Particle transport interception

The previous models were developed for Brownian particles, i.e. particles that are smaller than about 1 pm. Since most times particles that are industrially codeposited are larger than this, Fransaer developed a model for the codeposition of non-Brownian particles [38, 50], This model is based on a trajectory analysis of particles, including convective mass transport, geometrical interception, and migration under specific forces, coupled to a surface immobilization reaction. The codeposition process was separated in two sub-processes the reduction of metal ions and the concurrent deposition of particles. The rate of metal deposition was obtained from the diffusion... 

Theoretical dependence of filter efficiency of a single collector (proportional to the rate at which particle contacts occur between particles and the filter grain by mass transport) on particle diameter. For particles of small diameters transport by diffusion increases with decreasing size. Contact opportunities of the larger particles with the filter grain are due to interception and sedimentation they increase with increasing size. 

Airborne particles may be delivered to surfaces by wet and dry deposition. Several transport mechanisms, such as turbulent diffusion, precipitation, sedimentation, Brownian diffusion, interception, and inertial migration, influence the dry deposition process of airborne particles. Large particles (dNIOAm) are transported mainly by sedimentation hence, large particulate PAHs tend to be deposited nearer the sources of emission Small particles (dblAm), which behave like gases, are often transported and deposited far from where they originated (Baek et al., 1991 Wu et al., 2005). 

Dry deposition refers to transport between and during precipitation events. Particles may deposit by sedimentation, inertial impaction, interception, diffusion,... 

The coefficients a(p, c) and tj(p, c) describe chemical and physical effects on the kinetics of deposition. The transport of particles from the bulk of the flowing fluid to the surface of a collector or media grain by physical processes such as Brownian diffusion, fluid flow (direct interception), and gravity are incorporated into theoretical formulations for fj(p, c), together with corrections to account for hydrodynamic retardation or the lubrication effect as the two solids come into close proximity. Chemical effects are usually considered in evaluating a(p, c). These include interparticle forces arising from electrostatic interactions and steric effects originating from interactions between adsorbed layers of polymers and polyelectrolytes on the solid surfaces. 

Principles of basic importance during the separation are based on the effect of inertial and electric forces, gravity, and the resistance of a fluid medium. Besides this, the diffusion, the interception principle and other effects find application. In particular types of industrial separators, a combination of these principles is usually used and, in addition, the particle motion may be affected by further transport phenomena, such as thermophoresis, diffusion and coagulation. The separation process is naturally affected by characteristics of the particles to be separated, by the technical operating parameters of the gas to be purified, and also by certain characteristics of the separator itself. Thus, the separation process can hardly be exactly described mathematically, and most separators are designed on the basis of experimental data rather than pure theoretical principles. 

Following Spielman and the aims of this book, our discussion is confined to the capture of particles in liquid suspension from low-speed laminar flows, where the particles are generally small compared with the collector. The two principal transport mechanisms are (a) Brownian diffusion for submicrometer-size particles, and (b) interception of micrometer-size, nondiffusing, inertia free particles with the collector as a consequence of geometrical collision due to particles following fluid streamlines. Inertial impaction, which can be important for gas-borne particles, is usually unimportant for particles in liquids, because the particle—fluid density difference is smaller and the higher viscosity of liquids resists movement relative to the fluid (Spielman 1977). In this section we shall... 

This filter model considers that particles are transported from the flowing fluid to the filter media by Brownian diflFusion, fluid flow (interception), and settling. The eflFects of each of these mechanisms are assumed to be additive. Happel s (26) equations for flow in a packed bed as used by PfeflFer (27) are assumed in calculating the diflFusion and interception transport mechanisms. 

Naturally the rate of electron transport through the semiconductor to the anode, in direct competition with recombination and interception, is pertinent in the overall performance of a DSSC. Photo-injected electrons are transported by diffusion in a free random walk [15] as a result of an electron concentration gradient. The diffusion time will depend on the distance to the anode (the semiconductor film thickness) and the diffusion coefficient of electrons. But electrons also seem to become trapped within the semiconductor particles for some time (picoseconds to nanoseconds). This trapping and thermal release (detrapping) mechanism requires energy, and is important in retarding charge recombination in DSSCs. The process... 

Very detailed models of granular filtration have been developed using such idealizations of the porous medium (Tien, 1989). A simple aspect of this filtration is that, as the liquid flows down the porous medium, particles are transported perpendicular to the flow by electrostatic force. Brownian difiusion, various surface interaction forces and interception. Gravitational force is also present its... 

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