Gases Stefan flow

Diffusion of Vapor through a Stationary Gas.-Stefan Flow... 

The other mechanism appears in scrubbers. When water vapor diffuses from a gas stream to a cold surface and condenses, there is a net hydrodynamic flow of the noncondensable gas directed toward the surface. This flow, termed the Stefan flow, carries aerosol particles to the condensing surface (Goldsmith and May, in Davies, Aero.sol Science, Academic, New York, 1966) and can substantially improve the performance of a scrubber. However, there is a corresponding Stefan flow directed away from a surface at which water is evaporating, and this will tend to repel aerosol particles from the surface. 

Figures 4.34 and 4.35 represent two extreme cases. Drying processes represent the case shown in Fig. 4.34 and distillation processes represent Fig. 4.35. Neither case represents a convective mass transfer case while the gas flow is in the boundary layer, other flows are Stefan flow and turbulence. Thus Eqs. (4.243) and (4.244) can seldom be used in practice, but their forms are used in determining the mass transfer factor for different cases.

Condensation Scrubbing The collection efficiency of scrubbing can be increased by the simultaneous condensation of water vapor from the gas stream. Water-vapor condensation assists in particle removal by two entirely different mechanisms. One is the deposition of particles on cold-water droplets or other surfaces as the result of Stefan flow. The other is the condensation of water vapor on particles as nuclei, which enlarges the particles and makes them more readily collected by inertial deposition on droplets. Both mechanisms can operate simultaneously. However, for the buildup of particles by condensation to be effective, there must be adequate time for the particles to grow substantially before the principal gas-liquid-contacting operation takes... 

Elace. Hence, if particle buildup is to De sought, the scrubber should e preceded by an appropriate gas-conditioning section. On the other hand, particle collection by Stefan flow can be induced simply by scrubbing the hot, humid gas with sufficient cold water to bring tne gas below its initial dew point. Any practical method of inducing condensation on the dust particles will incidentally afford opportunities for the operation of the Stefan-flow mechanism. The hot gas stream must, of course, have a high initial moisture content, since the magnitude of the effects obtained is related to the quantity of water vapor condensed. 

For oxidation of solid carbon to produce CO (either by 02 or C02), two moles of gaseous combustion products are produced per mole of gaseous reactant, resulting in a net gas flow away from the particle surface. This Stefan flow reduces the rates of heat and, especially, mass transfer from the boundary layer to the particle surface (akin to drag reduction on a flat surface with... 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species ... 

An element in a thermally radiative environment absorbs, reflects, refracts, diffracts, and transmits incoming radiative heat fluxes as well as emits its own radiative heat flux. Most solid materials in gas-solid flows, including particles and pipe walls, can be reasonably approximated as gray bodies so that absorption and emission can be readily calculated from Stefan-Boltzmann s law (Eq. (1.59)) for total thermal radiation or from Planck s formula (Eq. (1.62)) for monochromatic radiation. Other means of transport of radiative... 

These two conditions (Eqs. (4.97) and (4.98)) are usually sufficient for assuming the medium as quiescent in dilute systems in which both cua.s and cda,oo are small. However, in nondilute or concentrated systems the mass transfer process can give rise to a convection normal to the surface, which is known as the Stefan flow [Taylor and Krishna, 1993]. Consider a chemical species A which is transferred from the solid surface to the bulk with a mass concentration cua.oo- When the surface concentration coa,s is high, and the carrier gas B does not penetrate the surface, then there must be a diffusion-induced Stefan convective outflux, which counterbalances the Fickian influx of species B. In such situations the additional condition for neglecting convection in mass transport systems is [Rosner, 1986]... 

This relation is known as Stefan s law, and the induced convective flow described that enhance.s mass diffusion is called the Stefan flow. Noting that y, — P/P and C = P/RJT for an ideal gas mixture, the evaporation rate of spccie /4 can also be expressed a.s... 

There are several possible mechanisms to explain the enhancement of absorption during surface renewal. The Marangoni Effect results from the fact that dilute solutions of water C10 %) exhibit abnormalities in regard to surface tension. Jones and Ray [8] have observed that absorption of ions at the surface continues until a specific number of sites are occupied. The concentration of these sites is about 5 per 10 surface molecules. If liquid vapor is continually condensed on the drop surface, new surface for sites is being formed at a rate fixed by condensation. A second mechanism for enhancement, Stefan flow, is a trapping of the gas molecules into the liquid phase by the condensing vapor flux. The Stefan flow flux can be expressed as [9] ... 

We re not sure exactly what s accounting for this surface effect. It could be a Stefan-flow phenomenon where a lot of water vapor molecules push along the SO2, or the third gas component, into the droplet involuntarily or at greater rates. 

The /th species mass flux, j, and the total heat flux, q, can be expressed in terms of transfer coefficients. This is useful in situations where the liquid or gas phase is not completely resolved, or when the flow conditions are not exactly known. Often, these transfer coefficients are determined experimentally for a particular flow situation. For instance, different expressions are used, depending on whether the transfer is due to pure conduction or whether it is dominated by ccaivection. Also, the type of convection plays a role, that is, if the convection is forced or non-forced. A forced convection has a non-zero relative velocity between droplet and environment, whereas for a non-forced convection, the relative drop-gas velocity is zero and only the Stefan flow dominates. Note that the natural convection due to gravity is taken to be zero since gravity is an external force, and external forces are neglected in this article. In addition, in forced convection, the nature of the flow, that is, whether the flow is laminar or turbulent, plays an important role. These issues will be discussed in more detail in the following subsections. 

The model was validated on NaCl solutions. In Eq. 6.3, Di is the diffusion coefficient of the solute in the liquid phase, Dg is the diffusion coefficient of the solvent vapor in the gas phase, Qi and pg are the liquid and gas densities, respectively. Sh is the dimensionless mass transfer rate in the vapor phase. This modified Sherwood number, that accounts for the film thinning effect of Stefan flow, lies typically in the range 2 < Sh < 5. The quantity Bm is the Spalding transfer number according to Abramzonand Sirignano (1989) (Sirignano (1999), compare with Eq. 1.66 in Volume... 

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