Drop Size Distributions

When an impeller is rotated in an agitated tank containing two immiscible Hquids, two processes take place. One consists of breakup of dispersed drops due to shearing near the impeller, and the other is coalescence of drops as they move to low shear zones. The drop size distribution (DSD) is decided when the two competing processes are in balance. During the transition, the DSD curve shifts to the left with time, as shown in Figure 18. Time required to reach the equiHbrium DSD depends on system properties and can sometimes be longer than the process time. 

Fig. 18. Variation in drop size distribution with time.

Static mixing of immiscible Hquids can provide exceUent enhancement of the interphase area for increasing mass-transfer rate. The drop size distribution is relatively narrow compared to agitated tanks. Three forces are known to influence the formation of drops in a static mixer shear stress, surface tension, and viscous stress in the dispersed phase. Dimensional analysis shows that the drop size of the dispersed phase is controUed by the Weber number. The average drop size, in a Kenics mixer is a function of Weber number We = df /a, and the ratio of dispersed to continuous-phase viscosities (Eig. 32). 

Information on the coefficients is relatively undeveloped. They are evidently strongly influenced by rate of drop coalescence and breakup, presence of surface-active agents, interfacial turbulence (Marangoni effect), drop-size distribution, and the like, none of which can be effectively evaluated at this time. 

In backlight or shadowgraph technique, the light comes from behind and is directed toward the camera. This technique is very useful in measuring bubble or drop size distributions (Figure 15.3). 

Giardino NJ, Esmen NA, Andelman JB. 1992. Modeling volatilization of trichloroethylene from a domestic shower spray the role of drop-size distribution. Environmental Science and Technology 26 1602-1606. 

V. Mishra, S. M. Kresta, J. H. Masliyah 1998, (Self-preservation of the drop size distribution function and variation in the stability ratio for rapid coalescence of a polydisperse emulsion in a simple shear field), J. Colloid Interface Sci. 197, 57. 

Illustration Drop size distributions produced by chaotic flows. Affinely deformed drops generate long filaments with a stretching distribution based on the log-normal distribution. The amount of stretching (A) determines the radius of the filament locally as... 

Illustration Effect of viscosity ratio on drop size distributions. 

Fig. 25. Drop size distributions f(V,p)] based on drop volume (V) obtained by repeated stretching and breakup in a journal bearing flow for different viscosity ratios (p) (left). The curves for the different distributions overlap when the distribution is rescaled (right) (Muzzio, Tjahjadi, and Ottino, 1991).

Muzzio, F. J., Tjahjadi, M., and Ottino, J. M., Self-similar drop size distributions produced by breakup in chaotic flows. Phys. Rev. Lett. 67, 54-57 (1991b). 

Collins and Knudsen (C6) recently reported drop-size distribution produced by two immiscible liquids in turbulent flow, and the average drop size can be calculated from these distributions. From a knowledge of the average drop size, the interfacial area per drop a and the drop volume can be calculated. The number of drops per unit volume is given by... 

Abismad B, Canselier JP, Wilhelm AM, Delmas H, Gourdon C (1999) Emulsification by ultrasound Drop size distribution and stability. Ultrason Sonochem 6 75-83... 

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. 

Furthermore, the physics of the interaction between turbulence and bubbles in the complex flow of a stirred vessel, with its implications for coalescence and break-up of bubbles and drops, is still far from being understood. Up to now, simple correlations are available for scale-up of industrial processes generally, these correlations have been derived in experimental investigations focusing on the eventual mean drop diameter and the drop size distributions as brought... 

Colenbrander, G. W., Experimental Findings on the Scale-Up Behaviour of the Drop Size Distribution of Liquid-Liquid Dispersions in Stirred Vessels . Proceedings of the 10th European Conference on Mixing, Delft, Netherlands, 173-180 (2000). 

K2. Keily, D. P., Measurement of drop size distribution and liquid water content in natural clouds, Dept, of Meteorol., Mass. Inst, of Tech., Contr. No. AF19(628)-259, NASA Rept. No. N64-30005 (1964). 

The range of dispersed-phase velocity studied by Keith and Hixson (K3) is from 10 to 30 cm/sec which, according to those authors, is of industrial interest. The results obtained by them in the absence of mass transfer can be predicted roughly by extrapolation of the Hayworth and Treybal correlation. In the presence of mass transfer, the results obtained (F2), the drop size distribution, flooding, etc. are different from those observed in the absence of mass transfer. There is no reliable theory at present which can predict the drop size distribution in sprays, though rough approximations are possible when mass transfer is completely avoided. 

Because of such factors as wave formation, jet turbulence, and secondary breakup, the drops formed are not of uniform size. Various ways of describing the distribution, including the methods of Rosin and Rammler (R9) and of Nukiyama and Tanasawa (N3), are discussed by Mugele and Evans (M7). A completely theoretical prediction of the drop-size distribution resulting from the complex phenomena discussed has not yet been obtained. However, for simple jets issuing in still air, the following approximate relation has been suggested (P3) ... 

The rate of mass transfer is a funetion, among other variables, of the drop size distribution or interfaeial area between the phases. The drop size is governed by the surface tension, and densities of the two phases and the type of agitation and design of the eontaetor. Up to a point, the smaller the drop, the greater the rate of mass transfer. 

The area between phases A is the surface area of the drops. It will clearly be a strong function of the stirring characteristics (we assume that stirring is always fast enough to mix both phases). The presence of surfactants, drop size distributions, stirrer design, and circulation patterns. Interfacial area is frequently an unknown in emulsion reactors, but the above formulation should be applicable. Another complication in emulsion reactors is the fact that mass transfer coefficients depend strongly on drop size and stirring rate. The relevant parameter in an emulsion reactor is A km wilh neither factor known very well. 

In liquid-liquid reacting systems, one of the important parameters is the surface area per unit volume, a, in the dispersion, which can be related to the Sauter mean drop diameter dn- In some processes, the drop size distribution and especially the minimum drop size or the maximum stable drop diameter are also important factors in analysing the process results. 

Abismail, B., Canselier, J.P., Wilhelm, A.M., Delmas, H., Gourdon, C. (1999). Emulsification by ultrasound drop size distribution and stability. Ultrasonics Sonochemistry, 6, 75-83. 

Dock drainage. Federal regulations require that free oil be removed from deck drainage prior to disposal. It is extremely difficult to predict an oil drop size distribution for rainwater or washdown water collected in an open drain system, and regulations do not define what size droplet is meant by free oil. 

Conversely, if a vendor is provided the oil drop-size distribution of a given water he can quote the perfw-mance of a standard size corrugated plate interceptor tor a specified drop-size removal... 

Crude oil type. Strickland examined the effect of three crude oil types on dispersed-gas oil removal and found a significant difference. Oil concentration, drop size distribution, and water composition (10% NaCI) were the same for all tests. 

Each port was located in an area of turbulence with the sampling tube directed into the flow so that small and large oil drops entered with equal facility. A Coulter Counter Model T -X 11 was used to measure the oil-drop size distributions. A Beckman Model 915A Total Organic Carbon Analyzer was used to measure oil concentration. 

Computer programs accounted for the presence of oil drops below- the detection limit of the Coulter Counter. The data processing procedure, which assumed that the oil-drop size distribution was lognormal, yielded accurate estimates of the true mean and standard deviation describing the emulsion drop size distribution. The data-analysis procedure did not affect the actual measured drop populations which were used in the kinetic studies. The computer programs are described in detail by Bycscda.8... 

Experiments were conducted varying the residence time, air flowrate, and oil concentration over the same ranges used to study overall system performance. The oil concentrations and drop-size distributions were measured at the entrance and exit of each stage. Table 2 shows typical results. Most of the drop removal for the large drops and production of the small drops occurred in the first stage. The third notation cell had the lowest rates of drop production and aggregation and the largest drops which were least influenced by these effects. Thus, this portion of the data was analyzed to determine the order of the kinetic process for drop removal by air bubbles. A typical plot of the oil removal rate vs. the outlet oil concentration is shown in Fig. 4 the oil removal process is first-order with respect to the concentration of oil drops. 

The observation by Strickland that different crude oils can exhibit large differences in overall removal efficiency even when the inlet drop size distributions... 

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