Velocity, particle

In a horizontal pipeline the velocity of the particles will typically be about 80% of that of the air. This is usually expressed in terms of a slip ratio, defined in terms of the velocity of the particles divided by the velocity of the air transporting the particles, and in this case it would be 0.8. The value depends upon the particle size, shape and density, and so the value can vary over an extremely wide range. In vertically upward flow in a pipeline a typical value of the slip ratio will be about 0.7 in comparison. 

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The squares visible in figure 5 represent the position of hard particles at the moment of recording. Therefore the time distance between two video records is about 1,3 ms at a record rate of 750 Hz. With these data it is possible to calculate particle velocity. Figure 8 shows the particle movement in the molten bath caused by flow processes. The particles are captured at the contour of the molten bath and transported into the liquid phase. 

The transducer is modelled by a distribution of particle velocity source over the radiating surface Tr as... 

The physical situation of interest m a scattering problem is pictured in figure A3.11.3. We assume that the initial particle velocity v is comcident with the z axis and that the particle starts at z = -co, witli x = b = impact parameter, andy = 0. In this case, L = pvh. Subsequently, the particle moves in the v, z plane in a trajectory that might be as pictured in figure A3.11.4 (liere shown for a hard sphere potential). There is a point of closest approach, i.e., r = (iimer turning point for r motions) where... 

Time-of-flight experiments are used to measure particle velocities and particle mass per charge. The typical experiment... 

The topological (or Berry) phase [9,11,78] has been discussed in previous sections. The physical picture for it is that when a periodic force, slowly (adiabatically) varying in time, is applied to the system then, upon a full periodic evolution, the phase of the wave function may have a part that is independent of the amplitude of the force. This part exists in addition to that part of the phase that depends on the amplitude of the force and that contributes to the usual, dynamic phase. We shall now discuss whether a relativistic electron can have a Berry phase when this is absent in the framework of the Schrddinger equation, and vice versa. (We restrict the present discussion to the nearly nonrelativistic limit, when particle velocities are much smaller than c.)... 

A number of simulation methods based on Equation (7.115) have been described. Thess differ in the assumptions that are made about the nature of frictional and random forces A common simplifying assumption is that the collision frequency 7 is independent o time and position. The random force R(f) is often assumed to be uncorrelated with th particle velocities, positions and the forces acting on them, and to obey a Gaussiar distribution with zero mean. The force F, is assumed to be constant over the time step o the integration. 

This method, because it involves minimizing the sum of squares of the deviations xi — p, is called the method of least squares. We have encountered the principle before in our discussion of the most probable velocity of an individual particle (atom or molecule), given a Gaussian distr ibution of particle velocities. It is ver y powerful, and we shall use it in a number of different settings to obtain the best approximation to a data set of scalars (arithmetic mean), the best approximation to a straight line, and the best approximation to parabolic and higher-order data sets of two or more dimensions. 

Why are fhese beams, or jefs, distinguished from effusive beams by fheir description as supersonic In some ways fhis description is rafher misleading, firsf because particles in an effusive beam may well be fravelling af supersonic velocities and, second, because fhe name implies fhaf somefhing special happens when fhe particle velocities become supersonic whereas fhis is nof fhe case. Whaf supersonic is meanf fo imply is fhaf fhe particles may have very high Mach numbers (of fhe order of f 00). The Mach number M is defined as... 

The primary characteristic frequency of an ordinary gas is the rate of coUision f = V/X = ttVnD, where V is the mean particle velocity, and V = [SkT for particles of mass m. Among the special frequencies associated with plasmas, the most notable is the plasma frequency ... 

Restraining a gaseous plasma from expanding and compressing is also a form of plasma modification. Two reasons for plasma confinement are maintenance of the plasma and exclusion of contaminants. Plasmas may be confined by surrounding material, eg, the technique of wall confinement (23). A second approach to confinement involves the use of magnetic fields. The third class of confinement schemes depends on the inertial tendency of ions and associated electrons to restrain a plasma explosion for a brief but usehil length of time, ie, forces active over finite times are required to produce outward particle velocities. This inertial confinement is usually, but not necessarily, preceded by inward plasma motion and compression. 

Response to Electric and Acoustic Fields. If the stabilization of a suspension is primarily due to electrostatic repulsion, measurement of the zeta potential, can detect whether there is adequate electrostatic repulsion to overcome polarizabiUty attraction. A common guideline is that the dispersion should be stable if > 30 mV. In electrophoresis the appHed electric field is held constant and particle velocity is monitored using a microscope and video camera. In the electrosonic ampHtude technique the electric field is pulsed, and the sudden motion of the charged particles relative to their counterion atmospheres generates an acoustic pulse which can be related to the charge on the particles and the concentration of ions in solution (18). 

The primary mechanisms responsible for most particle segregation problems are sifting, particle velocity, air entrainment, particle entrainment, and dynamic effects (14). 

Particle Velocity on a. Surfa.ce. Smaller particles, those that are more irregular in shape and/or those that have a higher surface roughness, typically have a higher frictional drag on a hopper or chute surface. 

On a chute, higher drag results in lower particle velocity which can be accentuated by stratification on the chute surface because of the sifting mechanism. Concentrations of smaller particles close to the chute surface and larger particles at the top of the bed of material, combined with the typically higher frictional drag of finer particles, often result in a concentration of fine particles close to the end of the chute, and coarse particles farther away. This can be particulady detrimental if portions of the pile go to different processing points, as is often the case with multiple outiet bins or bins with vertical partitions. 

A steady-state rocket-type combustion spray unit has been developed, called high velocity oxy fuel (HVOF), that creates a steady state, continuous, supersonic spray stream (1.2—3 mm dia) resembling a rocket motor exhaust. The portable device injects and accelerates the particles inside a barrel (rocket nozzle). It produces coating quaHty and particle velocities equal to the D-gun at 5—10 times the spray rate with significantly reduced coating costs. 

Flame spraying is no longer the most widely used melt-spraying process. In the power-feed method, powders of relatively uniform size (<44 fim (325 mesh)) are fed at a controlled rate into the flame. The torch, which can be held by hand, is aimed a few cm from the surface. The particles remain in the flame envelope until impingement. Particle velocity is typically 46 m/s, and the particles become at least partially molten. Upon impingement, the particles cool rapidly and soHdify to form a relatively porous, but coherent, polycrystalline layer. In the rod-feed system, the flame impinges on the tip of a rod made of the material to be sprayed. As the rod becomes molten, droplets of material leave the rod with the flame. The rod is fed into the flame at a rate commensurate with melt removal. The torch is held at a distance of ca 8 cm from the object to be coated particle velocities are ca 185 m/s. 

HVOF = high velocity oxy fuel, particle velocity 700 800 m/s... 

This equation is a reasonable model of electrokinetic behavior, although for theoretical studies many possible corrections must be considered. Correction must always be made for electrokinetic effects at the wall of the cell, since this wall also carries a double layer. There are corrections for the motion of solvated ions through the medium, surface and bulk conductivity of the particles, nonspherical shape of the particles, etc. The parameter zeta, determined by measuring the particle velocity and substituting in the above equation, is a measure of the potential at the so-called surface of shear, ie, the surface dividing the moving particle and its adherent layer of solution from the stationary bulk of the solution. This surface of shear ties at an indeterrninate distance from the tme particle surface. Thus, the measured zeta potential can be related only semiquantitatively to the curves of Figure 3. 

The second method of exploitation occurs when the electric field is of a polarity such that the charged-particle migration occurs away from the filter medium. The contribution to the net-particle velocity of the elec trqphoreticaUy induced flow away from the filter medium is generally orders of magnitude less than the contribution to the net-... 

Figure 2.3. A rigid piston drives a shock wave into compressible fluid in an imaginary flow tube with unit cross-sectional area. The shock wave moves at velocity U into fluid with initial state 0, which changes discontinuously to state 1 behind the shock wave. Particle velocity u is identical to the piston velocity.

To permit a more general discussion, we can replace the snowplow with a piston, and replace the snow with any fluid (Fig. 2,3), We consider the example shown in a reference frame in which the undisturbed fluid has zero velocity. When the piston moves, it applies a planar stress, a, to the fluid. For a non-viscous, hydrodynamic fluid, the stress is numerically equal to the pressure, P, The pressure induces a shock discontinuity, denoted by which propagates through the fluid with velocity U. The velocity u of the piston, and the shocked material carried with it (with respect to the stationary frame of reference), is called the particle velocity, since that would be the velocity of a particle caught up in the flow, or of a particle of the fluid. 

The importance of the distinction between shock velocity and particle velocity cannot be overemphasized. The particle velocity refers to the velocity... 

The basic concepts of shock and particle velocities are well illustrated by an example first introduced by Duvall and Band (1968). Here we assume that a string of beads of diameter d, mass m, and spaced a fixed distance / apart on a smooth (frictionless) wire is impacted by a rigid, massive piston at velocity v. Each bead is assumed to undergo perfectly elastic, rigid-body motion upon impact with its neighbor. 

After impact the first bead assumes a velocity 2v, due to its rigid elastic response. This is the instantaneous particle velocity that the bead acquires. The first bead travels across the gap d and impacts the second bead. The only way by which momentum and energy can be simultaneously conserved is for the first bead to come to rest at the instant the second bead acquires a velocity... 

Figure 2.4. Velocity history of the first bead on a wire. Average velocity v is identified with drift or with the particle velocity of the bead.

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is... 

Note that this is faster than the particle velocity u = v. 

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