Representative droplet diameter

To characterize a droplet size distribution, at least two parameters are typically necessary, i.e., a representative droplet diameter, (for example, mean droplet size) and a measure of droplet size range (for example, standard deviation or q). Many representative droplet diameters have been used in specifying distribution functions. The definitions of these diameters and the relevant relationships are summarized in Table 4.2. These relationships are derived on the basis of the Rosin-Rammler distribution function (Eq. 14), and the diameters are uniquely related to each other via the distribution parameter q in the Rosin-Rammler distribution function. Lefebvre 1 calculated the values of these diameters for q ranging from 1.2 to 4.0. The calculated results showed that Dpeak is always larger than SMD, and SMD is between 80% and 84% of Dpeak for many droplet generation processes for which 2left-hand side of Dpeak. The ratio MMD/SMD is... 

Figure 5.12 represents the evolution in time of the surface-averaged droplet diameter for different amounts of solid particles. The kinetic curves confirm the qualitative evolution previously described. The droplet growth is initially rapid but the coalescence rate progressively decreases until the average diameter reaches an asymptotic value. Figure 5.13 shows the change in the droplet size distribution... 

They are emulsions with droplet diameters in the range 0.01 to 0.1 pm. It is formed when the oil-water interfacial tension approaches zero. Micro emulsions represents an intermediate state between micelles and ordinary emulsions. They are usually of low viscosity. 

As discharge velocity at the nozzle outlet increases, the following states appear in succession dripping, laminar jet breakup, wave disintegration, and atomization. These states of fiow are described in a pi space Re, Fr, Wep, whereby Wep = pv dp/a represents the Weber number formed by the droplet diameter, dp. To eliminate the fiow velocity, v, these numbers are combined to give... 

For these reasons the selection of an appropriate oil is limited to some extent by the need to use metabolizable long-chain triglycerides. These are represented by natural oils such as olive or soy oil or the short-chain triglycerides obtained from coconut oils. The chain length and degree of unsaturation of the oil, as well as the molecular weight, influence the droplet diameter and polarity once formed. 

Whereas few actual values of n for sprays from various fuel injectors are reported, it is usually possible to obtain a fairly reliable estimate of x. This is so because x is uniquely related to various mean droplet diameters solely in terms of n, and data for Sauter mean diameter are rather frequently reported. Sauter mean diameter (SMD) is that diameter representative of the surface area per unit volume which is characteristic of the actual spray. 

ATOMIZED PROPELLANTS. For those combustors in which the propellants persist in droplet form for a large percentage of the length of the chamber, it is apparent that the available propellant must be represented as a heterogeneous mass of liquid and vapor in which the vapor concentration will vary with distance from the injector. As Figure 4 shows that the vapor concentration can be determined from droplet evaporation considerations, the equation for available propellant W can be written in terms of the square of the relative droplet diameter s = (D/D0)2 ... 

A practical approach is to use the venturi tube (see Fig. 10.13) with a swarm of representative droplets of a certain diameter to estimate an effective mass transfer coefficient, including diffusional and reactive resistances. The value obtained would be... 

From the above outline, the mass-transport problem is seen to consist of coupled boundary value problems (in gas and aqueous phase) with an interfacial boundary condition. Cloud droplets are sufficiently sparse (typical separation is of order 100 drop radii) that drops may be treated as independent. For cloud droplets (diameter 5 ym to 40 pm) both gas- and aqueous-phase mass-transport are dominated by molecular diffusion. The flux across the interface is given by the molecular collision rate times an accommodation coefficient (a 1) that represents the fraction of collisions leading to transfer of material across the interface. Magnitudes of mass-accommodation coefficients are not well known generally and this holds especially in the case of solute gases upon aqueous solutions. For this reason a is treated as an adjustable parameter, and we examine the values of a for which interfacial mass-transport limitation is significant. Values of a in the range 10 6 to 1 have been assumed in recent studies (e.g.,... 

Figure 2. Change in droplet diameter of multiple emulsions as a function of the concentration of secondary emulsifier (il) and of the calculated weighted or apparent HLB of the surfactant system. Hatched regions represent boundaries for inversion. Reprinted with permission from Ref. 28. Copyright 1979, Academic Press.

The steeply rising portion of the Kohler curves represents a region where solute effects dominate. As the droplet diameter increases, the relative importance of the Kelvin effect... 

The steeply rising portion of the Kohler curves represents a region where solute effects dominate. As the droplet diameter increases, the relative importance of the Kelvin effect over the solute effect increases, and finally beyond the critical diameter the domination of the Kelvin effect is evident. In this range all Kohler curves approach the Kelvin equation, represented by the equilibrium of a pure water droplet. Physically, the solute concentration is so small in this range (recall that each Kohler curve refers to fixed solute amount) that the droplet becomes similar to pure water. 

The Rosin-Rammler distribution is used to represent sprays from nozzles. It is anpirical and relates the volume percentage oversize Vq to droplet diameter D. The mathematical form is as follows [23] ... 

A 3D liquid spraying is modeled by introducing 20 spatial droplet streams into the computational domain, as shown in Figure 10.5. In turn, each droplet stream is represented by 10 injections of different droplet diameters minimum and maximum diameters are 10.0 and 138.0 pm, whereas the intermediate droplet sizes are calculated by applying Rosin-Rammler distribution function with 70.5 pm of droplet average size as given by Equation 10.37. 

Droplet Dispensing, Fig. 7 Different breakup regimes represented by the relationship of the velocity v versus the droplet diameter D for water as ejected liquid... 

The equivalent electrical circuit, rearranged under the influence of an apphed physical field, is considered as a parallel resonant circuit coupled to another circuit such as an antenna output circuit Thus, in Figure 15.4c, Wj, Cd, La, and Ra correspond to the circuit elements each Wd represents active emitter-coupled oscillator and Cd, Ld, and Rd, represent passive capacitive, inductive, and resistive elements respectively. The subscript d is related to the particular droplet diameter, that is, the droplet under consideration. Now, again the initial electromagnetic oscillation is represented by... 

---