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Particle damping

As indicated in Section 9.1.4.1, particle damping can be of greater significance. The theory of sound attenuation by spherical inert particles in the gas is well developed [44]-[49]. A number of different regimes may occur [7], but that of greatest practical interest has [Pg.312]

Evaluation of the average in equation (43) necessitates investigation of the oscillatory velocity fields. If equation (24) is employed for the gas velocity and a similar representation, = Re V , is introduced for the particle velocity, then by use of the equation of motion for a particle. [Pg.313]

By substitution of equations (28), (45), and (47) into equation (43), we can show that [Pg.313]

In Section 9.1.4, many different approaches to the analysis of various types of damping mechanisms were indicated. The variety of formulations exposed may help to show alternative paths to damping calculations. [Pg.314]

FIGURE 9.3. Comparison of theory and experiment concerning particle attenuation, showing dimensionless damping coefficient as a function of dimensionless particle radius [50], [Pg.314]


According to the theory proposed by Horton and McGie,[io] the particle damping constant is determined according to ... [Pg.395]

In this section, we extend the previous study to the case of non-Ohmic dissipation, in the presence of which the particle damped motion is described by a truly retarded equation even in the classical limit, and either localization or anomalous diffusion phenomena are taking place. Such situations are encountered in various problems of condensed matter physics [28]. [Pg.296]

In the presence of impurities the Mahan-Nozieres-de Dominicis singularity is broadened due to scattering of band electrons, as shown by Doniach and Sunjic (1970). This effect gives rise to additional quasi-particle damping and resistivity. One simple way to incorporate the impurity effect in the band calculation is to replace the temperature T by T -F Tp, where is the Dingle temperature which measures impurity scattering. The calculated resistivity curves for various values of are shown in fig. 44. These curves compare well with the data for Ce Lai. Pbj in fig. 7 and for Laj, Ce,Sn3 in fig. 9. [Pg.136]

Roadbed Stabilization/Dust Control. One of the earliest uses of calcium chloride was for dust control and roadbed stabilization of unpaved gravel roads. Calcium chloride ia both dry and solution forms are used both topically and mixed with the aggregate. When a calcium chloride solution is sprayed on a dusty road surface, it absorbs moisture from the atmosphere binding the dust particles and keeping the surface damp. Calcium chloride does not evaporate, thus this dust-free condition is retained over along period of time. [Pg.416]

Drag reduction has been reported for low loadings of small diameter particles (<60 [Lm diameter), ascribed to damping of turbulence near the wall (Rossettia and Pfefl er, AIChE J., 18, 31-39 [1972]). [Pg.656]

The diffusion constant should be small enough to damp out inertial motion. In the presence of a force the diffusion is biased in the direction of the force. When the friction constant is very high, the diffusion constant is very small and the force bias is attenuated— the motion of the system is strongly overdamped. The distance that a particle moves in a short time 8t is proportional to... [Pg.213]

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". [Pg.24]

We now want to study the consequences of such a model with respect to the optical properties of a composite medium. For such a purpose, we will consider the phenomenological Lorentz-Drude model, based on the classical dispersion theory, in order to describe qualitatively the various components [20]. Therefore, a Drude term defined by the plasma frequency and scattering rate, will describe the optical response of the bulk metal or will define the intrinsic metallic properties (i.e., Zm((a) in Eq.(6)) of the small particles, while a harmonic Lorentz oscillator, defined by the resonance frequency, the damping and the mode strength parameters, will describe the insulating host (i.e., /((0) in Eq.(6)). [Pg.97]

Fig. 7. Model calculations for the reflectivity (a) and the optical conductivity (b) for a simple (bulk) Drude metal and an effective medium of small metallic spherical particles in a dielectric host within the MG approach. The (bulk) Drude and the metallic particles are defined by the same parameters set the plasma frequency = 2 eV, the scattering rate hr = 0.2 eV. A filling factor/ = 0.5 and a dielectric host-medium represented by a Lorentz harmonic oscillator with mode strength fttOy, 1 = 10 eV, damping ftF] = I eV and resonance frequency h(H = 15 eV were considered for the calculations. Fig. 7. Model calculations for the reflectivity (a) and the optical conductivity (b) for a simple (bulk) Drude metal and an effective medium of small metallic spherical particles in a dielectric host within the MG approach. The (bulk) Drude and the metallic particles are defined by the same parameters set the plasma frequency = 2 eV, the scattering rate hr = 0.2 eV. A filling factor/ = 0.5 and a dielectric host-medium represented by a Lorentz harmonic oscillator with mode strength fttOy, 1 = 10 eV, damping ftF] = I eV and resonance frequency h(H = 15 eV were considered for the calculations.
The mechanism of suspension is related to the type of flow pattern obtained. Suspended types of flow are usually attributable to dispersion of the particles by the action of the turbulent eddies in the fluid. In turbulent flow, the vertical component of the eddy velocity will lie between one-seventh and one-fifth of the forward velocity of the fluid and, if this is more than the terminal falling velocity of the particles, they will tend to be supported in the fluid. In practice it is found that this mechanism is not as effective as might be thought because there is a tendency for the particles to damp out the eddy currents. [Pg.215]

The intensity of the energy dissipation can be estimated by the damping force acting on a particle i vibrating in a velocity Vi, which follows a linear relation [21]. [Pg.177]


See other pages where Particle damping is mentioned: [Pg.395]    [Pg.395]    [Pg.312]    [Pg.314]    [Pg.336]    [Pg.312]    [Pg.314]    [Pg.336]    [Pg.395]    [Pg.395]    [Pg.312]    [Pg.314]    [Pg.336]    [Pg.312]    [Pg.314]    [Pg.336]    [Pg.862]    [Pg.442]    [Pg.405]    [Pg.153]    [Pg.250]    [Pg.46]    [Pg.233]    [Pg.432]    [Pg.485]    [Pg.20]    [Pg.1560]    [Pg.1599]    [Pg.57]    [Pg.673]    [Pg.1131]    [Pg.746]    [Pg.747]    [Pg.756]    [Pg.96]    [Pg.130]    [Pg.177]    [Pg.177]    [Pg.79]    [Pg.293]    [Pg.341]   


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