Droplet size parameters

The visibility function can be reduced to a droplet size parameter (droplet diameter/fringe spacing) analytically. The appropriate equations and their analysis have been presented by Farmer (2). He has shown that under certain constraints, V reduces to ... 

The principal parameters affecting the size of droplets produced by twin-fluid atomizers have also been discussed (34). These parameters include Hquid viscosity, surface tension, initial jet diameter (or film thickness), air density, relative velocity, and air—Hquid ratio. However, these parameters may have an insignificant effect on droplet size if atomization occurs very rapidly near the atomizer exit. 

Both effects can produce coarser atomization. However, the influence of Hquid viscosity on atomization appears to diminish for high Reynolds or Weber numbers. Liquid surface tension appears to be the only parameter independent of the mode of atomization. Mean droplet size increases with increasing surface tension in twin-fluid atomizers (34). is proportional to CJ, where the exponent n varies between 0.25 and 0.5. At high values of Weber number, however, drop size is nearly proportional to surface tension. 

The study of the combustion of sprays of Hquid fuels can be divided into two primary areas for research purposes single-droplet combustion mechanisms and the interaction between different droplets in the spray during combustion with regard to droplet size and distribution in space (91—94). The wide variety of atomization methods used and the interaction of various physical parameters have made it difficult to give general expressions for the prediction of droplet size and distribution in sprays. The main fuel parameters affecting the quaHty of a spray are surface tension, viscosity, and density, with fuel viscosity being by far the most influential parameter (95). 

Emulsions Almost eveiy shear rate parameter affects liquid-liquid emulsion formation. Some of the efrecds are dependent upon whether the emulsion is both dispersing and coalescing in the tank, or whether there are sufficient stabilizers present to maintain the smallest droplet size produced for long periods of time. Blend time and the standard deviation of circulation times affect the length of time it takes for a particle to be exposed to the various levels of shear work and thus the time it takes to achieve the ultimate small paiTicle size desired. 

An example of liquid/liquid mixing is emulsion polymerization, where droplet size can be the most important parameter influencing product quality. Particle size is determined by impeller tip speed. If coalescence is prevented and the system stability is satisfactory, this will determine the ultimate particle size. However, if the dispersion being produced in the mixer is used as an intermediate step to carry out a liquid/liquid extraction and the emulsion must be settled out again, a dynamic dispersion is produced. Maximum shear stress by the impeller then determines the average shear rate and the overall average particle size in the mixer. 

The critical radius at Tg is a multiple of Droplets of size N > N are thermodynamically unstable and will break up into smaller droplets, in contrast to that prescribed by F N), if used naively beyond size N. This is because N = 0 and N = N represent thermodynamically equivalent states of the liquid in which every packing typical of the temperature T is accessible to the liquid on the experimental time scale, as already mentioned. In view of this symmetry between points N = 0 and N, it may seem somewhat odd that the F N) profile is not symmetric about. Droplet size N, as a one-dimensional order parameter, is not a complete description. The profile F N) is a projection onto a single coordinate of a transition that must be described by order parameters—the... 

A Malvern Mastersizer (Malvern Instruments Ltd, Malvern, UK) with optical parameters defined by the manufacturer s presentation code 0505 was used to determine the droplet size distribution. The measurement was made in triplicate at room temperature. Water was used to disperse the emulsion droplets. 

Figure 2.11 Tailored particle size is ensured by the emulsion chemistry, as the droplet size where the sol-gel polycondensation takes place is easily controlled by the emulsion parameters. (Reproduced from ref. 8, with permission.)...

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. 

To characterize a droplet size distribution, at least two parameters are typically necessary, i.e., a representative droplet diameter, (for example, mean droplet size) and a measure of droplet size range (for example, standard deviation or q). Many representative droplet diameters have been used in specifying distribution functions. The definitions of these diameters and the relevant relationships are summarized in Table 4.2. These relationships are derived on the basis of the Rosin-Rammler distribution function (Eq. 14), and the diameters are uniquely related to each other via the distribution parameter q in the Rosin-Rammler distribution function. Lefebvre 1 calculated the values of these diameters for q ranging from 1.2 to 4.0. The calculated results showed that Dpeak is always larger than SMD, and SMD is between 80% and 84% of Dpeak for many droplet generation processes for which 2left-hand side of Dpeak. The ratio MMD/SMD is... 

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. 

The process parameters influencing droplet sizes may include liquid pressure, flow rate, velocity ratio of air to liquid (mass flow rate ratio of air to liquid), and atomizer geometry and configuration. It has been clearly established that increasing the velocity ratio of air to liquid is the most important practical method of improving atomization)211] In industrial applications, however, the use of mass flow rate ratio of air to liquid has been preferred. As indicated by Chigier)2111 it is difficult to accept that vast quantities of air, that do not come into any direct contact with the liquid surface, have any influence on atomization although mass flow rates of fluids include the effects of velocities. 

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. 

In fan spray atomization, the effects of process parameters on the mean droplet size are similar to those in pressure-swirl atomization. In general, the mean droplet size increases with an increase in liquid viscosity, surface tension, and/or liquid sheet thickness and length. It decreases with increasing liquid velocity, liquid density, gas density, spray angle, and/or relative velocity between liquid and surrounding air. 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

The studies on the performance of effervescent atomizer have been very limited as compared to those described above. However, the results of droplet size measurements made by Lefebvre et al.t87] for the effervescent atomizer provided insightful information about the effects of process parameters on droplet size. Their analysis of the experimental data suggested that the atomization quality by the effervescent atomizer is generally quite high. Better atomization may be achieved by generating small bubbles. Droplet size distribution may follow the Rosin-Rammler distribution pattern with the parameter q ranging from 1 to 2 for a gas to liquid ratio up to 0.2, and a liquid injection pressure from 34.5 to 345 kPa. The mean droplet size decreases with an increase in the gas to liquid ratio and/or liquid injection pressure. Any factor that tends to impair atomization quality, and increase the mean droplet size (for example, decreasing gas to liquid ratio and/or injection pressure) also leads to a more mono-disperse spray. 

Generally, the mean droplet size is proportional to liquid surface tension, and inversely proportional to liquid density and vibration frequency. The proportional power index is —1/3 for the surface tension, about -1/3 for the liquid density, and -2/3 for the vibration frequency. The mean droplet size may be influenced by two additional parameters, i.e., liquid viscosity and flow rate. As expected, increasing liquid viscosity, and/or flow rate leads to an increase in the mean droplet size,[13°h482] while the spray becomes more polydisperse at high flow rates.[482] The spray angle is also affected by the liquid flow rate, vibration frequency and amplitude. Moreover, the spray shape is greatly influenced by the direction of liquid flow (upwards, downwards, or horizontally).[482]... 

As described above, a number of empirical and analytical correlations for droplet sizes have been established for normal liquids. These correlations are applicable mainly to atomizer designs, and operation conditions under which they were derived, and hold for fairly narrow variations of geometry and process parameters. In contrast, correlations for droplet sizes of liquid metals/alloys available in published literature 318]f323ff328]- 3311 [485]-[487] are relatively limited, and most of these correlations fail to provide quantitative information on mechanisms of droplet formation. Many of the empirical correlations for metal droplet sizes have been derived from off-line measurements of solidified particles (powders), mainly sieve analysis. In addition, the validity of the published correlations needs to be examined for a wide range of process conditions in different applications. Reviews of mathematical models and correlations for... 

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