Inertia of particles

Fig. 10.1. The influence of the inertia of particles on their trajectory in the vicinity of the floating bubble.

In the following discussion we neglect the inertia of particles. We also ignore surface (molecular and electrostatic) interactions. The proper account of surface forces will be made in the following section, and of inertia - in Section 10.5. Problems on deposition of small particles on obstacles are presented in works [36, 52, 58, 61],... 

If inertia of particles is neglected, the limiting trajectory passes at a distance Up from the body. In Ref [58] this effect is called the effect of hooking. It has been shown in the same work that, for a potential flow around the sphere we have... 

If the probe is not aligned with the flow streamlines then there are losses due to the inertia of particles which are required to follow a new direction depending upon the angle of the problem relative to the wind direction. This effect was also clearly illustrated by May as shown in Figure 13.3. 

In case of a CFB, the amount of sampled solids is not sensitive to the gas suction velocity because of frequent ups and downs of solids in the riser and because of high inertia of particles, as reported e.g., by Monceaux et al. (1986), van Breugel et al. (1969), and Herb et al. (1992). There is a certain suction velocity window where the suction velocity does not affect the solid mass flux, as shown in Fig. 28, and the nonisokinetic sampling is more practical. 

Hi, the height between the two layers with two constant temperatures at the top and the bottom in the packed bed, m moment of inertia of particle i, kg rr ... 

The attenuation of ultrasound (acoustic spectroscopy) or high frequency electrical current (dielectric spectroscopy) as it passes through a suspension is different for weU-dispersed individual particles than for floes of those particles because the floes adsorb energy by breakup and reformation as pressure or electrical waves josde them. The degree of attenuation varies with frequency in a manner related to floe breakup and reformation rate constants, which depend on the strength of the interparticle attraction, size, and density (inertia) of the particles, and viscosity of the Hquid. 

For determination of the aerodynamic diameters of particles, the most commonly apphcable methods for particle-size analysis are those based on inertia aerosol centrifuges, cyclones, and inertial impactors (Lundgren et al.. Aerosol Measurement, University of Florida, Gainesville, 1979 and Liu, Fine Paiiicles—Aerosol Generation, Measurement, Sampling, and Analysis, Academic, New York, 1976). Impactors are the most commonly used. Nevertheless, impactor measurements are subject to numerous errors [Rao and Whitby, Am. Ind. Hyg. A.s.soc.]., 38, 174 (1977) Marple and WiUeke, "Inertial Impactors, in Lundgren et al.. Aerosol Measurement and Fuchs, "Aerosol Impactors, in Shaw, Fundamentals of Aerosol Sci-... 

On approaching a collecting body (fiber or liquid droplet), 0 porticle corried along by the gas stream tends to follow the stream but may strike the obstruction because of its inertia. Solid lines represent the fluid streamlines oround a body of diameter Dt, and the dotted lines represent the paths of particles that initially followed the fluid streamlines. X is the distance between the limiting streamlines A and B The fraction of particles initially present in a volume swept by the body that is removed by inertiol interception is represented by the quantity X/Dt, for a cylindrical collector and (X/Dt,) for a sphericol collector... 

If the probe velocity is less than the stack velocity, particles will be picked up by the probe, which should have been carried past it by the gas streamlines. The inertia of the particles allows them to continue on their path and be intercepted. If the probe velocity exceeds the stack velocity, the inertia of the particles carries them around the probe tip even though the carrying gases are collected. Adjustment of particulate samples taken anisokinetically to the correct stack values is possible if all of the variables of the stack gas and particulate can be accounted for in the appropriate mathematical equations. 

Figure 12-123B-2. Wear strip construction on induced draft fan for dirty gases. The inertia of suspended dust particles carries them toward the backplate or centerplate where the wear plate withstands the abrasion normally affecting the blade. (Used by permission Bui. 2-5100. The Howden Fan Co.)...

Thus, the inertia of the tunneling particle leads to two opposite effects a decrease of the transition probability due to the reorganization along the coordinate of the center of mass and an increase of the transition probability due to the increase of the Franck-Condon factor of the tunneling particle. Unlike the result in Ref. 66, it is found in Ref. 67 that for ordinary relationships between the physical parameters, the inertia leads to an increase of the transition probability. 

Two major effects contribute to the pressure drop in horizontal flow acceleration and friction loss. Initially the inertia of the particles must be overcome as they are accelerated up to speed, and then the friction loss in the mixture must be overcome. If Vs is the solid particle velocity and ms = ps I7s( l — ) is the solids mass flow rate, the acceleration component of the pressure drop is... 

The design of a cross-flow filter system employs an inertial filter principle that allows the permeate or filtrate to flow radially through the porous media at a relatively low face velocity compared to that of the mainstream slurry flow in the axial direction, as shown schematically in Figure 15.1.9 Particles entrained in the high-velocity axial flow field are prevented from entering the porous media by the ballistic effect of particle inertia. It has been suggested that submicron particles penetrate the filter medium and form a dynamic membrane or submicron layer, as shown in... 

The prime difficulty of modeling two-phase gas-solid flow is the interphase coupling, which deals with the effects of gas flow on the motion of solids and vice versa. Elgobashi (1991) proposed a classification for gas-solid suspensions based on the solid volume fraction es, which is shown in Fig. 2. When the solid volume fraction is very low, say es< 10-6, the presence of particles has a negligible effect on the gas flow, but their motion is influenced by the gas flow for sufficiently small inertia. This is called one-way coupling. In this case, the gas flow is treated as a pure fluid and the motion of particle phase is mainly controlled by the hydrodynamical forces (e.g., drag force, buoyancy force, and so... 

When the rate of rise of the bubble exceeds the velocity of the gas in the continuous phase, the gas leaving the top of the bubble is recycled and it re-enters the base. As a result, the gas in the bubble comes into contact with only those solid particles which immediately surround the bubble. Davidson 60 has analysed this problem and shown that if the inertia of the gas is neglected, the diameter dc of the cloud of recycling gas... 

It is seen in Chapter 3 that, as a particle moves outwards towards the walls of the bowl of a centrifuge, the accelerating force progressively increases and therefore the particle never reaches an equilibrium velocity as is the case in the gravitational field. Neglecting the inertia of the particle, then ... 

Kuz min et al. (15) pointed out a standard result of classical mechanics If a configuration of particles has a plane of symmetry, then this plane is perpendicular to a principal axis (19). A principal axis is defined to be an eigenvector of the inertial tensor. Furthermore, if the configuration of particles possesses any axis of symmetry, then this axis is also a principal axis, and the plane perpendicular to this axis is a principal plane corresponding to a degenerate principal moment of inertia (19). 

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