Mass transfer droplet-size effects

The volumetric coefficient h a from the combination of Eqs. (14-178) and (14-179) is useful in defining the effect of variable changes but is limited in value because of its dependence on D. The prodiicl of area and coefficient obtained from a given mass of hqiiid is proportional to (1/D ) for small diameters. The prime problem is that droplet-size estimating procedures are often no better than 50 percent. A secondary problem is that there is no that truly characterizes either the motion or transfer process for the whole spectrum of particle sizes present. See Eqs. (14-193) and (14-194). 

Droplet size and interfacial area. In the absence of interfacial effects accompanying mass transfer, the droplets break down by impact with elements of packing and finally reach an equilibrium size which is independent of the packing size. Conversely, small droplets gradually coalesce until the equilibrium size is attained. Pratt and his coworkers 5 29 showed that the mean droplet size attained in the tower is well represented by ... 

Once the number of transfer units has been found, the height of the tower is determined from the product of the number and the height of each transfer unit (HTU). The HTU is determined by physical parameters such as the droplet size, the flow patterns in the tower, and the effect of any packing. These all affect the rate of mass transfer, which is addressed in Chapter 9. Very often the rate of mass transfer cannot be estimated from first principles, and it is necessary to estimate the height by determining the number of transfer units achieved and then dividing the actual height of the column employed by the number of transfer units, i.e. ... 

Two effects are of predominant importance during drop formation. The primary goal of dispersing one phase into the other is to create a large interfacial area available for mass transfer. Subdivision into micron-size droplets will create enormous interfacial area. But one must also be concerned with the recovery of pure phases, and there is therefore an optimum drop size below which dispersion becomes undesirable. 

The absorption of ozone from the gas occurred simultaneously with the reaction of the PAH inside the oil droplets. In order to prove that the mass transfer rates of ozone were not limiting in this case, the mass transfer gas/water was optimized and the influence of the mass transfer water/oil was studied by ozonating various oil/water-emulsions with defined oil droplet size distributions. No influence of the mean droplet diameter (1.2 15 pm) on the reaction rate of PAH was observed, consequently the chemical reaction was not controlled by mass transfer at the water/oil interface or diffusion inside the oil droplets. Therefore, a microkinetic description was possible by a first order reaction with regard to the PAH concentration (Kornmuller et al., 1997 a). The effects of pH variation and addition of scavengers indicated a selective direct reaction mechanism of PAH inside the oil droplets... 

The effect of coalescence and break-up of droplets on the yield of chemical reactions was studied by Villermaux (33). Micromixing effects may occur even in batch reactors if there is a drop size distribution and mass-transfer control. Although practical rules for the design and scale-up of liquid-liquid reactors are available as Oldshue showed in the case of alkylation (152), many problems remain unsolved (.5) mass transfer effects, high hold-up fractions (> 20 %), large density differences, high viscosities, influence of surfactants. 

Fukai J, Ishizuka H, Sakai Y, Kaneda M, Morita M, Takahara, A. (2006) Effects of droplet size and solute concentration on drying process of polymer solution droplets deposited on homogeneous surfaces. Int Heat Mass Transfer 49 3561-3567. 

The gas-side mass-transfer coefficients kefl and ko increase with liquid feed rate or with gas velocity at each given position in the venturi scrubber and decrease at constant liquid rate and gas velocity with increasing distance from the point of liquid injection (J7, VI1). The values ofkifl generally increase with increasing liquid flow rate or gas velocity (often referred to as the velocity at the throat). However, ki,a will sometimes exhibit a maximum when the gas velocity increases the explanation is that, at higher gas velocities, an increase in turbulence in the throat of the venturi results in the formation of droplets smaller than the thin filaments first formed at lower gas velocities. Internal circulation is reduced in these smaller droplets, and there is also a reduction in the size of the zone of intense turbulence. These two phenomena lead to a maximum for the values of/cL. as found experimentally by Kuznetsov and Oratovskii (K15) and Virkar and Sharma (VI1). The values of the effective interfacial area a increase with both gas and liquid flow rates. 

The sections which follow outline the general multidimensional distribution theory. Applications of the theory are discussed to describe droplet size distributions and mixing frequencies in chemically equilibrated systems, the effects of droplet mixing on the extent of reaction, the analysis of mass transfer with and without chemical reaction, hydrocarbon fermentation, and emulsion polymerization. 

Valentas and Amundson (V3) studied the performance of continuous flow dispersed phase reactors as affected by droplet breakage processes and size distribution of the droplets. Various reaction cases with and without mass transfer were studied for both completely mixed or completely segregated dispersed phase. Droplet size distribution is shown to have a considerable effect on the efliciency of a segregated reaction system. They indicated that polydispersed drop populations require a larger reactor volume to obtain the same conversion as a monodispersed system for zero-order (or mass-transfer-controlled) reactions in higher conversion regions. As the dispersed phase becomes completely mixed, the distribution of droplet sizes becomes less important. These interactions are un-... 

The model can be employed to predict the effects of droplet size distribution and droplet coalescence-redispersion on conversion and selectivity for reacting dispersions. The reactions can occur in either phase simultaneously with interphase heat and mass transfer. 

From the calculations presented above, it should be clear that coupling effects in multicomponent mass transfer will be influenced not only by the structure of the Fick matrix [/)] but also by the hydrodynamics of two-phase contacting, which influences both the contact time between the phases and the distribution of sizes of droplets or bubbles. Very small bubbles (or drops) may approach the steady-state limit (largest influence of coupling), while larger bubbles will transfer mass in the short-contact regime (least influence of coupling). ... 

PTC incorporated with other methods usually greatly enhances the reaction rate. Mass transfer of the catalyst or the complex between different phases is an important effect that influences the reaction rate. If the mass transfer resistance cannot be neglected, an improvement in the mass transfer rate will benefit the overall reaction rate. The application of ultrasound to these types of reactions can be very effective. Entezari and Keshavarzi [12] presented the utilization of ultrasound to cause efficient mixing of the liquid-liquid phases for the saponification of castor oil. They used cetyltrimethylammo-nium bromide (CTAB), benzyltriethylammonium chloride (BTEAC), and tetrabutylammonium bromide (TBAB) as the catalysts in aqueous alkaline solution. The more suitable PT catalyst CTAB can accumulate more at the liquid-liquid interface and produces an emulsion with smaller droplet size this phenomenon makes the system have a high interfacial surface area, but the degradation of CTAB is more severe than that of BTEAC or TBAB because of more accumulation at the interface of the cavity under ultrasound. 

The addition of various surfactants and micelle-forming agents in the biphasic hydroformylation of olefins was also considered as a tool for enhancement of the reaction rates (see Section 2.3.4). Whereas the presence of a surfactant leads to a lower droplet size in the dispersed phase, thus increasing the liquid-liquid interfadal area and hence the mass-transfer rate, the formation of emulsions is considered as a maj or drawback of this system. Mass-transfer effects in biphasic hydroformylation of 1-octene in the presence of cetyltrimethylammonium bromide (CTAB) was studied by Lekhal et al. [37]. A mass-transfer model based on Higbie s penetration theory was proposed to predict the rate of hydroformylation in a gas-liquid-liquid system. 

In the case of liquid/liquid and gas/liquid dispersion, the above mixing mechanism does not hold and the operation is usually carried out in the turbulent region. The break-up of gas bubbles or liquid droplets to give a system of high interfacial area for mass transfer is brought about by the shear stresses in the system. These stresses are related to the pressure drop and hence flow rate through the mixer. Thus to get a smaller droplet size the fluid flow rate must be increased. It will not be effective to merely increase the number of elements (as was the case in laminar blending). 

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