Droplet lifetime

The effects of microexplosions of droplets of two different initial diameters (but same core size) are shown in Fig. 7.9. The flow fields are significantly different in the two cases. In the first case (Fig. 7.9a), there is some local effect on the flow field but the overall flow is quite similar to the nonmicroex-ploding case. When the initial droplet diameter is 50 /xm, the droplet lifetimes... 

Kobayasi (44) and Nishiwaki (62) noted the existence of both a preheat period, during which no change in diameter of the droplet was noted, and a vaporization period. Hottel, Williams, and Simpson (38) reported that, whereas the preheat time decreases with the furnace temperature, the vaporization rate remains unchanged. El Wakil and coworkers (16) noted a high degree of circulation in the drops during the preheat period and found that the droplets lifetime increased with the number of carbon atoms and decreased with air temperature. 

Figure 4 shows that after the initial 10-20% of the droplet lifetime, the droplet surface area appears to regress quite linearly with time. Hence if one is only interested in approximate estimates for the droplet size, then overall quasi-steadiness can be considered to be attained in about 20% of the droplet lifetime. However, if detailed droplet temperature variation is needed, then one would consider that imsteadiness prevails throughout the droplet lifetime. 

Typical droplet lifetimes and hence particle formation rates can occur over a range of time.scales from milliseconds to minutes. Particle formation time is controlled by both the initial liquid droplet size and evaporation rate. The latter is dictated by the heat transfer to the droplet, mass transfer of the vapor away from the droplet into the process gas stream and the specific formulation components. The rate of particle formation is a key parameter which dictates the size of the drying chamber, and hence the scale of equipment required to produce a desired particle size at the target production rate. 

The second stage occurs when the liquid droplet has established equilibrium evaporation of the carrier solvent into the surrounding gas stream. This constant rate evaporation process is commonly modeled u.sing the d law methodology, which states that droplet size decreases linearly with respect to the square of the droplet diameter (35,36). The results of these droplet lifetime calculations applied to water droplets with initial diameters of 5-50 pm and surrounding gas temperatures from 40 to 60 C are shown if Figure 10. These calculations assume 0% relative humidity in the gas stream... 

FIGURE 10 Calculated water droplet lifetime using d law, relative humidity =0%. Source From Ref. 36. 

This linear shrinkage law differs this case from the d o law represented by Eq. (40). Equation (63) shows that the droplet lifetime is equal to... 

In the case of gravity-driven coalescence of a droplet with its homophase, the driving force is given by Equation 5.269 and the mean drop radius is R = 2R. Then, from Equations 5.269 and 5.273 we can deduce the droplet lifetime in the so-called Taylor regime, corresponding to nonde-formed droplets (R = 0) ... 

Bt = Cp(Tg,p — 7 )/(A/tv), where FFg.p is the fuel vapor mass fraction interpolated to the droplet location. For 7 > Jb, By is set equal to Bj. The Clausius-Qapeyron equilibrium vapor-pressure relationship is used to compute the fuel mass fraction at the droplet surface. In addition, convective correction actors (based on Ranz and Marshall correlations) are applied to obtain spray evaporation rates at high Reynolds numbers. Liquid properties are evaluated using the one third rule for reference mass fractions [28]. Advanced models for droplet evaporation accounting for nonequilibrium effects can also be incorporated in the above framework by altering the timescales associated with the droplet lifetime and the convective heating. 

Figure 4.4 Rapid mixing using theta capillaries [98]. Reprinted with permission from Mortensen, D.N., Williams, E.R. (2014) Theta-Glass Capillaries in Electrospray Ionization Rapid Mixing and Short Droplet Lifetimes. Anal. Chem. 86 9315 9321. Copyright (2014) American Chemical Society...

In positive-mode experiments, Mirza and Chait showed that the charge-state distribution was influenced by the type of anion (conjugate base) that was used to acidify the solution. These authors considered that the anion remained associated with the multiply protonated protein in solution and that charge removal could occur via dissociation of the neutral acid (anion plus proton in tow) in the later moments of the droplet lifetime. Shortly afterwards, LeBlanc et al. proposed that neutral nitrogen bases that were noncovalently attached to gramicidin S peptide molecules also could serve to remove charge as the complex underwent collisions in the gas phase. These conclusions were reiterated by Hiraoka et al. in their work with amino acids. 

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