Droplet size correlations

Droplet radius, in polymer blends, 20 333 Droplet size correlations, 23 190-191 Droplet size distribution, in polymer blends, 20 332-333 Droplet sizes, in sprays, 23 185 Drop-on-demand (DOD) inkjet printing, 9 222... 

MEAN DROPLET SIZE CORRELATION FOR PRESSURE SWIRL ATOMIZER... 

Droplet Size Correlations. The majority of correlations found in the Hterature deal with mean droplet diameters. A usefiil equation for Sauter... 

Lefebvre [1] has compiled droplet size correlations for variety of spray nozzles. The present chapter extends the same compilation to include more recent correlations. The correlations provided are by no means exhaustive, yet they provide commonly used correlations. These correlations are provided in Tables 24.1-24.12 at the end of this chapter. The correlations are mainly based on the (i) fluid properties (mainly density, viscosity, and surface tension), (ii) nozzle geometry, such as the exit orifice diameter, impinging angle of the air on the liquid, etc., and (iii) operational parameters such as the flow rates of the liquid or gas. While some experiments have been conducted to consider the effects of all these three types of variables, many simply choose only to deal with a handful of them, and neglect the effects of others. Obviously, the more the experimental variables, the more difficult it is to obtain an accurate correlation for the droplet size. 

Ultrasonic nozzles are still largely in their development and research phase. And yet despite this, all the droplet size correlations that could be found in existing literature can be readily used without the need for further experiments. That is, none of them contain experimental constants or any properties that would be hard to determine. The three formulas presented for standing wave ultrasonic nozzles contain different variables and relationships. And yet the formulas obtained for the capillary wave design are very similar to each other. 

Abstract This chapter discusses several other types of atomizers that were not considered in the previous chapters. This includes swirl nozzles, T-jet nozzles, and vibrating mesh nebulizers. The droplet size correlations for different types of nozzles is provided in Chap. 24. 

For the successful preparation of emulsions, the wetting conditions on the membrane surface are crucial. It is necessary that the membrane surface is only wetted by the liquid that forms the continuous phase. The droplet size correlates with the membrane pore size by a simple relation, Dd = /Dm where / is a value typically between 2 and 8 (35). Droplets can be produced with diameters in the pm-, as well as in the sub-micrometre range. This technique has been successfully applied to produce monodisperse emulsions and multiple emulsions, as well as to carry out polymerizations leading to polymer particle in the pm size range with narrow size distributions (36, 37). Further advantages (38) are as follows the droplet size is controllable and generally a quite narrow DSD can be achieved, the method is reproducible and the scale-up is easy just by increasing the number of membrane modules, the characteristic features are independent of scale-up, batch as well as continuous operations modes are possible, the continuous phase is exposed to a lower stress. 

Table 5.2 Droplet size correlation for liquid-liquid dispersions in stirred tanks... 

FtoZXldPfeed Pressure nozzle preferred for most applications. Very small particles (e.g., for inhalation powders), feeds with large suspended particles and very viscous feeds, may require other atomization systems, namely two-fluid nozzle. Use droplet size correlations to select the most suited nozzle and atomization conditions... 

For viscosities below 3 cp. Equations (1.8a) and (1.8b) should be used. The two equations intersect at 3 cp, and electrostatic treaters would not be expected to operate less efficiently in this range. Additionally, the data from which the electrostatic treater droplet size correlation was developed did not include oil viscosities less than 7 cp. 

The energetics and kinetics of film formation appear to be especially important when two or more solutes are present, since now the matter of monolayer penetration or complex formation enters the picture (see Section IV-7). Schul-man and co-workers [77, 78], in particular, noted that especially stable emulsions result when the adsorbed film of surfactant material forms strong penetration complexes with a species present in the oil phase. The stabilizing effect of such mixed films may lie in their slow desorption or elevated viscosity. The dynamic effects of surfactant transport have been investigated by Shah and coworkers [22] who show the correlation between micellar lifetime and droplet size. More stable micelles are unable to rapidly transport surfactant from the bulk to the surface, and hence they support emulsions containing larger droplets. 

Correlations between droplet size and surrounding field conditions are also important. 

Flow Reactors Fast reactions and those in the gas phase are generally done in tubular flow reaclors, just as they are often done on the commercial scale. Some heterogeneous reactors are shown in Fig. 23-29 the item in Fig. 23-29g is suited to liquid/liquid as well as gas/liquid. Stirred tanks, bubble and packed towers, and other commercial types are also used. The operadon of such units can sometimes be predicted from independent data of chemical and mass transfer rates, correlations of interfacial areas, droplet sizes, and other data. 

Pinczewski and Fell [Trans. Inst. Chem E/ig., 55, 46 (1977)] show that the velocity at which vapor jets onto the tray sets the droplet size, rather than the superficial tray velocity. A maximum superficial velocity formulation that incorporates ( ), the fractional open area, is logical since the fractional open area sets the jet velocity. Stichlmair and Mers-mauu [Int. Chem. Eng., 18(2), 223 (1978)] give such a correlation ... 

The responses chosen all relate to important foam properties. We believed that yi, the emulsion droplet size, determines y2, the cell size in the resultant foam, and we wished to determine whether this is true over this range of formulations. The foam pore size ys should determine the wetting rate y7, so these responses could be correlated, and yg, the BET surface area, should be related to these as well. The density y and density uniformity ys are critical to target performance as described above, and ys, the compressive modulus, is an important measure of the mechanical properties of the foam. 

Wu, Ruff and Faethl249 made an extensive review of previous theories and correlations for droplet size after primary breakup, and performed an experimental study of primary breakup in the nearnozzle region for various relative velocities and various liquid properties. Their experimental measurements revealed that the droplet size distribution after primary breakup and prior to any secondary breakup satisfies Simmons universal root-normal distribution 264]. In this distribution, a straight line can be generated by plotting (Z)/MMD)°5 vs. cumulative volume of droplets on a normal-probability scale, where MMD is the mass median diameter of droplets. The slope of the straight line is specified by the ratio... 

In practical fan sheet breakup processes, sheet thickness diminishes as the sheet expands away from the atomizer orifice, and liquid viscosity affects the breakup and the resultant droplet size. Dombrowski and Johns[238] considered these realistic factors and derived an analytical correlation for the mean droplet diameter on the basis of an analysis of the aerodynamic instability and disintegration of viscous sheets with particular reference to those generated by fan spray atomizers ... 

Atomization, or generally speaking droplet generation, is an extremely complex process that cannot yet be precisely predicted theoretically. The lack of general theoretical treatment of droplet processes has led to the development of numerous empirical correlations for droplet properties as a function of process parameters and material properties. In this chapter, empirical and analytical correlations for the prediction of droplet properties, such as droplet size distribution and droplet deformation characteristics will be summarized from experimental observations and theoretical analyses in available literature. 

Mathematical representation of droplet size distribution has been developed to describe entire droplet size distribution based on limited samples of droplet size measurements. This can overcome some drawbacks associated with the graphical representation and make the comparison and correlation of experimental results easier. A number of mathematical functions and empirical equations1423 427 for droplet size distributions have been proposed on the basis of... 

It has been indicated 323 that for some distributions it is possible to find, at least, an empirical correlation between the mean droplet size and the standard deviation. Gretzinger and Marshall 102 have proposed such empirical equations relating the mean droplet size and the standard deviation for water-air system. Thus, once the mean droplet size is determined from a mathematical model, an empirical correlation, and/or experimental data, the entire droplet size distribution can be then predicted quantitatively. 

In many atomization processes, physical phenomena involved have not yet been understood to such an extent that mean droplet size could be expressed with equations derived directly from first principles, although some attempts have been made to predict droplet size and velocity distributions in sprays through maximum entropy principle.I252 432] Therefore, the correlations proposed by numerous studies on droplet size distributions are mainly empirical in nature. However, the empirical correlations prove to be a practical way to determine droplet sizes from process parameters and relevant physical properties of liquid and gas involved. In addition, these previous studies have provided insightful information about the effects of process parameters and material properties on droplet sizes. 

In the following sections, the correlations for droplet sizes generated by different types of atomizers will be summarized, and the effects of process parameters and material properties on droplet sizes will be discussed on the basis of the analytical and experimental studies available in published literature. 

Table 4.3. Correlations for Mean, Minimum and Maximum Droplet Sizes Generated in Pressure Jet Atomization by Plain-Orifice Atomizers... 

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Various correlations for mean droplet size generated using pressure-swirl and fan spray atomizers are summarized in Tables 4.4 and 4.5, respectively. In the correlations for pressure-swirl data, FN is the Flow number defined as FN = ml/APlpl) )5, l0 and d0 are the length and diameter of final orifice, respectively, ls and ds are the length and diameter of swirl chamber, respectively, Ap is the total inlet ports area, /yds the film thickness in final orifice, 6 is the half of spray cone angle, and Weyis the Weber number estimated with film... 

Table 4.4. Correlations for Mean Droplet Size Generated by Pressure-Swirl Atomizers...

As ambient air pressure is increased, the mean droplet size increases 455 " 458] up to a maximum and then turns to decline with further increase in ambient air pressure. ] The initial rise in the mean droplet size with ambient pressure is attributed to the reduction of sheet breakup length and spray cone angle. The former leads to droplet formation from a thicker liquid sheet, and the latter results in an increase in the opportunity for droplet coalescence and a decrease in the relative velocity between droplets and ambient air due to rapid acceleration. At low pressures, these effects prevail. Since the mean droplet size is proportional to the square root of liquid sheet thickness and inversely proportional to the relative velocity, the initial rise in the mean droplet size can be readily explained. With increasing ambient pressure, its effect on spray cone angle diminishes, allowing disintegration forces become dominant. Consequently, the mean droplet size turns to decline. Since ambient air pressure is directly related to air density, most correlations include air density as a variable to facilitate applications. Some experiments 452] revealed that ambient air temperature has essentially no effect on the mean droplet size. 

Various correlations for mean droplet sizes generated by air-assist atomizers are given in Table 4.6. In these correlations, mA is the mass flow rate of air, h is the height of air annulus, tf0 is the initial film thickness defined as tj ) = dQw/dan, d0 is the outer diameter of pressure nozzle, dan is the diameter of annular gas nozzle, w is the slot width of pressure nozzle, C is a constant related to nozzle design, UA is the velocity of air, and MMDC is the modified mean droplet diameter for the conditions of droplet coalescence. Distinguishing air-assist and air-blast atomizers is often difficult. Moreover, many... 

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