the accretion shock. Matter falling along the polar axis and within the equatorial plane arrive within 1600 yr almost simultaneously, which results in an almost instantaneous formation of an extended initial accretion disk [new model calculation following the methods in Tscharnuter (1987), figure kindly contributed by W. M. Tscharnuter],...

---

See also in sourсe #XX -- [ ]

---