Drop size distribution normal

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... 

In contrast to the large variety of averages and measures of dispersion prevalent in the literature, the number of basic distributions which have proved useful is relatively small. In droplet statistics, the best known distributions include the normal, log-normal, Rosin-Rammler, and Nukiyama-Tanasawa distributions. The normal distribution often gives a satisfactory representation where the droplets are produced by condensation, precipitation, or by chemical processes. The log-normal and Nukiyama-Tanasawa distributions often yield adequate descriptions of the drop-size distributions of sprays produced by atomization of liquids in air. The Rosin-Rammler distribution has been successfully applied to size distribution resulting from grinding, and may sometimes be fitted to data that are too skewed to be fitted with a log-normal distribution. 

Drop size distributions are often plotted as frequency vs. logarithm of diameter to test the symmetry around the first aridimetic mean value or first moment m of an assumed log normal rlistrihution. which is a quite common case. 

In [2,22], holography was used to measure drop-size distributions for DA < 0.1. In the bag and multimode regimes, the root-normal distribution with MMD/D32 1.2 fit... 

When we do this, the distributions usually considered for describing secondary atomization could be encompassed in two groups. One purely empirical, concerned about the shape and scale of the secondary drop size distribution (Weibull, Rosin-Rammler, Nukyiama-Tanasawa), and the second, a semiempirical group associated with the multiplicative meaning of the Log-normal distribution function. 

A systematic analysis has been made for the statistical approach to describe secondary drop size distributions. Two groups were identified. An empirical one based on the Weibull distribution where the scale and shape parameters can change according to the degree of control desired over the size and frequency range. The second group is semiempirical and is associated with a log-normal distribution function. The statistical meaning of the log-normal expresses the multiplicative nature of the secondary atomization process. 

Keywords Characteristic drop diameter Cumulative volume fraction Discrete probability function (DPF) Drop size distribution Empirical drop size distribution Log-hyperbolic distribution Log-normal distribution Maximum entropy formalism (MEF) Nukiyama-Tanasawa distribution Number distribution function Probability density function (pdf) Representative diameter Root-normal distribution Rosin-Rammler distribution Upper limit distribution Volume distribution... 

Cumulative drop size distributions can be plotted conveniently on linear or log probability paper. A straight line on linear or normal probability paper means that the drop sizes follow a normal or Gaussian distribution. If data form a straight line on log probability paper, the distribution is referred to as lognormal. 

A commonly used measure of the breadth of a size distribution is the coefficient of variation, CoV. This can be determined easily from normal or lognormal plots of cumulative frequency data. The smaller the value of the CoV, the narrower the drop size distribution ... 

Fortunately, it turns out (AIChE, 1978) that the width of the drop size distribution is strongly dependent upon the volume or mass average droplet size, Xmedi as previously computed. Furthermore, if the drop size distribution [z.e., F x)] is normalized by dividing each x by Xmed then, as a rough approximation, all droplet distributions are identical and can be represented as shown in Table 13.4.1 and 13.4.2 ... 

Fig. 23. (a) Distribution of drop sizes for mother droplets and satellite droplets (solid lines) produced during the breakup of a filament (average size = 2 x 10 5 m) in a chaotic flow. The total distribution is also shown (dashed line). A log-normal distribution of stretching with a mean stretch of 10 4 was used, (b) The cumulative distribution of mother droplets and satellite droplets (solid line) approaches a log-normal distribution (dashed line). 

The frozen-drop technique was naturally adopted in measuring molten metal droplet size before any other methods became available. Similarly to the methods for normal liquids, the freeze-up and collection of molten metal droplets may be carried out in many different ways. For example, metal droplets can solidify during flight in gaseous or liquid medium in a spray chamber. 13H51 The solidified particles are subsequently sieved to obtain the size distribution. 

Practically, no emulsion is monodisperse and drops of the inner phase have different sizes. To characterize their size distribution, the following log-normal distribution function has proved to be useful ... 

In the considered case, the basic mechanisms of formation of droplets in the turbulent gas flow are processes of coagulation and breakage of drops. These two processes proceed simultaneously. As a result, the size distribution of the drops is established. Assuming homogeneity and isotropy of the turbulent flow, this distribution looks like a logarithmic normal distribution [1] ... 

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