Turbulent dispersions, drop size

Drop breakage occurs when surrounding fluid stresses exceed the surface resistance of drops. Drops are first elongated as a result of pressure fluctuations and then spHt into small drops with a possibiUty of additional smaller fragments (Fig. 19). Two types of fluid stresses cause dispersions, viscous shear and turbulence. In considering viscous shear effects, it is assumed that the drop size is smaller than the Kohnogoroff microscale, Tj. 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

Microemulsions, like micelles, are considered to be lyophilic, stable, colloidal dispersions. In some systems the addition of a fourth component, a co-surfactant, to an oil/water/surfactant system can cause the interfacial tension to drop to near-zero values, easily on the order of 10-3 - 10-4 mN/m, allowing spontaneous or nearly spontaneous emulsification to very small drop sizes, typically about 10-100 nm, or smaller [223]. The droplets can be so small that they scatter little light, so the emulsions appear to be transparent. Unlike coarse emulsions, microemulsions are thought to be thermodynamically stable they do not break on standing or centrifuging. The thermodynamic stability is frequently attributed to a combination of ultra-low interfacial tensions, interfacial turbulence, and possibly transient negative interfacial tensions, but this remains an area of continued research [224,225],... 

The combination of reducing the flow and increasing the turbulence level has been shown by Brown and Pitt (4) to decrease emulsion drop size and, in systems as we have here with a fixed amount of dispersed phase, increase the emulsion surface area. 

Sprow FB. Distribution of drop sizes produced in turbulent liquid-liquid dispersion. Chem Eng Sci 1967 22 435-442. 

Kataoka T and Nishiki T. Dispersed mean drop sizes of (W/0)/W emulsions in a stirred tank. J Chem Eng Jpn 1986 19 408-412. Nishikawa M, Mori F, and Fujieda S. Average drop size in a liquid-liquid phase mixing vessel. J Chem Eng Jpn 1987 20 82-88. Nishikawa M, Mori F, Fujieda S, and Kayama T. Scale-up of liquid-liquid phase mixing vessel. J Chem Eng Jpn 1987 20 454—459. Berkman PD and Calabrese RV. Dispersion of viscous liquids by turbulent flow in a static mixer. AIChE J 1988 34 602-609. Chatzi EG, Gavrielides AD, and Kiparissides C. Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels. Ind Eng Chem Res 1989 28 1704—1711. 

The presence of the dispersed phase, for small holdup fraction, should not have a signiflcant effect on the turbulent characteristics of the dispersion. Investigators (Cll, C12, RIS, R16) found that for high holdup fraction their developed models for drop size distribution fltted experimental data better by taking into account a damping effect on turbulence by the dispersed phase. Doulah (Dll) developed a theory for the increase of drop size due to this damping of turbulence effect. Experiments (LI) on two-phase jet flows show that the damping of turbulence can be approximated by... 

A. Maximum and Minimum Drop Size in Turbulent Dispersions... 

Delichatsios and Probstein (D4-7) have analyzed the processes of drop breakup and coagulation/coalescence in isotropic turbulent dispersions. Models were developed for breakup and coalescence rates based on turbulence theory as discussed in Section III and were formulated in terms of Eq. (107). They applied these results in an attempt to show that the increase of drop sizes with holdup fraction in agitated dispersions cannot be attributed entirely to turbulence dampening caused by the dispersed phase. These conclusions are determined after an approximate analysis of the population balance equation, assuming the size distribution is approximately Gaussian. 

Arai K., Konno M., Matunaca Y., Saito S., Effect of dispersed-phase viscosity on the maximum stable drop size for breakup in turbulent flow, J. Chem. Engng. Japan 10 (1977) 4, p. 325-330... 

Current spray models may not have the correct physics, may have unknown limits of applicability, and may contain empirical constants. In a recent test conducted by the author and United Technologies Research Center (UTRC), models of primary atomization, secondary atomization, droplet breakup, droplet collision, and turbulent dispersion were applied to an air blast spray. The predictions were compared to experimental data taken at UTRC. The predicted drop size was as much as 35% different from the measured values [8]. In contrast to the typical conference or journal publication, the models were not adjusted to make the agreement as close as possible. They were taken from the literature as is. The conclusion is that physical models of high-speed spray behavior are still lacking, despite years of research in this area. Primary atomization, the beginning of the spray, is one area that is particularly poorly understood. 

A dispersion of one liquid in another can be obtained by passing the mixture in turbulent flow through a pipe. The largest stable drop size depends on the ratio of the disruptive forces caused by turbulent shear to the stabilizing forces of surface tension and drop viscosity. For low-viscosity drops such as benzene or water, the elfect of viscosity is negligible, and a force balance for drops smaller than the main eddies leads to... 

The turbulent flow characteristics of the static mixer are less well documented than those for laminar flow, probably because of the more recent emphasis on turbulent applications and the background of development for laminar flow applications. Turbulent mixing has been modelled in terms of eddy size for the Sulzer mixer. Measurements of mass transfer have been made and data are available for drop size in liquid-liquid dispersions for Kenics - ", Sulzer and Lightnin mixers. 

The fundamentals are as follows. For immiscible liquids flowing in turbulent flow in a pipe of diameter, D, the dispersed phase breaks up into drops with the diameter of the maximum (or 95th percentile) size drop predicted as follows (Dp 95/D) = 4 [1/We] where We = Weber number. Since most drop size distributions are geometrically distributed and since the geometric standard deviation is about 2, the geometric mass average is about 30% of the Dp 95. Thus, the average size drop would be 300 pm if the predicted Dp, 95 = 1000 pm. 

The size of drops encountered in stirred dispersions is comparable to the size of energy transmitting eddies. By consideration of stresses exerted on a drop in this range of the turbulence spectrum, Hinze (12) characterized the maximum drop size by a critical Weber number... 

A turbulent flow is also capable of fragmenting bubbles or drops. We have presented in section 9.2.3, the model by Kolomogorov and by Hinze, which rely the maximum diameter of fluid particles in an emulsion to the rate of turbulent energy dissipation and to surface tensiom In the same way, indicated for the formation of clusters in a dispersion of solid particles, it is difficult to determine the bubble or drop size in a dispersion of fluid particles. We will not discuss this issue any further in this book, and hence refer the reader to more speciahzed volumes. ... 

For this example we combine the approaches used in Examples 2-lb and 2-lc, neglecting turbulent dispersion (see Section 2-3). Since the eddies are all assumed to be at their minimum size, all we need to determine is the time needed for the diffusion across an eddy radius (lt/2 = 0.05 mm) for 99% diffusion. If the turbulence in the various test and commercial units does not change, the calculation will be the same for all cases, as it is based on a fixed eddy size, not on the system size. Of course, the total power will increase with the volume of the system. The only real difference from Example 2-lb is that we need to consider a sphere rather than a slab. The value of DabI/L drops from 2.0 to 0.56 (see Brodkey and Hershey, 1988, p. 680), giving a diffusion time of... 

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