Factor turbulent diffusion

With good diy scrubbing sorbents, the controlling resistance for gas cleaning is external turbulent diffusion, which also depends on energy dissipated by viscous and by inertial mechanisms. It turns out to Be possible to correlate mass-transfer rate as a fimctiou of the fric tiou Factor. 

Another design method uses capture efficiency. There are fewer models for capture efficiency available and none that have been validated over a wide range of conditions. Conroy and Ellenbecker - developed a semi-empirical capture efficiency for flanged slot hoods and point and area sources of contaminant. The point source model uses potential flow theory to describe the flow field in front of a flanged elliptical opening and an empirical factor to describe the turbulent diffusion of contaminant around streamlines. 

Different. Ingham (1975) diffusion deposition but corrected by turbulent diffusion factors in airways 0 to 6 as measured by Cohen (1986). 

It is well known that enhanced deposition in the first few airways occurs due to the turbulence produced. Turbulent diffusion is accounted for by using factors (ratio of observed deposition to calculated diffusion deposition) to correct the diffusion deposition. These had formerly been measured by Martin and Jacobi (1972) in a dichotomous plastic model of the upper airways. The data used here are from measurements performed by Cohen (1986) using hollow casts of the upper bronchial tree which included a larynx. This cast was tested using cyclic flow with deposition measured for 0.03, 0.15 and 0.20 urn diameter particles. Her turbulent diffusion factors are used in the calculation here (14 for generation 0, and 2 for generations 1 to 6). 

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) ... 

All of the above discussion of diffusion considers physical motion of particles excited by thermal energy of the system (because the system is not at 0 K), rather than by outside factors. Eddy diffusion is different. It is due to random disturbance in water by outside factors, such as fish swimming, wave motion, ship cruising, and turbulence in water. On a small length scale (similar to the length scale of disturbance), the disturbances are considered explicitly as convection or flow in the mass transfer equation (Equation 3-19). On a length scale much larger than the individual disturbances, the collective effect of all of the disturbances... 

Other factors also come into play in laboratory systems. For example, McMurry and Rader (1985) have shown that particle deposition at the walls of Teflon smog chambers is controlled by Brownian and turbulent diffusion for particles with Dp 0.05 yxm and by gravitational settling for particles with Dp > 1.0 yxm. However, in the 0.05- to 1.0-yxm range, the deposition is controlled by electrostatic effects Teflon tends to... 

It is interesting to note that in a study by A. P. Mirabel and A. S. Monin, written after Ya.B. s paper, the expression for the turbulent diffusion coefficient in a two-dimensional turbulent field differs from the one obtained by Ya.B. by a factor which is equal to some logarithmic power of the ratio of the mixing scale to the energy-supply scale. 

Experimental investigations of turbulence diffusion. A factor in transportation of sediment in open channel flow. J Applied Mechanics, 12 A91-A100. 

FIGURE 3-17 Dispersion of a pulse of a tracer substance in a sand column experiment. Note the parallel between this and the corresponding dispersion of a tracer in a flowing river (Fig. 2-4). The same equation, with a correction factor for porosity in the case of the sand column, describes both situations. However, the physical processes responsible for the Fickian transport differ mechanical dispersion dominates in the sand column, while turbulent diffusion and the dispersion associated with a nonuniform velocity profile dominate in the river. 

Matrix of mass transfer rate factors in linearized film model (Eq. 8.4.4) [ - ] Matrix of mass transfer rate factors in turbulent diffusion model (Eq. 10.3.9) [-]... 

The effective bed conductivity has a static or zero-flow term, which is usually about 5k when the particles are a porous inorganic material such as alumina, silica gel, or an impregnated catalyst, and kg is the thermal conductivity of the gas. The turbulent flow contribution to the conductivity is proportional to the mass flow rate and particle diameter, and the factor 0.1 in the following equation agrees with the theory for turbulent diffusion in packed beds ... 

In considering the volatilization of contaminants, the factors that must be considered are (a) escape from the interface, (b) diffusion through the surface boundary layer, and (c) turbulent diffusion in the atmosphere. - The escape from the surface depends mainly on the vapor pressure of the contaminant at a given temperature, the molecular weight, and Henry s coefficient. After the contaminant has escaped from the surface, it must diffuse outward in the stagnant boundary layer that is normally present. Then, the contaminant will be transported away from the stagnant layer by advection and turbulent diffusion... 

Consider particles of radius a Ao and assume that in the course of their motion in the liquid, they are completely entrained by turbulent pulsations that play the basic role in the mechanism of mutual approach of suspended particles. Then it can be assumed that particle transport is performed via isotropic turbulence. Since particles move chaotically in the liquid volume, their motion is similar to Brownian one and can be considered as diffusion with some effective factor of turbulent diffusion Dr. In the same manner as in the case of Brownian coagulation, it is possible to consider the diffusion flux of particles of radius U2 toward the test particle of radius Uj. The distribution of particles U2 is characterized by the stationary diffusion equation... 

The role of hydrodynamic interaction in Brownian diffusion was discussed in Section 8.2. Consider now its effect on turbulent coagulation. Formally, it can be taken into account in the same manner as in Brownian motion, by introducing a correction multiplier into the factor of turbulent diffusion (10.57). Another, more correct way (see Section 11.3) is to use the Langevin equation that helped us determine the factor of Brownian diffusion in Section 8.2. As was demonstrated in [60], the factor of turbulent diffusion is inversely proportional to the second power of the hydrodynamic resistance factor ... 

The use of turbulent emulsion flow regime to facilitate integration of drops is justifled by the substantial increase of collision frequency that is achieved in a turbulent flow as compared to the collision frequency during the sedimentation of drops in a quiescent liquid or in a laminar flow. Particles suspended in the liquid are entrained by turbulent pulsations and move chaotically inside the volume in a pattern similar to Brownian motion. Therefore this pulsation motion of particles can be characterized by the effective factor of turbulent diffusion Dj, and the problem reduces to the determination of collision frequency of particles in the framework of the diffusion problem, as it was first done by Smoluchowsld for Brownian motion [18]. A similar approach was first proposed and realized in [19] for the problem of coagulation of non-interacting particles. The result was that the obtained frequency of collisions turned out to be much greater than the frequency found in experiments on turbulent flow of emulsion in pipes and agitators [20, 21]. 

Thus, to determine the frequency of collision of particles or drops, it is necessary to determine the forces of particle interaction first, and then to find the trajectories of their motion and the collision cross-section or the diffusion flux. In the latter case, it is necessary to And the turbulent diffusion factor. As a result, the kernel of the kinetic equation is determined. If the kernel thus derived appears to be asymmetric, it should be symmetrized. After that, one can proceed to study the kinetics of coalescence for the considered process, including the time rate of change of size distribution of particles and the parameters of this distribution. 

In case of turbulent diffusion, the situation is somewhat different. Motion of particles under action of turbulent pulsations is not connected to thermal fluctuations. Therefore B = const and the factor of turbulent diffusion is inversely proportional to the second power of factor of hydrodynamic resistance. 

The equation (11.69) describes, for small displacements, the motion similar to motion of a non-constrained particle with similarity factor, equal to hf/K. This result allows one to present the factor of turbulent diffusion (11.66) in a similar form... 

Expression (11.70) for the factor of turbulent diffusion does not take into account motion of the second particle. To take proper account of mutual influence of particles on the velocity of their approach, it should proceed as follows. Let u be the velocity of one particle relative to another, and Ui and Ui - the particles velocities relative to a reference frame whose origin lies between the particles on the line connecting their centers. Then u = ui — U2. Forces Fading on particles, are equal in magnitude and opposite in diredions. Then the fador of hydrodynamic resistance to particles approach can be written as... 

Substitution of relations (11.56), (11.72), and (11.74) into (11.70) results in the following expression for the mutual turbulent diffusion factor of spherical particles in the presence of hydrodynamic interaction... 

At J —> 0, the expression for h of a drop with mobile surface has an integrable singularity. So, in a laminar flow, particularly, in the process of gravitational sedimentation, a contact between drops is possible even in the absence of molecular forces. In a turbulent flow, the turbulent diffusion factor is Dj 1/H, therefore in the absence of molecular forces, any contact between drops with fully mobile surfaces is also impossible. 

The factor of mutual turbulent diffusion was obtained earlier (see (11.70)) ... 

For Browrtian diffusion of small particles, the influence of hydrodynamic interaction on the collision frequency was studied in works [28, 29], which also mention the decrease in the collision frequency by a factor of 1.5-2. This decrease is not as large as in the case of turbulent coagulation. There are two reasons why the effect of hydrodynamic interaction on the collision frequency of particles differs so substantially in the cases of turbulent flow and Brownian motion. First, the particle size is different in these two cases (the characteristic size of particles participating in Brownian motion is smaller than that of particles in a turbulent emulsion flow). Second, the hydrodynamic force behaves differently (the factor of Browrtian diffusion is inversely proportional to the first power of the hydrodynamic resistance factor h, and the factor of turbulent diffusion - to the second power of h). 

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