Critical relative velocity

Subjected to steady acceleration, a droplet is flattened gradually. When a critical relative velocity is reached, the flattened droplet is blown out into a hollow bag anchored to a nearly circular rim which contains at least 70% of the mass of the original droplet. Surface tension force is sufficient to allow the bag shape to develop. The bag, with a concave surface to the gas flow, is stretched and swept off in the downstream direction. The rupture of the bag produces a cloud of very fine droplets presumably via a perforation mode, and the rim breaks up into relatively larger droplets, although all droplets are at least an order of magnitude smaller than the initial droplet size. This is referred to as bag breakup (Fig. 3.10)T2861... 

Howarth (H15) developed an expression for collision efficiencies by assuming an analogy to bimolecular gas reactions. He assumed that a critical relative velocity IV exists along the lines of centers of two colliding drops which must be exceeded for a collision to result in a coalescence. By assuming that the three-dimensional Maxwell s equation describes the drop turbulent velocity fluctuations, he obtained the coalescence efficiency as the fraction of drops which have kinetic energy exceeding IV. Thus,... 

To implement the Doppler-selected TOF measurement, the initial relative velocity is arranged to be parallel to the propagation vector of the probe laser. This critical configuration can readily be achieved in this rotating sources machine.36 Under this configuration, each Doppler-sliced 2D distribution exhibits a cylindrical symmetry The slit in front of the TOF spectrometer allows only those products with a rather small vx to be detected. Hence, only the -distribution, obtained by the TOF measurement, is needed to completely characterize the Doppler-sliced 2D (vx — vy) distribution. 

The critical resulting velocity of the liquid relative to the bubble, v el, can be evaluated from the critical Weber number, We ... 

Prediction of Critical Sizes. In order to use the above model for actual predictions, it is necessary to assign values to the relative velocity U0 this is, at the present level of knowledge, an extremely difficult task since, due to bubble motion (and perhaps the presence of fixed and moving internals in a fluid bed such as, for example, draft tubes) the particle movement in a fluidized bed is extremely complex. Some crude estimates of the relative velocity between particles have been made (Ennis etal., 1991) and these were expressed as... 

In some practical processes, a high relative velocity may not exist and effects of turbulence on droplet breakup may become dominant. In such situations Kolmogorov, 280 and Hinze[27°l hypothesized that the turbulent fluctuations are responsible for droplet breakup, and the dynamic pressure forces of the turbulent motion determine the maximum stable droplet size. Using Clay s data, 2811 and assuming isotropic turbulence, an expression was derived for the critical Weber number 270 ... 

MMD pGU2R Q 1 a f 10 Tt 2/3 J 0 V 1/12 fnLPLPG(J L. 4 A Pl J Derived from spray data for wax melts using micromerograph and shifting technique Crossstream and co-stream injections of liquid into air Relative velocity is important Properties of fluids are less critical Geometry and operation of the injection is of least importance. Weiss Worsham [259]... 

The hematite with adsorbed Co-57 or Sb-119 along with the solution was subjected to emission Mossbauer measurement at 24 1°C with the experimental setup shown in Figure 2. The absorber, Fe-57-enriched potassium ferrocyanide (0.5 mg Fe-57/cm2) or barium stannate (0.9 mg Sn-119/cm2), was driven by a Hanger 700-series Mossbauer spectrometer connected to a Tracor-Northern TN-7200 multi-channel analyzer. The Mosssbauer gamma-rays of Co-57 and Sb-119 were detected respectively with a Kr(+3% carbon dioxide)-filled proportional counter and with a 2 mm-thick Nal(Tl) scintillation counter through 65 pm-thick Pd critical absorber for Sn K X-rays. The integral errors in the relative velocity were estimated to be of the order of 0.05 mm/s by repeated calibration measurements using standard absorbers. 

Suppose that there is an energetic barrier e that must be overcome for a reaction to occur, for example, the energy needed to break a critical chemical bond. The translational energy of the relative velocity of the collision partners is available to surmount the reaction energy barrier. We consider a simple picture called the line-of-centers model of reactive collisions. In this model only the velocity directed along the line-of-centers between the two molecules at the point of collision is effective in overcoming the barrier to reaction. 

Once the relative impact velocity between two colliding spheres is higher than the critical yield velocity, plastic deformation must occur. Heat loss is another phenomenon often coupled with such collisions. Collisions with plastic deformation are referred to as inelastic collisions. All the energy transfer in the form of plastic deformation and heat loss in an inelastic collision is considered as a kinetic energy loss. 

In order for a reaction to occur, the energy of collision must equal or exceed some critical value called the threshold energy. The effective energy is, of course, not the total kinetic energy of the two colliding molecules but is, instead, the kinetic energy corresponding to the component of the relative velocity of the two... 

If we assume that the critical energy need not be localized in the two degrees of freedom of the relative velocity components but may be dispersed in internal degrees of freedom of the colliding molecules, then we find for the total frequency of collision in which there is at least energy E distributed in n chemical degrees of freedom "... 

A jet may be formed when two surfaces collide at high relative velocity and at certain angles. The Jet is made of material that has been stressed into plastic flow caused by high pressure at the collision interface. Jets, thus formed, are the critical element in two special areas of explosives applications cutting with shaped charges and explosive welding. 

Figure 1. Schematic presentation of a short segment of a trajectory passing through an element dS of the potential energy surface near the critical dividing strriace element dC. Defined are the relevant components of the relative velocity v of the collision partners. R is the vector joining the centers of mass of the colliding species, n is the rmit vector in the direction of the potential gradient at dS.

Figure 5. Schematic representation of O + H2 and O + HO IDCI) collisions. The heavy line repesents a part of the critical dividing surface, lighter lines represent equipotential contours. Ellipsoidal approximations are used for both kind of surfaces as described in the text, v is the relative velocity of the collision partners, R is their center-of-mass separation vector, y is te Jacobi angle, n is the normal to the equipotential energy surfeces. The coordinate origin is at the center of mass of the molecule axis x coincides with its longitudinal axis. In the present model calculations, straight line trajectories up to the critical dividing surface are assumed...

Slip, or relative velocity between phases, occurs for vertical flow as well as for horizontal. No completely satisfactory, flow regime-independent correlation for volume fraction or holdup exists for vertical flow. Two frequently used flow regime-independent methods are those by Hughmark and Pressburg AIChE J., 7, 677 [1961]) and Hughmark Chem. Eng. Prog., 58[4], 62 [April 1962]). Pressure drop in upflow may be calculated by the procedure described in Hu mark Ind. Eng. Chem. Fundam., 2, 315-321 [1963]). The mechanistic, flow regime-based methods are advisable for critical applications. 

Pollutant Fluxes. Hourly deposition velocities were multiplied by hourly pollutant concentrations to get hourly pollutant fluxes. These were summed over exposure periods for hours of wetness with different critical relative humidity criteria (75 to 90% in 5% intervals). Average fluxes were then calculated by dividing by the time-of-wetness. The results were compared with fluxes calculated by multiplying average deposition velocities for a period by the average pollutant concentration during times of wetness. The values by the two methods were fairly consistent. 

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