Aerosols particle motion

The motion of a charged aerosol particle in a gas is governed by the electrostatic force and the aerodynamic forces. The theory dealing with the particle motion has been discussed in several books (see, e.g., Hinds- ). The electrostatic force F caused by the electric field E is given by... 

These compressed air nebulizers produce polydisperse aerosols. After the aerosol is produced, the size distribution may change due to evaporation of liquid from the droplets. In addition, the particles may be electrically charged due to an ion imbalance in the droplets as they form if such charges become further concentrated due to evaporation, the particle may break up into smaller particles. Thus electrical neutralization of the aerosol, for example, by exposure to a radioactive source, is usually necessary to prevent electrostatic effects from dominating the particle motion, coagulation, and other behavior. 

I. Theory of Particle Motion in Aerodynamic Lenses and Nozzle Expansions, Aerosol Sci. Technol., 22, 293-313 (1995a). 

The deposition of particles on macroscopic surface is the primary goal in CVD processes, bnt rednces the efficiency of vapor phase particle synthesis. Particles can deposit by Brownian motion, bnt in high-temperature reactors, thermophoretic deposition often dominates. Thermophoresis is the migration of small aerosol particles as a resnlt of a temperatnre gradient. It causes particles carried in a hot gas to deposit on a cool surface. Eor small particles, Kn 1, a dimensionless group can be created to describe thermophoresis, Th ... 

As Martell has pointed out (30), in the region of the stratospheric large particle layer near 18-20 km. altitude, radioactive aerosol particles become attached to natural sulfate particles in the size range of about 0.1-0.4 jumeter radius. Subsequent upward transport of the radioactive aerosols is opposed by gravitational sedimentation. This combination of processes affords an explanation for the observed accumulation of 210Pb near 20 km. in the tropical stratosphere (2). At higher latitudes where slow mean motions are directed poleward and downward, no such accumulation is possible. 

Baron, P. A., and Willeke, K. Gas and particle motion, in Aerosol Measurement Principles, Techniques and Applications, 2d ed. New York Wiley, 2001. 

In filtration of gas-borne aerosol particles by microfiltration membranes, capture by adsorption is usually far more important than capture by sieving. This leads to the paradoxical result that the most penetrating particle may not be the smallest one. This is because capture by inertial interception is most efficient for larger particles, whereas capture by Brownian motion is most efficient for smaller particles. As a result the most penetrating particle has an intermediate diameter, as shown in Figure 2.35 [55,56],... 

FIGURE 2 Particle motion in aerosol flow around obstacles (dashed line), (a) Flow around a cylinder of radius a (b) flow around a flat plate inclined at an angle to the aerosol flow. 

As already mentioned the present treatment attempts to clarify the connection between the sticking probability and the mutual forces of interaction between particles. The van der Waals attraction and Born repulsion forces are included in the calculation of the rate of collisions between two electrically neutral aerosol particles. The overall interaction potential between two particles is calculated through the integration of the inter-molecular potential, modeled as the Lennard-Jones 6-12 potential, under the assumption of pairwise additivity. The expression for the overall interaction potential in terms of the Hamaker constant and the molecular diameter can be found in Appendix 1. The motion of a particle can no longer be assumed to be... 

A model for Brownian coagulation of equal-sized electrically neutral aerosol particles is proposed. The model accounts for the van der Waals attraction and Born repulsion in the calculation of the rate of collisions and subsequent coagulation. In this model, the relative motion between two particles is considered to be free molecular in the neighborhood of the sphere of influence. The thickness of this region is taken to be equal to the correlation length of the relative Brownian motion. The relative motion of the particles outside this region is described... 

The relative Brownian motion between the constituents of doublets consisting of sufficiently small equal-size aerosol particles is described by a one-dimensional Fokker-Planck equation in the particle energy space. A first passage time approach is employed for the calculation of the average lifetime of the doublets. This calculation is based on the assumption that the initial distribution of tire energy of the relative motion of the constituent particles is Maxwellian. The average dissociation time of doublets, in air at 1 atm and 298 K, for a Hamaker constant of 10 12 erg has been calculated for different sizes of the constituent particles. The calculations are found to be consistent with the assumption that the... 

Equations of motion presented here were developed for cases of uniform medium velocity and are oversimplified for many other cases regarding aerosols. In addition, evaluation of the equations for the trajectories of aerosol particles is sometimes impossible because of the difficulty in accurately describing the field of flow. Although for laminar flow Eq. 6.6 can be separated into x and y components, with increasing Reynolds number the nonlinearity of the resisting force prevents separation of the vector equation. Fortunately, most aerosol problems can be treated in the low-Reynolds-number regime. 

Two-dimensional trajectories of a typical gas molecule and a typical aerosol particle can be compared in Fig. 9.2. The molecule shows sharp changes in direction, each change occurring when it strikes another molecule. As discussed in Chap. 3, the average distance between hits is defined as the mean free path of the molecule. For the particle, a hit by a single molecule does not appreciably affect its motion. Therefore, its path is not characterized by sharp changes in direction, but by smooth curves representing the combined effect of hits by many molecules. 

Since aerosol particles are continually undergoing molecular bombardment, their paths are smooth curves rather than segments of straight lines. It still is possible to define an apparent mean free path for the aerosol particles (Fuchs, 1964). This is the distance traveled by an average particle before it changes its direction of motion by 90°. The apparent mean free path represents the distance traveled by an average particle in a given direction before particle velocity in that direction equals zero. But this is just the stop distance. 

The equation of motion for an aerosol particle including an electric force present FE can be written as... 

An aerosol is a suspension of particles in a gaseous medium. Without the medium there would be no aerosol. The medium acts to restrain random particle motion, supports the particles against the strong pull of gravity, and in some cases acts as a buffer between particles. It is impossible to properly study aerosol behavior without first considering the medium in which the particles are suspended. 

We can now consider the resistance offered by the medium to the motion of an aerosol particle. Some of the earliest interest in the motion of a body moving through a fluid arose from the desire to know where a cannonball, once fired, would land. 

Consider the case of a spherical aerosol particle in a homogeneous air-stream with no forces acting on the particle except gravity. For simplicity the motion will be assumed to occur only in the Stokes region (in most cases this assumption is valid). Then (similar to Example 6.2),... 

If gravity is neglected, the equation of motion for the aerosol particles flowing in the airstream is... 

Thermal gradients either within particles or in the supporting medium can be responsible for motion of aerosol particles by creating forces which act on the individual particles. Here the discussion is not about convective motion of the medium set up by thermal gradients which carries particles with it, but with thermal forces which act directly on individual particles to cause motion. 

It was initially thought that Epstein s theory satisfactorily described the thermal motion of large aerosol particles (Rosenblatt and LaMer, 1946). The theory, however, predicted essentially no thermal force acting on particles of high thermal conductivity (since HE 0). Experiments by Schadt and Cadle (1957, 1961) and others showed that thermal forces do indeed act on highly conductive as well as poorly conducting particles. 

The main reason for evaluating the charges on aerosol particles and the electric fields that act on these charges is to develop models which describe the effect on particle motion of the electric force. 

The term fv is the ratio of the evaporation rate for the particle in moving air to the evaporation rate of the particle in still air. Because in a moving airstream a small aerosol particle rapidly attains the velocity of the medium around it, in most cases droplet motion can be neglected in considering evaporation and condensation estimates, unless the droplet diameters exceed 40 pm. 

The collection of the pyrolysis oils is difficult due to their tendency to form aerosols and also due to the volatile nature of many of the oil constituents. As the aerosols agglomerate into larger droplets, they can be removed by cyclonic separators. However, the submicron aerosols cannot be efficiently collected by cyclonic or inertial techniques, and collection by impact of the aerosols due to their Brownian or random motion must be utilized. A coalescing filter is relatively porous, but it contains a large surface area for the aerosol particles to impact by Brownian motion as they are swept through by the pyrolysis gases. Once the aerosol droplets impact the filter fibers, they are captured and coalesce into large drops that can flow down the fibers and be collected. 

The motion of aerosol droplets following space spraying is governed by gravity and the resistance of air particle motion. Droplet settlement depends on the size of the droplet. The droplet settling velocity (Vi) (m/s) is given by Stokes law (Hinds, 1982) ... 

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