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. 

W [Stefan flow], movement in a temperature gradient [thermophoresis j, and sprays), (. i steam condensation onto aerosols, and (4) homogeneous nudeation of water droplets. 

The net flow of component A with Stefan flow taken into consideration is... 

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.

The term p/(p-p ) derives from assumption (4.313) representing the effects of Stefan flow. If e = 1, Eq. (4.318) gives the diffusion flow in a free space. 

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 ... 

In nonreacting, continuum fluid mechanics the fluid velocity normal to a solid wall is zero, which is a no-slip boundary condition. However, if there are chemical reactions at the wall, then the velocity can be nonzero. The so-called Stefan flow velocity occurs... 

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]... 

In very concentrated systems, the increased contribution of the Stefan flow leads the diffu-sional mass transfer rate corresponding to the Sh for quiescent systems to be modified as [Rosner, 1986]... 

The Stefan convection, however, does not alter the analogy between heat and mass transfer because the laws governing the change in the Nusselt number with the Stefan flow are identical to those governing Shs. 

Analysis. To answer this question formally the fuel species and oxidizer species conservation equations would have to be solved. But again, we found a posteriori that the condition for group combustion corresponded to such a dilute cloud that these continuity equations could be approximated accurately enough by neglecting the terms involving Stefan flow convection. Therefore ... 

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

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... 

C What is Stefan flow Write the expression for Stefan s law and indicate what each variable represents. 

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