Average drop size

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). 

The largest droplet in a spray poprJation is 3 times the diameter of the average drop size [see Eq. (12-66)]. 

However, any average drop size is fictitious, and none is completely satisfactory. For example, there is no way in which the high surface and transfer coefficients in small drops can be made avail le to the larger drops. Hence, a process calculation based on a given droplet size describes only what happens to that size and gives at best an approximation to the total mass. 

Effect of Pressure Drop and Nozzle Size For a nozzle with a developed pattern, the average drop size can be estimated to fall with rising AP (pressure drop) by Eq. (14-196) ... 

Drop Size and Interfacial Area The drops produced have a size range [SuUivan and Lindsey, Ind. Eng. Chem. Fundam., 1, 87 (1962) Sprow, Chem. Eng. Sci., 22, 435 (1967) and Chen and Middleman, Am. Inst. Chem. Eng. J., 13, 989 (1967)]. The average drop size may be expressed as... 

The conversion reaches a maximum at 30 Hz. At a higher rate of rotation the increased separatory power of the centrifuge leads to a reduction of the volume of the mixed phase in which the reaction takes place. At reduced rotational speeds of the centrifuge the mixing process becomes less efficient, resulting in larger average drop sizes in the dispersed phase and thus to reduced mass transfer rates and conversion levels. 

Viscosity ratio p = 1 does not produce the finest dispersion average drop sizes decrease with viscosity ratio. 

The average drop size increases with decrease in continuous or dispersed phase viscosity. 

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... 

Optical Methods. Optical methods, based on the scattering of light by dispersed droplets, provide a relatively simple and rapid measure of particle size. However, optical techniques give data concerning the average drop size or the predominant size only, and size-distribution data cannot be obtained. Optical methods are more suited to the size analysis of aerosols and extremely fine mists than to the analysis of typical fuel sprays. 

The effect of a low-pressure atmosphere on jet disintegration was studied by Garner and Henny (21), who reported a marked increase in average drop size with a decrease in... 

Drop size distribution is a measure of the effectiveness of the atomization process. Depending upon the design of the injection system, drop sizes may range from 1 to 60 microns (118). The distribution of drop sizes follows the Rosin-Rammlcr law (104) Average drop size decreases with increases in jet velocity and in density of the air into which fuel is injected (118). The largest drops are found at the center of the disintegrating jet and the smallest at the periphery (86). 

Pinczewski and Fell [Trans. Inst. Chem Eng., 55, 46 (1977)] show that the velocity at which vapor jets onto the tray sets the droplet size, rather than the superficial tray velocity. The power/mass correlation predicts an average drop size close to that measured by Pinczewski and Fell. Combination of this prediction with the estimated fraction of the droplets entrained gave a relationship for entrainment, Eq. (14-202). The dependence of entrainment with the eighth power of velocity even approximates the observed velocity dependence, as flooding is approached. 

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. 

It should be pointed out that various investigators have reported a local variation of the drop sizes (C14, M19, P4, SI I, S29) throughout the vessel. Thus when modeling mass transfer in dispersions, either a global-average drop size distribution or models with spatial dependence of drop size distribution may be needed for accurate analysis of such rate processes. 

Delichatsios M.A., Probstein R.F., The ejffect of Coalescence on the Average Drop Size in Liquid-Liquid Dispersions, Ind. Eng. Chem. Fundam., 15 (1976)... 

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