Spray statistics

A two-component phase Doppler interferometer (PDI) was used to determine droplet size, velocity, and number density in spray flames. The data rates were determined according to the procedure discussed in [5]. Statistical properties of the spray at every measurement point were determined from 10,000 validated samples. In regions of the spray where the droplet number density was too small, a sampling time of several minutes was used to determine the spray statistical characteristics. Results were repeatable to within a 5% margin for mean droplet size and velocity. Measurements were carried out with the PDI from the spray centerline to the edge of the spray, in increments of 1.27 mm at an axial position (z) of 10 mm downstream from the nozzle, and increments of 2.54 mm at z = 15 mm, 20, 25, 30, 35, 40, 50, and 60 mm using steam, normal-temperature air, and preheated air as the atomization gas. 

The practice of estabHshing empirical equations has provided useflil information, but also exhibits some deficiencies. Eor example, a single spray parameter, such as may not be the only parameter that characterizes the performance of a spray system. The effect of cross-correlations or interactions between variables has received scant attention. Using the approach of varying one parameter at a time to develop correlations cannot completely reveal the tme physics of compHcated spray phenomena. Hence, methods employing the statistical design of experiments must be utilized to investigate multiple factors simultaneously. 

Diverse techniques have been employed to identify the sources of elements in atmospheric dust (and surface dust) (Table V). Some involve considering trends in concentration and others use various statistical methods. The degree of sophistication and detail obtained from the analyses increases from top left to bottom right of the Table. The sources identified as contributing the elements in rural and urban atmospheric dusts are detailed in Table VI. The principal sources are crustal material, soil, coal and oil combustion emissions, incinerated refuse emissions, motor vehicle emissions, marine spray, cement and concrete weathering, mining and metal working emissions. Many elements occur in more than one source, and they are classified in the... 

More detailed statistical analyses (chemical element balance, principal component analysis and factor analysis) demonstrate that soil contributes >50% to street dust, iron materials, concrete/cement and tire wear contribute 5-7% each, with smaller contributions from salt spray, de-icing salt and motor vehicle emissions (5,93-100). A list is given in Table VII of the main sources of the elements which contribute to street dust. 

Chronic health complications that may develop from eating food that contains traces of harmful spray residues depend upon the amount present and the extent to which daily or recurrent ingestion of the contaminated food continues. Not all foods included in the daily diet carry spray residue. Based upon statistics obtained from The Western Canner and Packer and the U. S. Department of Agriculture (8, 4 approximate percentages of various foods eaten per person in the United States are given in Table II. 

Some other distribution functions have also been derived from analyses of experimental data,1429114301 or on the basis of probability theory J431] Hiroyasu and Kadota 3l l reported a more generalized form of droplet size distribution, i.e., /-scpta/e distribution. It was shown that the -square distribution fits the available spray data very well. Moreover, the -square distribution has many advantages for the representation of droplet size distribution due to the fact that it is commonly used in statistical evaluations. 

Detailed modeling study of practical sprays has a fairly short history due to the complexity of the physical processes involved. As reviewed by O Rourke and Amsden, 3l() two primary approaches have been developed and applied to modeling of physical phenomena in sprays (a) spray equation approach and (b) stochastic particle approach. The first step toward modeling sprays was taken when a statistical formulation was proposed for spray analysis. 541 Even with this simplification, however, the mathematical problem was formidable and could be analyzed only when very restrictive assumptions were made. This is because the statistical formulation required the solution of the spray equation determining the evolution of the probability distribution function of droplet locations, sizes, velocities, and temperatures. The spray equation resembles the Boltzmann equation of gas dynamics[542] but has more independent variables and more complex terms on its right-hand side representing the effects of nucleations, collisions, and breakups of droplets. 

D5. Dodd, E. E., The statistics of liquid spray and dust electrification by the Hopper and Laby method, J. Appl. Phys. 24, 73 (1953). 

For the control of this disease Bordeaux mixture in combination with better cultural practices has been recommended. Garces (17) recommended similar treatment, but when the pods are still young. Although only preliminary trials have been made on the chemical control of Monilia pod rot in Colombia, initial reports indicated that substantial control was being obtained with fungicidal sprays, but when the results were analyzed statistically they were not significant (18). 

Liquid crystals are mainly used for decorative purposes in cosmetics. Cholesteric liquid crystals are particularly suitable because of their iridescent color effects, and find applications in nail varnish, eye shadow, and lipsticks. The structure of these thermotropic liquid crystals changes as a result of body temperature, resulting in the desired color effect. In recent times, such thermotropic cholesteric liquid crystals have been included in body care cosmetics, where they are dispersed in a hydrogel. Depending whether this dispersion requires stirring or a special spraying process, the iridescent liquid crystalline particles are distributed statistically in the gel (Estee Lau-... 

Fig. 25.4 Epithelialisation rate achieved by in vitro cultured autologous sprayed keratinocytes, when applied over granulating full-thickness wound or Permacol M paste on days 0, 3, and 6 and measured on days 14, 17 and 21. Keratinocytes applied over Permacol paste not only survived, but showed a steady increase in the extent of epithelialisation, whereas epithelialisation remained extremely low in the wounds where cells were sprayed directly onto the wound bed. Error bars represent standard deviation, ANOVA (Tukey Test), statistical significance atp<0.0S...

Mortalities observed in tests of a series of oil dosages against adult female California red scale or eggs of the citrus red mite indicated a positive relation between increased dosage and increased kill. The fit of the points to the line was much better for oil dosages expressed as deposit than for those expressed as spray concentration. However, the variance observed indicated that statistical procedures would be required to arrive at the best fit for a line through the observed points. The method of probit analysis chosen was that proposed by Bliss (2) and modified by Finney (11) for data adjusted for mortality in the controls. 

The same research group evaluated neem oil in the field [54]. They sprayed a 5% solution of the oil on infested honey bee colonies, killing about 90% Varroa mites but obtaining only a slight but not statistically significant decrease in tracheal mite infestation levels. Unfortunately this treatment caused 50% queen loss and the treated colonies showed one-third as many adult bees and one-sixth as much brood as untreated... 

The obvious question arises as to how much influence two droplets in a spray may have upon one another as regards vaporization. Directly, on a statistical approach, they should not have much. For reasonable fuel-air ratios and reasonable air temperatures, complete vaporization is far short of saturation of the air. In addition, for equal droplet spacing, the droplets must be rather far apart from one another. For example, kerosine droplets of uniform size and uniform dispersion in a stoichiometric quantity of room temperature air would have center-to-center spacing of more than 17 diameters. 

In any spray of droplets there is a statistical distribution of sizes dependent upon the conditions of atomization. Some particular types of fuel injectors can create nearly uniform sizes, but generally a fairly wide range of droplet diameters results. According to Equations 2, 3, and 4, individual droplets of a fuel spray will complete vaporization over a range of elapsed times. Consequently analysis becomes complicated (85). 

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. 

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