Relative velocities

In centrifugal scruhhers (Fig. 11.26), an attempt is made to increase the relative velocity of particles and droplets by centrifuging the droplets in an outward direction. 

The coefficient of friction may also depend on the relative velocity of the two surfaces. This will, for example, affect the local temperature, the extent... 

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

B2.2.2.3 ENERGY AND ANGULAR MOMENTUM CENTRE OF MASS AND RELATIVE VELOCITY... 

Figure B2.3.16. Velocity diagram for die reaction of a photolytically generated reagent with an assumed stationary co-reagent. In this case, the relative velocity of the reagents is parallel to the velocity c of the centre of mass.

This dissipative force is proportional to the relative velocity of the two beads and acts so as tc reduce their relative momentum, v is tire difference between the two velocities (Vy = v, — v ) and vP rjj) is a weight function that depends upon the distemce and disappears for interbead distances greater than unity (i.e. r ). 

If a gas flows over the surface of a liquid, certain effects ensue. Only the relative velocity of the liquid surface and gas is important in giving rise to nebulization. Thus, some pneumatic nebulizers... 

In pneumatic nebulizers, the relative velocity of gas and liquid first induces a reduction in pressure above the surface of the liquid (see the calculation in Figure 19.4). The reduction in pressure is sufficient to cause liquids to flow out of capillary tubes, in accord with Poiseuille s formula (Figure 19.5). As the relative velocity of a liquid and a gas increases — particularly if the mass of liquid is small — this partial vacuum and rapid flow cause the surface of the liquid to be broken into droplets. An aerosol is formed. 

The size of the droplets formed in an aerosol has been examined for a range of conditions important in ICP/MS and can be predicted from an experimentally determined empirical formula (Figure 19.6). Of the two terms in the formula, the first is most important, except at very low relative flow rates. At low relative velocity of liquid and gas, simple droplet formation is observed, but as the relative velocity increases, the stream of liquid begins to flutter and to break apart into long thinner streamlets, which then break into droplets. At even higher relative velocity, the liquid surface is stripped off, and the thin films so-formed are broken down into... 

For a longitudinal disturbance of wavelength 12 pm, the droplets have a mean diameter of about 3-4 pm. These very fine droplets are ideal for ICP/MS and can be swept into the plasma flame by a flow of argon gas. Unlike pneumatic forms of nebulizer in which the relative velocities of the liquid and gas are most important in determining droplet size, the flow of gas in the ultrasonic nebulizer plays no part in the formation of the aerosol and serves merely as the droplet carrier. 

In the gas/liquid spray form of nebulizer, a stream of gas interacts with a stream of liquid. Depending on the relative velocity of the two streams and their relative orientation, the liquid flow is broken down into a spray of droplets, as in the common hair sprays. 

Figure 9.1 Distortion of flow streamlines around a spherical particle of radius R. The relative velocity in the plane containing the center of the sphere equals v, as r ...

Collection. IDPs can be coUected in space although the high relative velocity makes nondestmctive capture difficult. Below 80 km altitude, IDPs have decelerated from cosmic velocity and coUection is not a problem however, particles that are large or enter a very high velocity are modified by heating. Typical 5-)J.m IDPs are heated to 400°C during atmospheric entry whereas most particles larger than 100 ]Am are heated above 1300°C, when they melt to form cosmic spherules (Pig. 6). 

Extensional flows occur when fluid deformation is the result of a stretching motion. Extensional viscosity is related to the stress required for the stretching. This stress is necessary to increase the normalized distance between two material entities in the same plane when the separation is s and the relative velocity is ds/dt. The deformation rate is the extensional strain rate, which is given by equation 13 (108) ... 

The Weber number becomes important at conditions of high relative velocity between the injected Hquid and surrounding gas. Other dimensionless parameters, such as the Ohnesorge ((We /Re), Euler (AP/Pj y i)y and Taylor (Re/ We) numbers, have also been used to correlate spray characteristics. These parameters, however, are not used as often as the Reynolds and Weber numbers. 

The principal parameters affecting the size of droplets produced by twin-fluid atomizers have also been discussed (34). These parameters include Hquid viscosity, surface tension, initial jet diameter (or film thickness), air density, relative velocity, and air—Hquid ratio. However, these parameters may have an insignificant effect on droplet size if atomization occurs very rapidly near the atomizer exit. 

Most studies indicate that air velocity has a profound influence on mean droplet size in twin-fluid atomizers. Generally, the droplet size is inversely proportional to the atomizing air velocity. However, the relative velocity between the Hquid and air stream is more important than the absolute air velocity. 

Droplet size, particularly at high velocities, is controlled primarily by the relative velocity between liquid and air and in part by fuel viscosity and density (7). Surface tension has a minor effect. Minimum droplet size is achieved when the nozzle is designed to provide maximum physical contact between air and fuel. Hence primary air is introduced within the nozzle to provide both swid and shearing forces. Vaporization time is characteristically related to the square of droplet diameter and is inversely proportional to pressure drop across the atomizer (7). 

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

S] Correlates large amount of published data. Compares number of correlations, v,. = relative velocity, uVs. In packed bed, v,. = i>s pe,./e. 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Ap = projected particle area in direction of motion p = density of surrounding fluid u = relative velocity between particle and fluid... 

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