Particle acceleration coefficient

The simplest model potentials that form liquid crystals are the hard ellipsoid fluid and the hard cylinder fluid [4]. Linear and angular momenta are constant between collisions so that very efficient molecular dynamics algorithms can be devised. Unfortunately, when transport coefficients are calculated external fields and thermostats are often applied. That means that the particles accelerate between collisions. The advantages of using hard body fluids is conse-... 

The virtual mass coefficient for a sphere in an invicid fluid is thus Cy = The basic model (5.111) is often slightly extended to take into account the self-motion of the fluid. In general the added mass force is expressed in terms of the relative acceleration of the fluid with respect to the particle acceleration. 

A portion of this supersonic velocity will be transferred to the injected powder particles, that is the powder particles will gain acceleration from the plasma jet by momentum transfer. The particle acceleration dUp/df is proportional to the drag coefficient CD and the velocity gradient between the gas velocity and the particle velocity, Vg — Vp and inversely proportional to the particle diameter dp and the particle density pp as expressed by the Basset-Boussinesq-Oseen equation of... 

A large part of the electric energy spent on ionisation of the plasma gas will be recovered by recombination in the form of heat. Hence, the hot plasma will heat the powder particles accelerated by momentum transfer along a trajectory in the jet. The amount of heat a particle acquires can be approximated by the balance of the amounts of heat gained by convective energy transfer, Qc = h A (T - Ts) and of heat lost by radiative energy transfer, QR = convective heat transfer coefficient, A = surface area of the particle, Tx =free-stream plasma temperature, Ts = particle surface temperature, Ta = temperature of the surrounding atmosphere, a = Stefan-Boltzmann coefficient and e = particle emissivity. The heat transfer coefficient between a gas and a (spherical) particle can be expressed as a function of the non-dimensional Nusselt number, Nu as... 

In continuous separations, a sample mixture is continuously introduced to a spinning rotor as the clarified supernatant continuously exits. Continuous-feed centrifuges may be used for rate, pelleting, filtration, or isopycnic separations. They are best suited for applications in which large volumes and/or low-concentration samples must be processed, the particle sedimentation coefficient is high 50s, or long acceleration/deceleration times are required. 

By using rather than C/g, the effective Reynolds mmiber is reduced so that the calculated Nusselt numbers tend toward the conservative conduction limit of 2. Obviously this approach greatly simplifies the actual phenomena, and disregards the complications of particle acceleration, clustering, and downflow at walls. Estimates of the particle/gas heat transfer coefficient (/jp) from Eqs. (11) and (52) should be considered only as approximate. 

The stationary-state velocity per unit acceleration is a parameter which characterizes the settling particle and is called the sedimentation coefficient s ... 

We now have all the information necessary to develop some working expressions for particle settling. Look back at equation 3 (the resistance force exerted by the water), and the expressions for the drag coefficient (sidebar discussion on page 261). The important factor for us to realize is that the settling velocity of a particle is that velocity when accelerating and resisting forces are equal ... 

The added mass force accounts for the resistance of the fluid mass that is moving at the same acceleration as the particle. Neglecting the effect of the particle concentration on the virtual-mass coefficient, for a spherical particle, the volume of the added mass is equal to one-half of the particle volume, so that... 

D=mass diffumsion coefficient Z)T=fiiermal diffusion coefficient /=friction coefficient G=(oh (centrifugal acceleration) / =Boltzniann constant meff=particle effective mass r=radius of centrifuge basket s=sedimentation coefficient T = absolute temperature =geometric volume of die channel w=channel thickness y=diermal expansion coefficient p=electrophoretic... 

The range between these small and large particles is less well understood although some experimental studies have been reported (K9, Ul). Similar problems arise in interpretation as with accelerated motion (see Chapter 11). Measurements are commonly correlated by a turbulence-dependent drag coefficient, which contains a number of possible acceleration-dependent components. With fundamental understanding so poorly advanced, it is impossible to say to what extent results are specific to the experimental conditions employed. 

It is believed that this can be related to the differences in coefficient of restitution between the conveyed particles and the pipeline walls. On impact with the rubber, the particles will be decelerated, since the rubber will absorb much of the energy of impact. As a consequence, the particles will have to be re-accelerated back to their terminal velocity. The coefficient of restitution of the particles against the steel pipeline wall will be very much lower. This effect is clearly magnified by increase in velocity and explains why there is little difference between the two pipeline materials in low velocity dense phase conveying, but differ by 50% in high velocity dilute phase conveying. The results obtained with the barite were very similar. 

On one hand, solid materials to be processed with an impinging stream device have various sizes, while, on the other hand, the relative velocity between gas and particles varies from time to time in acceleration and deceleration stages of particle motion. Both factors make the value for Rep vary continuously with considerably large amplitude, which may be across various flow regimes. So, the variation of the drag coefficient, Cd, in various flow regimes has to be taken into account in the solution of the motion equations for the particle in various stages. 

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