Mass boundary layer

Implicit in this model is the assumption that molecular diffusivity and Henry s Law constant are directly and inversely proportional, respectively, to the gas flux across the atmosphere-water interface. Molecular diffusion coefficients typically range from 1 x 10-5 to 4 x 10-5 cm2 s-1 and typically increase with temperature and decreasing molecular weight (table 5.3). Other factors such as thickness of the thin layer and wind also have important effects on gas flux. For example, wind creates shear that results in a decrease in the thickness of the thin layer. The sea surface microlayer has been shown to consist of films 50-100 pm in thickness (Libes, 1992). Other work has referred to this layer as the mass boundary layer (MBL) where a similar range of film thicknesses has been... 

Aside from the studies referred to in this chapter, there is a lot of information available on the boundary layer flows of non-Newtonian fluids over plates, cylinders, and needles. A partial review of momentum boundary layers has been provided by Schowalter (1977), whereas that of heat and mass boundary layers have been given by Shenoy and Mashelkar (1982), Chhabra (1993b, 1993c), and, more recently, Ghosh et al. (1994). The viscoelastic diffusion and thermal boundary layers have been revisited recently by Ruckenstein (1994). 

The crosspoint of the dashed lines indicates the upper boundary of the hypothetical mass boundary layer (MBL), having a thickness 8. The image shows that a significant part of the mass-transfer resistance can be situated outside the biofilm... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

Fig. 1. General dialysis is a process by which dissolved solutes move through a membrane in response to a difference in concentration and in the absence of differences in pressure, temperature, and electrical potential. The rate of mass transport or solute flux, ( ), is directly proportional to the difference in concentration at the membrane surfaces (eq. 1). Boundary layer effects, the difference between local and wall concentrations, are important in most...

External mass tran.sfer between the external surfaces of the adsorbent particles and the surrounding fluid phase. The driving force is the concentration difference across the boundary layer that surrounds each particle, and the latter is affected by the hydrodynamic conditions outside the particles. 

For a gas in laminar flow over a condensed phase sample of length L, the mass transport across the boundary layer, in terms of the flux of molecules from the sample to die gas phase, is therefore... 

The comparison of the magnitude of the two resistances clearly indicates whether tire metal or the slag mass transfer is rate-determining. A value for the ratio of the boundary layer thicknesses can be obtained from the Sherwood number, which is related to the Reynolds number and the Schmidt number, defined by... 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

Thus the driving force for fuming is approximately equal to that for free evaporation. Using dre experimental data, and the normal expression for mass transfer across a boundary layer, it is concluded that the boundary layer thickness which would account for this rate should be about 2 x 10 cm (Turkdogan et al., 1963). 

Fujii, T., and Shinzato, K., Various Formulas and Their Accuracy Concerning Heat and Mass Transfer in the Vapor Boundary Layer in the Case of Laminar Film Condensation of Binary Vapor Mixtures, Int. J. Heat Mass Transfer, Vol. 36, No. 1, pp27-33, 1993. 

When we consider many particles settling, the density of the fluid phase effectively becomes the bulk density of the slurry, i.e., the ratio of the total mass of fluid plus solids divided by the total volume. The viscosity of the slurry is considerably higher than that of the fluid alone because of the interference of boundary layers around interacting solid particles and the increase of form drag caused by particles. The viscosity of a slurry is often a function of the rate of shear of its previous history as it affects clustering of particles, and of the shape and roughness of the particles. Each of these factors contributes to a thicker boundary layer. 

Heat and Mass Transfer Differential Equations in the Boundary Layer and the Corresponding Analogy 131... 

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.

Considering the case of Eq. (4.244), it is normal to describe a real mass transfer case by taking into consideration the boundary layer flows and the turbulence by using a mass transfer factor which is defined by... 

In a boundary layer equation the mass center is considered with the help of the velocity (u, Uy, u ) and therefore a distribution of the velocity of the mass center is desirable. The diffusion velocity and diffusion factor are determined with regard to velocity v, giving a formula for Vax /x, but not for /ax - x useful approach is offered by Eq. (4.268c), using the artificial multiplication factor (v - ax /... 

The preceding discussion has attempted to formulate the situation for laminar boundary layer flow as accurately as possible and to obtain precise correlation between the heat transfer and mass transfer factors. 

To calculate the conductance of the boundary layer we first calculate rhf mass transfer factor using Eq. (4.300) ... 

In the stratification strategy with a replacing air distribution in the lower zone, the height of the boundary layer between the lower and upper zones can be determined with the criteria of the contaminant interfacial level.This level, where the air mass flow in the plumes is equal to the air mass flow of the supply air, IS presented in Fig. 8,4. In this ideal case the wait and air temperatures are equal on the interfacial level. In practical cases they are not usually equal and the buoyancy flows on the walls will raise the level and decrease the gradient. 

Wetted wall column An experimental apparatus used to determine the mass transfer that takes place through laminar boundary layers. 

Liquid veloeity around a partiele affeets its mass transfer boundary layer (Figure 5.3) and lienee the mass flux. In foreed eonveetion, the dependenee of the mass transfer eoeffieient on hydrodynamies is given by the Frdssling equation... 

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