Particle inertia

Most diy-mihing circuits use air classifiers. There are a number of types, but all use the principles of air drag and particle inertia, which... 

The use of a Reynolds number based on relative velocity rather than superficial velocity in setting these limits was suggested by Horio (1990). In setting viscous or inertial limits, it is the interphase drag which is characterized as being dominated by viscous or inertial forces. The particle inertia is important even if the interphase drag is viscous dominated. This is because of the typically large solid-to-gas density ratio. 

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... 

When the particle inertia overcomes the surface-tension-induced force, the particle will penetrate the bubbles. Recognizing that particle penetration may not lead to bubble breakage, details of bubble instability due to particle collision are given in Chen and Fan (1989a, b). 

Since there are three dimensions, two dimensionless groups, e.g., and defined in Chapter 5, suffice to describe the motion. If the motion is unsteady, it is necessary to introduce the particle density explicitly, since it determines the particle inertia as well as the net gravity force. Also, since L/r varies with time and position, a further parameter must be introduced. This may be the distance x moved since the start of the motion. Equation (11-1) is then replaced by... 

By performing a radial force balance, Spieiman and Fitzpatrick (1973) determined the radial velocity of a particle attracted to a spherical collector by Loudon forces when particle inertia and Brownian motion are... 

Particle inertia has been assumed to be substantially smaller than the viscous drag force. This assumption will be valid provided the Reynolds number ppOp/iU/it is sufficiently small, which is more likely to he the case with liq-... 

Denote by F( ext and Tf ext the external force and torque (about 0.) acting on particle i. Neglect of particle inertia then leads to the equation... 

A second prominent feature here is the ergodic character (or lack thereof) of the process, depending on the rationality or irrationality of <. This leads inevitably to the fascinating question, Does a real system choose between these values of , and if so, how The boundaries themselves remain neutral with respect to the choice of whenever they are compatible with the flow. Thus, for a slide flow, the walls must be parallel to the slides, whereas for a tube flow, they must be parallel to the tube. In both cases there remains an additional degree of freedom, which is precisely the choice of f. Other examples of indeterminancy arise from the neglect of fluid and particle inertia, as already discussed in Section I (see also the review in Leal, 1980). Whether or not inclusion of nonlinear inertial effects can remove the above indeterminacy, as it often does for the purely hydrodynamic portion of the problem, is a question that lies beyond the scope of the present (linear) Stokesian context. 

For turbulence it is convenient to describe particle flux in terms of an eddy diffusion coefficient, similar to a molecular diffusion coefficient. Unlike a molecular diffusion coefficient, however, the eddy diffusion coefficient is not constant for a given temperature and particle mobility, but decreases as the eddy approaches a surface. As particles are moved closer and closer to a surface by turbulence, the magnitude of their fluctuations to and from that surface diminishes, finally reaching a point where molecular diffusion predominates. As a result, in turbulent deposition, turbulence establishes a uniform aerosol concentration that extends to somewhere within the viscous sublayer. Then molecular diffusion or particle inertia transports the particles the rest of the way to the surface. 

The magnitude of the accelerating force that acts on a particle in curvilinear motion depends on the particle inertia. The greater the inertia of the particle, the greater will be the displacement. Inertia depends on particle mass and velocity. Heavy particles will be displaced more from the streamlines in which they are traveling than light ones, and increases in velocity will increase displacement for a particle of given mass. 

When ti>7, Eq. 9.28 reduces to Eq. 9.19, an expression for the displacement of a particle at constant velocity. Since our observation times will generally always be greater than t, we can conclude that in most instances particle inertia can be neglected in considering particle diffusion. 

Example 9.6 Find the ratio of tlt such that the root-mean-square displacement estimated considering particle inertia (Eq. 9.28) is 10 percent less than the estimate when inertia is not considered (Eq. 9.19). 

FIGURE 4.10 Air classification equipment (a) cyclone, (b) expansion chamber, (c) modern complex air classifier, and (d) classifier based on particle inertia. 

Particle diffusion considered to stabilize while particle inertia forces promote the amplitude. 

The forces one must include in such a simulation include electrostatic, hydrodynamic, and steric forces. For small particles, Brownian forces might also be present, but since these break up particle structures, it is desirable to use particles big enough (> 1 /xm) to suppress Brownian motion. Ordinarily, particle inertia can be neglected. Simulations can be greatly simplified by making drastic approximations, including the point-dipole approximation, and the Stokes -drag approximation. Both of these approximations are only really valid for widely separated particles. 

Particle Inertia. Particle inertia is a major source of sampling errors when the densities of the two phases are significantly different. Because particle inertia is different from that of an equivalent volume of fluid, particle motion does not follow the distorted fluid streamlines. Consequently, sample solids concentration and composition will be significantly different from those in the pipe. Sampling errors due to inertia depend on... 

Thin L-shaped probes are commonly used to measure solids concentration profile in slurry pipelines (28-33), However, serious sampling errors arise as a result of particle inertia. To illustrate the effect of particle inertia on the performance of L-shaped probes, consider the fiuid streamlines ahead (upstream) of a sampling probe located at the center of a pipe, as shown in Figure 2. The probe has zero thickness, and its axis coincides with that of the pipe. The fluid ahead of the sampler contains particles of different sizes and densities. Figure 2A shows the fluid streamlines for sampling with a velocity equal to the upstream local velocity (isokinetic sampling). Of course, the probe does not disturb the flow field ahead of the sampler, and consequently, sample solids concentration and composition equal those upstream of the probe. 

The preceding discussion shows that the sampling efficiency for thin L-shaped probes is a function of two parameters the deviation from the isokinetic conditions and the response of the particles to the deflection of the fluid streamlines upstream of the sampler. The deviation from the isokinetic conditions is a function of the velocity ratio (U/Uq), whereas the particle response is a function of the ratio of particle inertia to fluid drag. This ratio in a dimensionless form is known as the particle inertia parameter, the Stokes number, or the Barth number (K), defined as ... 

K particle inertia parameter based on probe radius (also called Stokes number or Barth number)... 

One of the challenges is that the fine powder particles tend to stick to each other. These clumps can be difficult to break apart into breathable particles for slow inhalation by the patient. Breath-powered powder inhalers for asthmatics attempt to apply the forces generated by a rapid forceful inspiration to break apart the powder clumps. But vigorous rapid inhalation does not efficiently deaggregate and target the very fine powder clumps to the deep lung. This is mainly because particle inertia causes impaction of most of the medication in the oropharynx. 

Inertial impaction, where particle inertia causes it to leave the flow streamlines and impact on the flber ... 

Inertial Impaction Particle inertia causes it to leave flow stream lines and impact on fiber... 

The probability of oropharyngeal deposition is determined more by droplet size than by velocity and density because the particle inertia is proportional to the density, velocity, and the square of the diameter. It, therefore, follows that oropharyngeal drug deposition is reduced and the respirable drug delivery is increased when MDI sprays are finely atomized and evaporate rapidly. Such MDI sprays are generally promoted by increasing the propellant vapor pressure and reducing the actuator spray nozzle diameter.f ... 

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