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Charge Limits on Droplets during Evaporation Kuo-Yen Li, Haohua Tu, and Asit K. Ray* Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky 40506-0045 Received August 12, 2004. In Final Form: February 15, 2005 We have examined charge stability limits of single evaporating microdroplets that were suspended in an electrodynamic balance. A high precision light scattering technique based on optical resonances was used to determine the size and the size change of a droplet at a charge instability induced breakup. The charge level and the charge loss at the breakup were obtained from the dc voltages required to balance the droplet prior to and following the breakup. The results on droplets of diethyl phthalate (DEP), diethylene glycol (DEG), triethylene glycol (TEG), and hexadecane show that breakups due to the charge instability occur at the Rayleigh charge limit. The observed charge losses during breakups range from about 15.3% for hexadecane droplets to about 41.1% for TEG droplets. Hexadecane droplets lose about 1.5% of their mass, while DEP droplets, about 2.3%. Within the detectable limit of 0.03%, no mass losses were observed during breakups of DEG and TEG droplets. The observation of extremely low mass losses that accompany high charge losses from DEG and TEG droplets suggests that the process of breakups of DEG and TEG droplets is distinct from that of DEP and hexadecane droplets. An analysis of the results indicates that breakups of DEP and hexadecane droplets result in the formation of a few large progeny droplets, while TEG and DEG droplets produce thousands of fine progeny droplets.
Introduction Various atmospheric and industrial processes involve the evaporation of charged droplets. Examples include electrified cloud droplets, combustion of fuel droplets, spray painting, crop spraying, and inkjet printing. The surface charge density of a droplet increases during evaporation. When the charge density reaches or surpasses a threshold at which the repulsive electrostatic force equals or exceeds the cohesive force due to the surface tension, the droplet becomes unstable. The instability causes breakup of the droplet, leading to the formation of progeny droplets. This phenomenon reduces the droplet charge below the instability limit and is referred to variously as the Coulombic fission, droplet explosion, and Rayleigh discharge. In recent years, the phenomenon of droplet breakups has received careful attention because of the ability of the electrospray ionization to produce macromolecular ions. In electrospray ionization, the evaporation of progeny droplets produced by breakups of solution droplets causes further instabilities, leading to the formation of smaller and smaller droplets that ultimately produce gas phase ions by two possible mechanisms.1,2 In this study, we focus on the stability of microdroplets, and there is a general agreement that the charge instability in such a droplet causes breakups that lead to the formation of multiple progeny droplets.3-5 Rayleigh6 provided the earliest analysis on the stability of a charged droplet. His analysis, valid for a macroscopic incompressible droplet of an inviscid and perfectly con* To whom correspondence should be addressed. E-mail:
[email protected]. (1) Dole, M.; Mack, L. L.; Hines, R. L. J. Chem. Phys. 1968, 49, 22402249. (2) Iribarne, J. V.; Thomson, B. A. J. Chem. Phys. 1976, 64, 22872294. (3) Znamenskiy, V.; Marginean, I.; Vertes, A. J. Phys. Chem. A 2003, 107, 7406-7412. (4) Duft, D.; Achtzehn, T.; Muller, R.; Huber, B. A.; Leisner, T. Nature 2003, 421, 128-128. (5) Feng, X.; Bogan, M. J.; Agnes, G. R. Anal. Chem. 2001, 73, 44994507. (6) Rayleigh, L. Philos. Mag. 1882, 14, 184-186.
ducting liquid, shows that a droplet becomes unstable when the charge on the droplet reaches a critical value that is given by
qR ) 8πx0γa3
(1)
where 0 is the permittivity constant, γ is the surface tension of the droplet, and a is the droplet radius. At or above this critical value (i.e., q g qR), the disturbances due to shape oscillations grow, leading to the breakup of the droplet. The Rayleigh charge limit, as expressed by eq 1, has been corroborated by other theoretical analyses7,8 and also found to be applicable to dielectric droplets.9 It should be noted that Taylor7 analyzed the stress on a charged spheriod or an uncharged spheriod in a uniform external electric field parallel to the major axis, and the result of the analysis correctly yields the Rayleigh charge limit for a sphere. Furthermore, the presence of an external electric field lowers the critical charge limit, but the external electric field has a negligible effect on the charge limit when the external electric field strength is less than 5% of the field strength due to charge on the droplet surface at the Rayleigh limit. Several experimental studies have examined the stability limits of charge droplets. Early experiments10,11 conducted on single droplets in a Millikan type apparatus tend to confirm that droplet explosions occur near the Rayleigh charge limit. More recent studies using electrospray droplets purport to show that heptane droplet explosions occur at charge levels between 70 and 80% of the Rayleigh limit, with larger droplets exploding at higher charge levels,12 while n-octane and p-xylene droplets explode at about 90%, water, acetonitrile, and n-heptane (7) Taylor, G. I. Proc. R. Soc. London 1964, 280, 383-397. (8) Tang, H. H. K.; Wong, C. Y. J. Phys. A: Math. Nucl. Gen. 1974, 7, 1038-1050. (9) Carroll, C. E. J. Phys. A: Math. Gen. 1978, 11, 225-229. (10) Doyle, A.; Moffett, D. R.; Vonnegut, B. J. Colloid Interface Sci. 1964, 19, 136-144. (11) Abbas, M. A.; Latham, J. J. Fluid Mech. 1967, 40, 663-670. (12) Gomez, A.; Tang, K. Phys. Fluids 1994, 6, 404-414.
10.1021/la047973n CCC: $30.25 © 2005 American Chemical Society Published on Web 03/19/2005
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droplets explode at about 100%, and methanol droplets explode at about 120% of their respective Rayleigh charge limits.13,14 A number of studies on charge stability have been carried out on single evaporating droplets suspended in electrodynamic balances. Early studies15-18 using aerodynamic droplet sizing techniques validate the Rayleigh limit within the precision of the measurements. Richardson et al.19 and Taflin et al.20 were the first to apply a sizing technique based on resonances observed in light scattering to probe breakups of electrodynamically suspended droplets. Richardson et al.19 have observed breakups of dioctyl phthalate droplets nearly at the Rayleigh limit but reported lower limits (i.e., about 80%) for sulfuric acid droplets. The results of Taflin et al.20 on various organic compounds indicate droplet breakups in the range 72-86% of the Rayleigh limit. Similar results have also been reported for 1-dodecanol and water droplets containing surfactant.21 In a more recent study, Widmann et al.22 have claimed that droplet breakups occur far below the Rayleigh limit, as low as 3% of the charge limit. Recently, Duft et al.23 and Manil et al.24 have utilized the amplitude and phase of quadrupole shape oscillations of a charge droplet suspended in an electrodynamic balance to deduce the charge stability. This method does not require the knowledge of the charge and surface tension of the droplet but independently determines the value of X ) q2/(64π20γa3) at the droplet breakup from the amplitude and the phase shift of the quadrupole shape oscillations. Their results show that ethylene glycol droplets disintegrate at values close to X ) 1, thus confirming the Rayleigh charge limit. For the same droplets, they also found that the charge limits calculated from the measured droplet size and charge and the literature surface tension value were about 70% of their respective Rayleigh limits. They attributed this disparity between the charge limit values obtained from the two methods to the lowering of the droplet surface tension. During the process of attaining stability from an unstable state, a droplet loses a fraction of its charge and mass by spewing out a number of charged progeny droplets. Rayleigh’s analysis predicts the onset of instability but does not provide any information on the breakup process. Currently, we have only fragmentary understanding of the charge and mass loss phenomena during the breakup process. Experimental results on charge and mass losses differ considerably. Observed mass losses range from less than 0.1% to 30%, while charge loss data vary from 10 to over 80%.5,10,11,13-15,17,19-22 Richardson et al.19 have recorded the lowest mass loss, less than 0.1%,
for breakups of sulfuric acid droplets. Their exceptional observation of extremely low loss of mass accompanied by high of loss charge (i.e., about 50% charge) for sulfuric acid droplets has not been replicated by any other investigator. Richardson et al.19 have posited that the charge loss in a sulfuric acid droplet occurs via the direct emission of sulfate ions from the sharp tip of a Taylor cone.7 In a counterview, de la Mora25 has postulated that droplets of low conductivity liquids fragment into a few large droplets through “rough fission” modes, while breakups of droplets of high conductivity liquids proceed under “fine fission” modes with the formation of Taylor cones. In the latter case, a large number of fine droplets forms with significantly lower mass loss compared to that for low conductivity droplets. The prediction of de la Mora’s model25 for breakups of droplets of high conductivity liquids qualitatively agrees with the sulfuric acid data of Richardson et al.19 In addition, two recent studies tend to support the existence of two distinct modes for the formation of progeny droplets. The results on methanol droplets5 show that on average 13 large progeny droplets form, while ethylene glycol droplets4 produce more than 100 progeny droplets. Conflicting conclusions can be drawn from prior experimental studies on the charge limit at which a droplet breakup occurs. The experimental data on charge and mass losses during breakups also show wide variability. Even though no established model currently exists for the prediction of charge and mass losses, the experimental data and the model of de la Mora25 for conducting droplets suggest that the fractional mass and charge losses are related to the physical properties such as the dielectric constant and the electrical conductivity. The purpose of this study is to critically examine the droplet breakup phenomenon with an objective to understand whether the physical properties, such as the dielectric constant and the conductivity, of a droplet have any effect on its charge stability limit and on the amounts of charge and mass losses at a breakup. The experiments for this study were conducted on evaporating single droplets that were suspended in an electrodynamic balance. A light scattering technique26 based on resonances observed in scattering intensity versus time spectra was used to obtain absolute droplet size and size change at each explosion. The technique permits determination of the size and size change with relative errors of 1 part in 104. In this paper, we present results on a number of compounds with wide-ranging electrical properties.
(13) Smith, J. N.; Flagan, R. C.; Beauchamp, J. L. J. Phys. Chem. A 2002, 106, 9957-9967. (14) Grimm, R. L.; Beauchamp, J. L. Anal. Chem. 2002, 74, 62916297. (15) Ataman, S.; Hanson, D. N. Ind. Eng. Chem. Fundam. 1969, 8, 833-836. (16) Berg, T. G. O.; Trainor, R. J.; Vaughan, U. J. Atmos. Sci. 1970, 27, 1173-1181. (17) Schweiger, J. W.; Hanson, D. N. J. Colloid Interface Sci. 1971, 35, 417-423. (18) Roulleau, M.; Desbois, M. J. Atmos. Sci. 1972, 29, 565-569. (19) Richardson, C. B.; Pigg, A. L.; Hightower, R. L. Proc. R. Soc. London, Ser. A 1989, 422, 319-328. (20) Taflin, D. C.; Ward, T. L.; Davis, E. J. Langmuir 1989, 5, 376384. (21) Davis, E. J.; Bridges, M. A. J. Aerosol Sci. 1994, 25, 1179-1199. (22) Widmann, J. F.; Aardahl, C. L.; Davis, E. J. Aerosol Sci. Technol. 1997, 27, 636-646. (23) Duft, D.; Lebius, H.; Huber, B. A. Phys. Rev. Lett. 2002, 89, 845031-845034. (24) Manil, B.; Ntamack, G. E.; Lebius, H.; Huber, B. A.; Duft, D.; Leisner, T.; Chandezon, F.; Guet, C. Nucl. Instrum. Methods Phys. Res., Sect. B 2003, 205, 684-689.
Experiments were conducted on single charged droplets using the experimental setup shown in Figure 1. Tu26,27 has furnished a description of the setup in detail; here, we present a summary. An electrodynamic balance is mounted inside a temperaturecontrolled thermal diffusion cloud chamber. A charged droplet is suspended at the center of the balance through an appropriate dc voltage that produces an electrostatic counterweight for the gravitational force. A He-Ne laser beam (i.e., λ ) 632.8 nm) illuminates the suspended droplet, and two photomultiplier tubes (PMTs) in the planes parallel and perpendicular to the plane of incident light polarization measure the intensities of light scattered by the droplet at scattering angles of about 90°. The PMT in the perpendicular plane detects transverse electric (TE) mode scattering.
Experimental Section
(25) de la Mora, J. F. J. Colloid Interface Sci. 1996, 178, 209-218. (26) Tu, H.; Ray, A. K. Appl. Opt. 2001, 40, 2522-2534. (27) Tu, H. H. Application of Light Scattering in Studies of Transport, Thermodynamics, Light Absorption, and Electrical Properties of Single Droplets. Thesis, University of Kentucky, 2000.
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Figure 1. Experimental system for the suspension of a single droplet in an electrodynamic balance inside a diffusion cloud chamber. Table 1. Relevant Properties of the Compounds Studied physical properties
compound diethyl phthalate triethylene glycol diethylene glycol hexadecane
surface electrical tension, density, dielectric conductivity, 3 3 a γ × 10 (N/m) F (kg/m ) constant, K (µmho/m) 36.1 45.1 44.8 27.0
1118 1125 1118 773
7.34 23.69 31.69 2.05
