Boundary layer stripping

As described previously, in the atomization sub-model, 232 droplet parcels are injected with a size equal to the nozzle exit diameter. The subsequent breakups of the parcels and the resultant droplets are calculated with a breakup model that assumes that droplet breakup times and sizes are proportional to wave growth rates and wavelengths obtained from the liquid jet stability analysis. Other breakup mechanisms considered in the sub-model include the Kelvin-Helmholtz instability, Rayleigh-Taylor instability, 206 and boundary layer stripping mechanisms. The TAB model 310 is also included for modeling liquid breakup. 

Boundary layer stripping and possible evaporation of the fuel. 

Large melt droplets fragmented by boundary layer stripping... 

As already mentioned, we have chosen to use a boundary layer stripping model for fragmentation as this is thought to be the most appropriate for the study of vapor explosions. We have used the model proposed by Carachalios et al., , who suggest that the stripping rate... 

The length-scale of the droplets is changed by the ma s loss due to boundary layer stripping. For spherical drops it is easily shown that the mass loss rate given in Eq. (20) implies a length-scale source term of... 

When velocity gradients are small, for example, near the boundary layer separation point and at the rear of a cylinder in separated flow, Eq. (33) is inaccurate. The separation point was determined with an accuracy of 1 degree by using twin strip electrodes of 125 /im length, separated by... 

The working cathode also generates a boundary layer. The water that is reduced at the cathode is supplied by the bulk catholyte. This stripping effect forms a layer of approximately 37 wt.% caustic on the surface of the cathode. Again, the thickness of this layer is determined by the efficiency of the internal mixing within the cathode compartment. 

Figure 9.7a shows the formation of boundary layers in absorption operations, and Figure 9.7b shows the formation of boundary layers in stripping operations. The right-hand side in each of these figures represents the liquid phase as in the hquid phase of a droplet and the left-hand side represents the gas phase as in the gas phase of the air. 

FIGURE 9.7 Formation of interfacial boundary layers (a) absorption (b) stripping. 

FIGURE 13.3 Schematic concentration profile of each Ti(IV) chemical species, transported through the HLM system with hydrophobic membranes. Layers controlling the permeation rate are h(, feed-side aqueous boundary layer h, feed-side microporous membrane, immobilized by membrane solution h i, feed-side boundary layer of the membrane solution /r , strip-side boundary layer of the membrane solution h, strip-side microporous membrane, immobilized by membrane solution / , strip-side aqueous boundary layer. (From Kisbk, V. and Eyal, A., J. Mem. Sci., Ill, 259, 1996. With permission.)... 

Mass transfer in the feed and strip solutions is limited by the extent of concentration polarization. On the feed side of the membrane, concentration polarization refers to an increase in the concentration of solutes at and near the feed-membrane interface because of evaporation of water into the membrane pores (Fig. 1). The resulting solute concentration gradient between the membrane-feed interface, where the concentration is greatest, and the bulk solution induces diffusive transport of rejected solutes back through the concentration polarization boundary layer into the bulk stream. Bulk solution is simultaneously transported to the membrane wall by convection. When equilibrium has been established under a given set of operating conditions (stream flow rate, temperature, fluid dynamics imposed by membrane module design), the rate of back diffusion is equal to the rate at which the solutes are carried to the membrane surface by convective flow. ... 

Feed-side and strip-side concentration polarization result in a reduction in the driving force for mass transfer. There is a decrease in water activity at the feed-membrane interface and an increase at the strip-membrane interface. This results in a reduction in the water vapor pressure gradient across the membrane. The feed side and strip side mass transfer co-efficients, Kf and K, respectively, can be expressed in terms of the solute diffusion co-efficient in the boundary layer, D, ... 

The water flux achieved in OD can be described in terms of an overall mass transfer co-efficient, K, and the water vapor pressure gradient between the bulk feed and strip streams [Eq. (10)]. The total resistance to mass transfer, given by l/K, is the sum of three separate resistances in series [Eq. (11)]. Here, l/Kf, l/Kj and l/K are the resistances imposed by the feed-side boundary layer, the membrane, and the strip-side boundary layer respectively. 

Diffusion through the strip-side stagnant LM boundary layer Interdiffusion through the strip-side membrane support (/Zmr) Interaction with the stripping agent on the strip-side LM interface, as a result of different thermodynamic conditions, and partition into the strip phase... 

Diffusion through the strip-side stagnant boundary layer (h ) to the bulk strip... 

So, in all configurations we have (1) diffusion steps in aqueous feed and strip stagnant boundary layers, (2) diffusion of the complex solute-carrier in the LM phase and/or interdiffusion in the membrane support pores,... 

Individual mass-transfer coefficients of solute species in the feed, carrier, and strip interfacial boundary layers are determined experimentally by feed, carrier, and strip flow rate variations, using Eq. (20). 

Variations of the feed and strip flow rates have little effect on the cadmium transport performance the values of individual cadmium mass-transfer coefficients are similar at carrier or strip flow rates variations. Thus, diffusion of cadmium species through the feed and strip aqueous boundary layers does not control the transport rate. The ratecontrolling steps could act as resistances to diffusion of the cadmium species in the carrier solution layers, especially in the membrane pores or the interfacial backward-extraction reaction kinetics. 

Discrepancies between experimentally obtained and theoretically calculated data for cadmium concentration in the strip phase are 10-150 times at feed or strip flow rate variations. These differences between the experimental and simulated data have the following explanation. According to the model, mass transfer of cadmium from the feed through the carrier to the strip solutions is dependent on the diffusion resistances boundary layer resistances on the feed and strip sides, resistances of the free carrier and cadmium-carrier complex through the carrier solution boundary layers, including those in the pores of the membrane, and resistances due to interfacial reactions at the feed- and strip-side interfaces. In the model equations we took into consideration only mass-transfer relations, motivated by internal driving force (forward... 

The transport of the substances from the feed solution to the strip side can be divided into the foUowing steps diffusion of substance S across the boundary aqueous layer in the feed (donor) phase, extraction (sorption) of substance on the donor/membrane phase interface, diffusion across the boundary layer on the feed (donor) side, convection transport in the liquid membrane zone, diffusion across the boundary layer on the strip (acceptor) phase of LM, re-extraction (desorption) on the membrane/strip phase... 

These differences between the experimental and the simulated data have the following explanation. According to the model, mass transfer of titanium from the feed through the carrier to the strip solutions is dependent on the resistances boundary layer resistances on the feed and strip sides, resistances... 

---