Force diffusional

MORPHOLOGICAL EVOLUTION DUE TO CAPILLARY AND APPLIED FORCES DIFFUSIONAL CREEP AND SINTERING... 

The basic operations in dust collection by any device are (1) separation of the gas-borne particles from the gas stream by deposition on a collecting surface (2) retention of the deposit on the surface and (3) removal of the deposit from the surface for recovery or disposal. The separation step requires (1) application of a force that produces a differential motion of a particle relative to the gas and (2) a gas retention time sufficient for the particle to migrate to the coUecting surface. The principal mechanisms of aerosol deposition that are apphed in dust collectors are (1) gravitational deposition, (2) flow-line interception, (3) inertial deposition, (4) diffusional deposition, and (5) electrostatic deposition. Thermal deposition is only a minor factor in practical dust-collectiou equipment because the thermophoretic force is small. Table 17-2 lists these six mechanisms and presents the characteristic... 

Several investigators have attempted to modify the basic Deutsch equation so that it would more nearly describe precipitator performance. Cooperman ( A NewTheoiy of Precipitator Efficiency, Pap. 69-4, APCA meeting, New York, 1969) introduced correction fac tors for diffusional forces arising from variations in particle concentration along the precipitator length and also perpendiciilar to the collecting surface. Robinson [Atmos. Environ. 1(31 193 (1967)] derived an equation for collec tion efficiency in which two erosion or reentrainment terms are introduced. 

Limitations It is desirable to have an estimate for the smallest particle size that can be effectively influenced by DEP. To do this, we consider the force on a particle due to DEP and also due to the osmotic pressure. This latter diffusional force will randomize the particles and tend to destroy the control by DEP Figure 22-32 shows a plot of these two forces, calciilated for practical and representative conditions, as a func tion of particle radius. As we can see, the smallest particles that can be effec tively handled by DEP appear to be in range of 0.01 to 0.1 piTidOO to 1000 A). 

Fibrous or particulate filters are not important anymore because membrane filters are relatively compac t and perform veiy well. For filtration by straining, there is an intermediate air velocity at which filtration efficiency is a minimum because different collec tion mechanisms predominate at different ranges of velocity. At low velocities, diffusional and elec trostatic forces on the particle are important, and increased velocity shortens the time for them to operate. At high velocities, inertial forces that increase with air velocity come into play below a certain air velocity, their effect on collection is zero. Surges or brief power failures could change velocity and collection efficiency. 

The Batchelor microscale physically means a size of the region within which a compound moves due to diffusional forces. This does not occur outside these regions, where compounds move because of turbulences. 

Kramers HA. 1940. Brownian motion in a field of force and the diffusional model of chemical reactions. Physica7 284-304. 

Typical results, shown in Fig. 21(a), demonstrate that the rate constant for the reaction between TCNQ and aqueous Fe(CN)g increases with increasing driving force, promoted by decreasing [CIO4 as evidenced by the steeper Fe(CN)g concentration profiles. Moreover, the Tafel plot obtained for ET between Fe(CN)g and TCNQ is linear with an apparent measured a value of 0.31 0.02. In these studies, the concentration of reactant in the droplet phase was always at least 10 times the concentration of the reactant in the receptor phase, to ensure that depletion (and diffusional) effects within the droplet were negligible. 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

Weder s experiments were carried out with opposing body forces, and large current oscillations were found as long as the negative thermal densification was smaller than the diffusional densification. [Note that the Grashof numbers in Eq. (41) are based on absolute magnitudes of the density differences.] Local mass-transfer rates oscillated by 50%, and total currents by 4%. When the thermal densification dominated, the stagnation point moved to the other side of the cylinder, while the boundary layer, which separates in purely diffusional free convection, remained attached. 

It will be noted in Fig. 9 that diffusional forces are small compared with other forces for particles smaller than 1000 microns in diameter. Inertial forces can become significant with particles larger than 10 microns. Fluid drag forces can be of the same general order as van der Waal s forces at these assumed high velocity levels. Electrostatic forces can be quite large but only... 

There is apparently an inherent anomaly in the heat and mass transfer results in that, at low Reynolds numbers, the Nusselt and Sherwood numbers (Figures. 6.30 and 6.27) are very low, and substantially below the theoretical minimum value of 2 for transfer by thermal conduction or molecular diffusion to a spherical particle when the driving force is spread over an infinite distance (Volume 1, Chapter 9). The most probable explanation is that at low Reynolds numbers there is appreciable back-mixing of gas associated with the circulation of the solids. If this is represented as a diffusional type of process with a longitudinal diffusivity of DL, the basic equation for the heat transfer process is ... 

The thermal motion of molecules of a given substance in a solvent medium causes dispersion and migration. If dispersion takes place by intermolecular forces acting within a gas, fluid, or solid, molecular diffusion takes place. In a turbulent medium, the migration of matter within it is defined as turbulent diffusion or eddy diffusion. Diffusional flux J is the product of linear concentration gradient dCldX multiphed by a proportionality factor generally defined as diffusion coefficient (D) (see section 4.11) ... 

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