Empirical drop size distribution

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... 

Thus the volume fraction in drop size distribution is yielded by integrating of the following empirical function ... 

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. 

Drop size distributions are typically described using raie of four methods empirical, maximum entropy formalism (MEF), discrete probability function (DPF) method, or stochastic. The empirical method was most popular before about the year 2000, when drop size distributions were usually determined by fitting spray data to predetermined mathematical functions. Problems arose when extrapolating to regimes outside the range of experimental data. Two analytical approaches were proposed to surmount this, MEF and DPF, as well as one numerical approach, the stochastic breakup model. 

Four methods of modeling drop size distributions, empirical, maximum entropy formalism (MEF), Discrete Probability Function (DPF), and stochastic were reviewed. Key conclusions are ... 

Regardless of which distribution is best, Paloposki s [8] work underscores the key issue when using empirical distributions - no single distribution accurately fits even a large fraction of the available drop size data. This necessitates trial-and-error use of several distributions to determine which one best fits a particular data set. 

Semi empirical equations and numerical approaches are developed to describe the drop size of an atomization at different spraying parameters and material properties. Most of the empirical equations calculate the Sauter mean diameter (SMD) xi 2 representing the mean diameter of an area-based DSD Q2. Compared to a distribution of a certain number n of drops it is the one drop, of which diameter is Xi-2 and having the same surface area multiplied with n like the whole DSD. For most processes like spray drying, where the drying rate is directly proportional to the surface area, a parameter like the SMD is of great importance. 

Pressure drop is a critical factor in the design of adsorption systems, as it normally determines the allowable gas velocity and, therefore, the bed cross-sectional area. Although much work has been done on the subject, no completely satisfactory general correlation has been developed that takes into account the shapes of individual particles, size distribution, void fraction, and aging effects, as well as the more readily characterized gas properties and conditions. It is, therefore, common practice to use experimental and operating data and semi-empirical correlations aimed at specific adsorbent types and applications. Typical data and correlations are presented in subsequent sections covering dehydration with solid desiccants and organic vapor adsorption on activated carbon. 

As for natural rubber/SBR masterbatch blends, carbon black will migrate to the SBR gum phase. At equilibrium, the amount of carbon black in the natural rubber phase will depend on the particle size. For example, the amount of carbon black remaining in the natural rubber phase can drop from 41% for NSSO to only 27% when using N134. Other factors or empirical guidelines affecting the distribution of fillers include ... 

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