Particle diffusion coefficients

Altenberger and Tirrell [11] utilized the Langevin equation for particle motion coupled with hydrodynamics described by the Navier-S takes equation to determine particle diffusion coefficients in porous media given by... 

The Peclet number Pe = v /Dc, where Dc is the diffusion coefficient of a solute particle in the fluid, measures the ratio of convective transport to diffusive transport. The diffusion time Tp = 2/D< is the time it takes a particle with characteristic length to diffuse a distance comparable to its size. We may then write the Peclet number as Pe = xD/xs, where xv is again the Stokes time. For Pe > 1 the particle will move convectively over distances greater than its size. The Peclet number can also be written Pe = Re(v/Dc), so in MPC simulations the extent to which this number can be tuned depends on the Reynolds number and the ratio of the kinematic viscosity and the particle diffusion coefficient. 

Particle Diffusion Coefficient (cm7s) X 10 Molecular Mass (Daltons]... 

In this section, various issues concerning solid particles are presented. The analysis covers the most important particle properties (surface area, particle shape and size distribution, mechanical strength, and density) as well as the behavior of a single particle in suspension (terminal velocity) and of a number of particles in fluidization state. Finally, the diffusion of molecules in a porous particle (diffusion coefficients) is also discussed. 

TABLE 5.3 Calculated Particle Diffusion Coefficients"/) x 10scm2s-1... 

TABLE 5.4 Calculated Particle Diffusion Coefficients D and Other Pertinent Data for La3+, Tb3+, and Lu3+ Ions"... 

By refining column design, the Instrumental band broadening H, has been reduced to a level insignificant in comparison with the other terms of Equation 7. The nonequilibrium term, linear in carrier velocity , also depends on channel thickness w and inversely on particle diffusion coefficient D. The dependence of coefficient x on X is well known, although the function is complex (14). Its limiting form is described by... 

Table 1 compares the dimensionless coagulation coefficient predicted by the present model with other models. Since the Hamaker constant for most of the aerosol systems is of the order of 10"12 eig, this value is used in the calculation of the lower bound. Particle diffusion coefficients based on Philips slip correction factor for an accommodation coefficient of unity are used for the calculation of the coagulation coefficients ft (the Fuchs interpolation formula) and fts (the Sitarski... 

The Smoluchowski equation can also be extended to Knudsen numbers in the range 0.1 < Kn < 0.25 by introducing a slip correction factor C(Kn) in the expression for the particle diffusion coefficient. The empirical slip correction factor due to Millikan (3) has the form... 

As a correlation function is recorded, the correlator offers the decay time (x), particles diffusion coefficient (D), and particles mean radius (R). The two latters are related with by Stokes-Einstein equation [6],... 

Equation 9.12 indicates that the diffusion coefficient of an aerosol particle is independent of particle density and hence is independent of particle mass. But is this really so Since particle mass is so much greater than molecular mass and the particles are continually undergoing bombardment by the molecules, one would expect changes in the direction of the particle to be gradual, compared to the rapid changes in direction with molecular diffusion. But if this is true, then particle momentum (mass) should be considered in the particle diffusion coefficient equation. 

Aerodynamic diameter of a real median size particle Diffusion coefficient Sauter mean diameter Volume mean diameter Entrainment, mass liquid/mass gas Plate or stage efficiency, fractional Power dissipation per mass Murphree plate efficiency, with entrainment, gas concentrations, fractional... 

The particle diffusion coefficient is calculated from the Stokes-Einstein equation (24)... 

For adsorption onto colloidal particles two approaches are possible. The first is to determine vlscometrlcally the increase in the effective particle volume fraction upon adsorption, and the second is to measure the decrease in the particle diffusion coefficient. 

Howarth (HI5) assumed a mechanism analogous to Brownian motion. But his derivation for collision rates is wrong because he introduced a variable particle diffusion coefficient in the Smoluchowski equation (06, S27) which had been derived on the basis of a constant coefficient. 

Next, estimate the first-order decay constant. From Fig. 2-11, the particle diffusion coefficient in water for a 1 -/xm particle is approximately 5 X 10-9... 

Particle diffusion coefficients are small compared with the kinematic viscosity of a gas (large Schmidt numbers), so the region of the gas flow near the surface from which particles are depleted is usually very narrow. This narrow region, the concentration boundary layer, is very important to particle transport and is discussed in detail. 

The diffusion battery consists of banks of tubes, channels, or screens through which a submicron aerosol passes at a constant flow rale. Particles deposit on the surface of the battery elements, and the decay in total number concentration along the flow path i measured, usually with a condensation particle counter. The equations of convective diffusion (Chapter 3) can be solved for the rate of deposition as a function of the particle diffusion coefficient. Because the diffusion coefficient is a monotonic function of particle size (Chapter 2), the measured and theoretical deposition curves can be compared to detennine the size for a monodisperse aerosol. 

At low ionic strength (kR 1), other effects connected with the finite diffusivity of the small ions in the EDL surrounding the particle are present. The noninstantaneous diffusion of the small ions (with respect to the Brownian motion of the colloid particle) could lead to detectable reduction of the single particle diffusion coefficient, Dq, from the value predicted by the Stokes-Ein-stein relation. Equation 5.447. For spherical particles, the relative decrease in the value of Dq is largest at k/ 1 and could be around 10 to 15%. As shown in the normal-mode theory, the finite diffusivity of the small ions also affects the concentration dependence of the collective diffusion coefficient of the particles. Belloni et al. obtained an explicit expression for the contribution of the small ions in Ac)... 

As was briefly outlined at the end of Sec. II, an average hydrodynamic thickness Lr of the polymer layer can be determined from the decrease in the particle diffusion coefficient due to polyelectrolyte adsorption. 

Here u = hja and D, is the pair diffusion coefficient at large separation, i.e., twice the particle diffusion coefficient. 

A, B are empirical factors, Dp the particle diffusion coefficient and N,-iP the numbers of effective plates under film and particle control. 

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