Droplet properties empirical correlations

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. 

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. 

Thus, both the mean droplet size and the size distribution may be predicted using these correlations [Eqs. (26), (27), (28), or (29) and Eqs. (30), (31)] for given process parameters and material properties. For a given atomizer design, the standard deviation of droplet size distribution has been found to increase with the melt flow rate, but appears to be less sensitive to the gas flow rated5 Moreover, the variation of the standard deviation is very atomizer- and melt-specific. An empirical correlation which fits with a wide range of atomization data has the following form ... 

This approximate relationship is similar to those for centrifugal atomization of normal liquids in both Direct Droplet and Ligament regimes. However, it is uncertain how accurately the model for K developed for normal liquid atomization could be applied to the estimation of droplet sizes of liquid metals Tombergl486 derived a semi-empirical correlation for rotating disk atomization or REP of liquid metals with the proportionality between the mean droplet size, rotational speed, and electrode or disk diameter similar to the above equation. Tornberg also presented the values of the constants in the correlation for some given operation conditions and material properties. 

Several practical formulae have been developed for estimating the effect on emulsion viscosity of changes in key variables such as temperature, water content, and droplet size distribution, in which adjusting factors for each property are obtained from empirical correlations. An illustration is provided by Rimmer et al. [763]. Such formulae may also contain a term representing changes in emulsion droplet size due to droplet coalescence that occurs with time as the emulsion moves through the pipeline ( ageing ). 

This parameter may either be calculated from the droplet diameter or from empirical correlations. Since the droplet diameter can be of many sizes and is usually unknown, C is estimated from correlations based on experimental data. In one such method by Fair (1961), developed specifically for sieve and bubble cap trays, C is correlated as a function of liquid and vapor flow rates and densities, tray spacing, surface tension, foaming properties, and the ratio of the combined hole area in the tray to its active area. In this correlation, is based on the column cross-sectional area available for vapor flow, A -A, where A is the total tray area (or total inside column cross-sectional area) and A is the downcomer cross-sectional area. The parameter C is given as... 

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