PARTICLE TRANSPORT PROPERTIES

An understiinding of particle transport or movement from one poi nt to another in a gas is basic to the design of gas cleaning equipment and aerosol sampling instruments. The seuvungiiigufpanicuiaic matter from the atmosphere by dry and wet deposition processes is also determined by panicle iranspon processes. 

The classical problems of particle transport were studied by well-known physicists in the late nineteenth and early twentieth centuries. Stokc.s, Einstein, and Millikan investigated the motion of smalt spherical particles under applied forces primarily because of application to (at that lime) unsolved probleins in physics. They derived relatively simple relationships for spherical particles that can be considered as ideal cases irregular particles are usually discussed in terms of their deviations from spherical behavior. 

In this chapter, we consider Brownian diffusion, sedimentation, migration in an electric Reid, and thermophoresis. The last term refers to particle movement produced by a temperature gradient in the gas. We consider also the London-van der Waals forces that are important when a particle approaches a surface. The analysis is limited to particle transport in stationary —that is. nonllowing— gases. I ransporl in flow systems is discussed in the chapters which follow. 

The rate of transport of particles across a surface at a point, expressed as number per unit time per unit area, is culled the jinx at the point. Common dimensions for the flux are paTticle.s/cm. sec. Expressions for the diffusion flux and diffusion coefflcienl (hat apply to submicron particles are derived from first principles in this chapter. The presence of an external force Retd acting on the particles leads to an additional term in the flux. The transport of particles larger than about a micron is analyzed by solving a momentum balance that incorporates the external force fields. 

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Thus for standard atmospheric conditions, if the particle diameter exceeds 0.2 pm or so, Kn < 1, and with respect to atmospheric properties, the particle is in the continuum regime. In that case, the equations of continuum mechanics are applicable. When the particle diameter is smaller than 0.01 pm, the particle exists in more or less a Tarified medium and its transport properties must be obtained from the kinetic theory of gases. This Kn 1 limit is called the free molecule or kinetic regime. The particle size range intermediate between these two extremes (0.01-0.2 pm) is called the transition regime, and there the particle transport properties result from combination of the two other regimes. 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

It is clear that tire rate of growdr of a reaction product depends upon two principal characteristics. The first of these is the thermodynamic properties of the phases which are involved in the reaction since these determine the driving force for the reaction. The second is the transport properties such as atomic and electron diffusion, as well as thermal conduction, all of which determine the mobilities of particles during the reaction within the product phase. 

Natural colloid particles in aqueous systems, such as clay particles, silica, etc. may serve as carriers of ionic species that are being sorbed on the particulates (pseudocolloids). It seems evident that the formation and transport properties of plutonium pseudocolloids can not yet be described in quantitative terms or be well predicted. This is an important area for further studies, since the pseudocolloidal transport might be the dominating plutonium migration mechanism in many environmental waters. 

The electron transport properties described earlier markedly differ when the particles are organized on the substrate. When particles are isolated on the substrate, the well-known Coulomb blockade behavior is observed. When particles are arranged in a close-packed hexagonal network, the electron tunneling transport between two adjacent particles competes with that of particle-substrate. This is enhanced when the number of layers made of particles increases and they form a FCC structure. Then ohmic behavior dominates, with the number of neighbor particles increasing. In the FCC structure, a direct electron tunneling process from the tip to the substrate occurs via an electrical percolation process. Hence a micro-crystal made of nanoparticles acts as a metal. 

All the transport properties derive from the thermal agitation of species at the atomic scale. In this respect, the simplest phenomenon is the diffusion process. In fact, as a consequence of thermal kinetic energy, all particles are subjected to a perfectly random movement, the velocity vector having exactly the same probability as orientation in any direction of the space. In these conditions, the net flux of matter in the direction of the concentration gradient is due only to the gradient of the population density. 

Finally, it must be recalled that the transport properties of any material are strongly dependent on the molecular or ionic interactions, and that the dynamics of each entity are narrowly correlated with the neighboring particles. This is the main reason why the theoretical treatment of these processes often shows similarities with models used for thermodynamic properties. The most classical example is the treatment of dilute electrolyte solutions by the Debye-Hiickel equation for thermodynamics and by the Debye-Onsager equation for conductivity. 

In addition to the fact that MPC dynamics is both simple and efficient to simulate, one of its main advantages is that the transport properties that characterize the behavior of the macroscopic laws may be computed. Furthermore, the macroscopic evolution equations can be derived from the full phase space Markov chain formulation. Such derivations have been carried out to obtain the full set of hydrodynamic equations for a one-component fluid [15, 18] and the reaction-diffusion equation for a reacting mixture [17]. In order to simplify the presentation and yet illustrate the methods that are used to carry out such derivations, we restrict our considerations to the simpler case of the derivation of the diffusion equation for a test particle in the fluid. The methods used to derive this equation and obtain the autocorrelation function expression for the diffusion coefficient are easily generalized to the full set of hydrodynamic equations. 

Being mainly concerned with the derivation and treatment of the dynamical and symmetry properties of the relativistic standard map, some papers (Nomura et.al., 1992) do not concern with the kinetical aspects of this map. However, the kinetical properties are interesting for particle transport and acceleration processes. Here we calculate the time-dependence of the energy for various values of (3 including the resonance case. 

Atmospheric transport of chlordecone particles was reported as a result of emissions from a production facility in Virginia. Chlordecone concentrations at up to 15.6 miles away ranged from 1.4 to 20.7 ng/m (Epstein 1978). The long-range transport properties of chlordecone indicate that at least a portion of the emissions were of a fine particle size having a relatively long residence time in the atmosphere (Lewis and Lee 1976). 

Another approach is to consider petroleum constituents in terms of transportable materials, the character of which is determined by several chemical and physical properties (i.e., solubility, vapor pressure, and propensity to bind with soil and organic particles). These properties are the basis of measures of teachability and volatility of individual hydrocarbons. Thus, petroleum transport fractions can be considered by equivalent carbon number to be grouped into 13 different fractions. The analytical fractions are then set to match these transport... 

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