Sauter mean diameter droplet size

Thep and q denote the integral exponents of D in the respective summations, and thereby expHcitiy define the diameter that is being used. and are the number and representative diameter of sampled drops in each size class i For example, the arithmetic mean diameter, is a simple average based on the diameters of all the individual droplets in the spray sample. The volume mean diameter, D q, is the diameter of a droplet whose volume, if multiphed by the total number of droplets, equals the total volume of the sample. The Sauter mean diameter, is the diameter of a droplet whose ratio of volume-to-surface area is equal to that of the entire sample. This diameter is frequendy used because it permits quick estimation of the total Hquid surface area available for a particular industrial process or combustion system. Typical values of pressure swid atomizers range from 50 to 100 p.m. 

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

In order to estimate the specific surface area of the dispersed organic droplets, the mean droplet size (Sauter diameter 32) has to be determined, which can be calculated according to the Okufi equation (Eq. 5) ... 

The observed flame features indicated that changing the atomization gas (normal or preheated air) to steam has a dramatic effect on the entire spray characteristics, including the near-nozzle exit region. Results were obtained for the droplet Sauter mean diameter (D32), number density, and velocity as a function of the radial position (from the burner centerline) with steam as the atomization fluid, under burning conditions, and are shown in Figs. 16.3 and 16.4, respectively, at axial positions of z = 10 mm, 20, 30, 40, 50, and 60 mm downstream of the nozzle exit. Results are also included for preheated and normal air at z = 10 and 50 mm to determine the effect of enthalpy associated with the preheated air on fuel atomization in near and far regions of the nozzle exit. Smaller droplet sizes were obtained with steam than with both air cases, near to the nozzle exit at all radial positions see Fig. 16.3. Droplet mean size with steam at z = 10 mm on the central axis of the spray was found to be about 58 /xm as compared to 81 pm with preheated air and 96 pm with normal unheated air. Near the spray boundary the mean droplet sizes were 42, 53, and 73 pm for steam, preheated air, and normal air, respectively. The enthalpy associated with preheated air, therefore, provides smaller droplet sizes as compared to the normal (unheated) air case near the nozzle exit. Smallest droplet mean size (with steam) is attributed to decreased viscosity of the fuel and increased viscosity of the gas. 

In all these tasks, the achievable (as narrow as possible) droplet size distribution represents the most important target quantity. It is often described merely by the mean droplet size, the so-called Sauter mean diameter J32 (Ref. 19), which is defined as the sum of all droplet volumes divided by their surfaces. Mechanisms of droplet formation are ... 

When two liquids are immiscible, the design parameters include droplet size distribution of the disperse phase, coalescence rate, power consumption for complete dispersion, and the mass-transfer coefficient at the liquid-liquid interface. The Sauter mean diameter, dsy, of the dispersed phase depends on the Reynolds, Froudes and Weber numbers, the ratios of density and viscosity of the dispersed and continuous phases, and the volume fraction of the dispersed phase. The most important parameters are the Weber number and the volume fraction of the dispersed phase. Specifically, dsy oc We 06(l + hip ), where b is a constant that depends on the stirrer and vessel geometry and the physical properties of the system. Both dsy and the interfacial area aL remain unaltered, if the same power per unit volume (P/V) is used in the scale-up. 

The data indicated that droplet-size changes are primarily influenced by injection pressure and orifice size while secondary changes can be attributed to fluid properties, orifice shape, and the nozzle s internal length diameter ratio. This last point was not observed by Dombrowski and Wolfsohn (8) for more conventional swirl spray nozzles. Nevertheless, they present a useful correlation between Sauter mean diameter and operating conditions. 

In this section, we discuss the effects of solids addition on the rheology of oil-in-water emulsions, in particular, the effects of solids size (size distribution) and shape (spherical versus irregular). Because the type of the oil used to form an emulsion is important in determining the viscosity of the oil-in-water emulsion, the rheology of the emulsion-solids mixtures is also influenced by the type of oil. Thus, two distinct emulsion systems with added solids will be discussed (1) synthetic (Bayol-35) oil-in-water emulsions 21, 57) and (2) bitumen-in-water emulsions (58). The synthetic oil has a viscosity of 2.4 mPa s, whereas the bitumen has a viscosity of 306,000 mPa s at 25 C. The Sauter mean diameter of the oil droplets is 10 xm for synthetic oil, and 6 xm for bitumen-in-water emulsions. The synthetic OAV emulsions are fairly shear-thinning, whereas the bitumen OAV emulsions are fairly Newtonian. 

The Sauter mean diameter droplet size (D32) is plotted versus the air-to-Iiquid (ALR) mass ratio for a range of solution viscosities from water (0.001 kg/m/sec) up to 0.(X)2 kg/m/sec. The more viscous solutions produce both an elevated droplet size compared to water as well as a reduced sensitivity to atomization energy or ALR, with the highest viscosity solutions showing little improvement in droplet size above ALR =20. 

In the chemical industry (on the mega- as well as the micro-scale) fine emulsions have many useful applications in, e.g., extraction processes or phase transfer catalysis. Additionally, they are of interest for the pharmaceutical and cosmetic industry for the preparation of creams and ointments. Micromixers based on the principle of multilamination have been found to be particularly suitable for the generation of emulsions with narrow size distributions [33]. Haverkamp et al. showed the use of micromixers for the production of fine emulsions with well-defined droplet diameters for dermal applications [38]. Bayer et al. [39] reported on a study of silicon oil and water emulsion in micromixers and compared the results with those obtained in a stirred tank. They found similar droplet size distributions for both systems. However, the specific energy required to achieve a certain Sauter mean diameter was 3-1 Ox larger for the macrotool at diameters exceeding 100 pm. In addition, the micromixer was able to produce distributions with a mean as low as 3 pm, whereas the turbine stirrer ended up with around 30 pm. Based on energy considerations, the intensification factor for the microstirrer appears to be 3-10. 

Sauter mean diameter (D32) is reported frequently for fuel injectors because it is representative of the droplet size that has the same volume/surface area ratio as the whole spray. It is given by ... 

The effect of size distribution in ELM systems has been studied. Tereraoto et al. (98) studied the effect of globule size distribution on copper extraction. Their results indicated that the Sauter mean diameter was sufficient to characterize the membrane size and it was not necessary to use the size distribution. Hanna and Larson (99) studied the influence of ELM preparation on the Internal droplet size distribution. They demonstrated the Internal phase surface area can affect extraction rate with a copper extraction system. 

Note d 2 the Sauter mean diameter defined as the arithmetic mean of several measurements of the Sauter diameter SD (SD = 6 V/A with V the volume and A the surface area of the particle), d, the volume median diameter, which refers to the midpoint droplet size (mean), where half of the volume of spray is in droplets smaller and half of the volume is in droplets larger than the mean, p, p, and a, respectively the density, the viscosity, and the surface tension of liquid, D, the diameter of the disk, Q, the flow rate, and o> the angular speed of the disk. 

The mean size of droplet represents a single value that characterizes the whole spray distribution. This value, together with the size distribution, defines the spray characteristics. Many papers have appeared on the subject of drop size prediction. The so-called Sauter mean diameter seems to be the most suitable mean value to characterize the droplet cloud together with the size distribution. This is defined as the ratio of the total droplet volume to the total droplet surface [23] that is. 

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