CoaxialjetsgeneratedfromelectriedTaylorcones. Scalinglaws · 2007-04-23 · 536 J.M.Lopez-Herreraetal./AerosolScience34(2003)535–552& 1. Introduction Theproductionofveryhighqualityspraysofstructureddropletsorparticlessuchthateachparticle

Aerosol Science 34 (2003) 535–552www.elsevier.com/locate/jaerosci

Coaxial jets generated from electri ed Taylor cones.Scaling laws

J.M. L&opez-Herreraa, A. Barreroa;b;∗, A. L&opezc;1, I.G. Loscertalesb;d,M. M&arqueze; f ;g

aEscuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092 Sevilla, SpainbYFLOW S.L., Camilo Jos&e Cela 6, 41018 Sevilla, Spain

cEcole National Sup&erieure de M&ecanique et dA&erotechnique. T&el&eport 2-Futuroscope, 86960 Chasseneuil, FrancedEscuela T&ecnica Superior de Ingenieros Industriales, Universidad de M&alaga, 41013 M&alaga, Spain

eLos Alamos National Laboratory, Chemistry Division, Los Alamos, NM 87545, USAfComputational Chemistry Group, Physical and Chemical Properties Division, National Institute of Standards

and Technology, Gaithersburg, MD 20899, USAgKraft Foods R&D, The Nanotechnology Laboratory, Glenview, IL 60025, USA

Received 7 October 2002; accepted 13 January 2003

Abstract

An experimental investigation on the electri ed co-axial jets of two immiscible liquids issuing from astructured Taylor cone (Science 295 (5560) (2002) 1695) has been carried out. The structure of these almostconical electri ed menisci consists of an outer meniscus surrounding an inner one. The liquid threads whichissue from the vertex of each one of the menisci give rise to a two-concentric layered jet whose eventualbreakup results in an aerosol of relatively monodisperse compound droplets with the outer liquid encapsulatingthe inner one. The e;ect of the <ow rates of both liquids on the current transported by these coaxial jets andon the size of the compound droplets has been investigated. Several couples of liquids have been used toexplore the in<uence on the spraying process of the properties of the liquids: i.e. the electrical conductivityK , dielectric constant �, interfacial tension of the liquid couple �, viscosity �, etc. We have found that themeasurements of the current emitted through the coaxial jet when they are made dimensionless t satisfactorilythe current scaling law of regular electrosprays. Data of the mean diameter of the compound droplets havebeen obtained using a non-intrusive laser system. As expected the breakup process and therefore the dropletsize are strongly dependent on the liquid viscosities and on the ratio of the liquid <ow rates.? 2003 Elsevier Science Ltd. All rights reserved.

∗ Corresponding author. Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n,Sevilla 41092, Spain. Tel.: +34-95-448-7224; fax: +34-95-448-7224.

E-mail address: [email protected] (A. Barrero).1 Undergraduate student on leave under Erasmus program.

0021-8502/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0021-8502(03)00021-1

mailto:[email protected]

536 J.M. L&opez-Herrera et al. / Aerosol Science 34 (2003) 535–552

1. Introduction

The production of very high quality sprays of structured droplets or particles such that each particleis made of a core of a certain substance surrounded by another one, are of particular importancefor encapsulation of food additives (Yoshii et al., 2001; Hardas, Danviriyakul, Foley, Nawar, &Chinachoti, 2000; Lee & Rosenberg, 2000), targeted drug delivery (Mathiowitz et al., 1997; Bartus,Tracy, Emerich, & Zale, 1998; Langer, 2001), and special material processing (Lee, Kim, Jang,Choi, & Jhon, 2001; Burlak, Koshevaya, Sanchez-Mondragon, & Grimalsky, 2001), among othertechnological elds.Although the substance to be encapsulated may be either solid or liquid, the encapsulating agent is

usually a polymer carrying solution or a melted polymer. The polymerization process can be initiatedeither by the action of ultraviolet light in the case of a photopolymer or thermally, or chemically,under the use of appropriate agents. In any case, the key issue is the way to form micro/nano-sizedcapsules with controllable size and adjustable coating thickness from bulk materials.Among several methods described for encapsulation those based on the formation, control and

break up of jets have recently attracted the attention of many researchers and technologists: i.e.induced jet break up (IJB), electrospray (ES), selective withdrawal (SW), and <ow focusing (FF)techniques. In IJB, the break up of a capillary laminar jet is induced by applying an AC electric eld(Sakai, Sadakata, Sato, & Kimura, 1991; Sato, Kato, & Saito, 1996). In the ES technique, a liquidis slowly injected through an electri ed capillary needle. For appropriate values of both the appliedelectric potential and <ow rate, the meniscus at the needle exit develops an almost conical shape(Taylor, 1964). A very thin capillary jet issues from the vertex cone. In the simplest version of SW,Lister (1989) and Cohen, Li, Hougland, Mrksich, and Nagel (2001), the exit of a tube is located ata height H above the interface separating two immiscible <uids. For suLciently low <ow rates ofthe <uid withdrawal Q only the upper <uid is sucked through the tube. A suLcient increase of Q,or decrease of H , gives rise to a thin ligament of the lower liquid surrounded by the outer <uid. Inthe FF technique (Gan&an-Calvo, 1998; Gan&an-Calvo & Barrero, 1999), a liquid is injected througha capillary tube whose exit is located in front of a small hole drilled in a thin plate perpendicular tothe needle. A stream of another <uid surrounding the tube is forced through the hole in such a waythat the meniscus adopts a cusp-like shape by the action of the mechanical stresses. A thin jet issuesfrom the cusp whose diameter, as in the ES case, is independent of the much larger tube diameter.A method to generate electri ed compound jets of immiscible liquids using the ES technique

has been recently reported (Loscertales et al., 2002). Basically, when two immiscible liquids areinjected at appropriate <ow rates through two electri ed capillary needles, one of them inside theother, the menisci of both liquids adopt conical shapes with an outer meniscus surrounding the innerone. A liquid thread is issued from each one of the vertex of the two menisci in such a way thata compound, coaxial jet of two co-<owing liquids is formed downstream, see Fig. 1. This methodhas proved its ability to produce encapsulated particles in the micrometric range as well as in thenanometric one; the diameter of the smallest capsules was 150 nm (Loscertales et al., 2002). Themethod also allows for good control of the size of the coated particles, with narrow size dispersion,and good control over the thickness of the coating.A complete knowledge of the scaling laws of these electri ed coaxial jets generated via EHD as

a function of the <ow rates and the physical properties of the two liquids would be highly desirable;mainly, the current transported by them, the diameters of the inner and outer jets, and the size of

J.M. L&opez-Herrera et al. / Aerosol Science 34 (2003) 535–552 537

Fig. 1. Structured conical menisci. Dyed EG was injected at the rate of QEG = 5 ml=h while the <ow rate of somos wasQSOMOS = 6 ml=h; Applied voltage 6500 V; Needles to plate distance 2:5 cm; Outer needle ID = 1:1 mm, OD = 1:5 mm;Inner needle: OD = 0:9 mm, ID = 0:5 mm.

the droplets resulting from their break up. However, the task of nding the above dependences isundoubtedly extremely complex, much more complex for compound ESs than for simple ESs sincethe number of parameters and unknowns is larger in the former problem than in the later one.Because of its complexity, even the knowledge of simple cone–jet ESs is still incomplete, in

spite of the fact that the equations and boundary conditions that govern its electro-hydrodynamicbehavior are well known. The existence of very disparate scales in the cone–jet problem, a freeinterface whose position must be consistently calculated from the solution of the problem, and thetime-dependent break up of the jet are di;erent aspects of the problem which greatly contribute toits numerical complexity.Competing models on the emitted current and jet diameter in single ESs, based on di;erent

simplifying hypothesis, are found in the literature. They predict the same expression for the emittedcurrent except for a non-dimensional constant which either depends on the dielectric constant of theliquid, Fern&andez de la Mora and Loscertales (1994), Gan&an-Calvo et al. (1997) or it is independentof it, Gan&an-Calvo (1998). Even more unsatisfactory is the prediction of the jet diameter for whichthe existing models give di;erent dependences on the <ow rate and on the physical properties ofthe liquid. Unfortunately, the existing experimental measurements do not suLce to either completelysupport or reject some of these models since, for example, the jet diameter predicted by the di;erentmodels are comparable to the accuracy with which it can be experimentally sized (Gamero-Castano& Hruby, 2002). Therefore, more precise knowledge of the ESs must come from either numericalsimulations or more re ned experimental measurements. A numerical simulation of the transitionzone between the cone and the jet which can throw light on this complex problem has been recentlycarried out by Higuera (2003).We have initiated an experimental investigation with the aim of obtaining some valid information

on the behavior of these compound ESs and the electri ed coaxial jets issued from them. Usingdi;erent couples of liquids, we have obtained some experimental data of the current transported bythese jets and of their diameters to study their dependences on the <ow rates of the liquids and theliquid’s properties: electrical conductivity K , dielectric constant �, surface tension at the interface ofa <uid couple �, viscosity �, etc.


Fig. 2. Experimental setup.

The paper is arranged as follows. The experimental set up is described in Section 2. Section 3contains experimental data useful for introducing the driving liquid concept and to investigate thedependences of both the current and the jet diameter on the <ow rates and liquid’s properties. Finally,the results are summarized and discussed in Section 4.

2. Experimental set up

The basic experimental set up is sketched in Fig. 2. Two immiscible liquids, 1 and 2, are injectedat appropriate <ow rates through two stainless steel needles concentrically arranged as shown in theinjector sketched in Fig. 2. Both needles are connected to the same electrical potential, which inthis case was of a few kilovolts relative to a ground electrode (typical values were of the order of6 kV). Nevertheless, each needle could be connected at a di;erent electrical potential if the outerliquid was a dielectric one.Needles of di;erent diameters have been used in these experiments. Most of the experimental

data were obtained using an inner needle with 200 �m of inner diameter (ID) and 400 �m of outerdiameter (OD). The outer needle had 500 �m of ID and 900 �m of OD. In experiments usingde-ionized water and sun<ower oil, we have used the same inner needle but an outer needle with420 �m of ID and 800 �m of OD to achieve better control of the <ow rate of the sun<ower oil.When other needles have been used, mainly for visualization purposes, their diameters were indicatedat the proper place.


Table 1Relevant physical properties of the liquids used in the experiments

Liquid Density Conductivity, K Permittivity, � Viscosity, � Elec.relax.time, te (s)(kg m−3) (S m−1) (C2 N−1 m−2) (kg m−1 s−1)

EG-1 1060 1:1× 10−5 3:6× 10−10 1:6× 10−2 3:27× 10−5

EG-2 1060 2:0× 10−2 3:6× 10−10 1:6× 10−2 1:80× 10−5

EG-3 1060 2:1× 10−5 3:6× 10−10 1:6× 10−2 1:71× 10−5

EG-4 1060 4:0× 10−5 3:6× 10−10 1:6× 10−2 0:90× 10−5

EG-5 1060 2:5× 10−5 3:6× 10−10 1:6× 10−2 1:44× 10−5

Water 1000 1:4× 10−4 7:1× 10−10 1:0× 10−3 5:07× 10−6

Somos 1240 6:25× 10−5 1:2× 10−10 7:5× 10−1 1:92× 10−6

Sun-oil 840 8:0× 10−8 3:0× 10−11 4:3× 10−2 3:75× 10−3

Table 2Surface tension of the liquids employed in the experiments

Water EG Somos Sun<ower oil

Air 72:0× 10−3 46:6× 10−3 43:4× 10−3 32:8× 10−3

Sun<ower oil 16:6× 10−3 12:2× 10−3 — —

Values are measured in SI units.

For a certain range of values of the electrical potential and the injection <ow rates, a steadyconical structure with an outer meniscus surrounding the inner one, as shown in Fig. 1, is formed atthe exit of the needles. Liquids 1 and 2 are injected at controlled <ow rates through two Tygon Jtubes by means of two syringe pumps model ‘44’ from HARVARD APPARATUS. Each tube endsat a charged capillary needle connected to a high power supply model 250B-10R from BERTANat several kilovolts relative to a ground electrode located at a distance of a few centimetres of theneedle’s tip. The current transported by the compound jet was collected at the ground electrode andmeasured by a picoammeter model 485 from KEITHLEY INSTRUMENTS. To verify the steadinessof the compound cone–jet, the meniscus, jet and spray were permanently monitored in a TV set bymeans of a CCD camera model SSC-M370CE from SONY attached to a zoom microscope modelSMZ-2T from NIKON. Finally, to measure the droplet size resulting from the break up of thecompound jet, we have used a non-intrusive system model HELOS/BF-MAGIC from SYMPATEC.Table 1 summarizes the values of the relevant physical constants of the liquids used in these

experiments. Surface tensions of the di;erent <uid couples have been measured with a tensiometermodel K10 from KR TUSS. The measurement of the liquid viscosities have been measured with aviscosimeter model LVDVE 230 from BROOKFIELD. Electrical conductivities were determined bymeasuring the electrical resistivity across the ends of a capillary tube lled with the liquid sample.The dielectric constant of the Somos liquid (Somos J 6120 by DuPont) was measured with aLCR-meter model AG-4311B from ANDO. The remaining physical constants have been taken fromLide (1990) (Table 2).


3. Experimental results

3.1. The driving liquid concept

To obtain the structure given in Fig. 1, we injected Somos which <owed through the annular gapbetween the two needles. We then increased the electrical potential of the outer needle V1 until theSomos meniscus jumped into a stable cone–jet structure. In the present experiments, the electricalpotential of the inner needle was kept at V2 = V1. The viscosity of the outer liquid was suLcientlyhigh (Somos is 600 times more viscous than water) to di;use the electrical stresses acting on theliquid–air interface into the liquid bulk. Consequently, the liquid motion inside the Taylor cone isdominated by viscosity, so that the liquid velocity inside the cone is everywhere pointing towardsthe cone apex. Then, the inner liquid, ethylene-glycol (EG), was allowed to <ow through the innerneedle to form a new meniscus inside the Somos one. The motion of Somos deformed the EGmeniscus and sucked it to form a thin microthread. This microthread of EG merged downstreamwith that of Somos to nally form a two-concentric layered micro/nano jet, see Fig. 3. Interestinglyenough the resulting structure is steady for a range of values of the <ow rates and applied voltages.Measurements of the emitted current through the EG–Somos jet show that the current increases

when the Somos <ow rate increases too. However, for a given value of the Somos <ow rate, thecurrent underwent no noticeable variation when the EG <ow rate was increased by a factor of 40,see Fig. 4. In situations where the total current transported by the coaxial jet depends solely onone of the <ow rates of the two liquids, shall call driving liquid that for which the current dependson its <ow rate. It is worthy to note that the driving character of one of the liquids of a couplecan also be explained by a comparison of their electrical relaxation times. The electrical relaxationtime, te = ��o=K is the time required to smooth a perturbation in the electric charge; �o being thevacuum permittivity and � is the dielectric constant of the liquid. Free charges in the bulk reachthe interface in times of the order of magnitude of te. The condition that te is the smallest timescale of the problem, much smaller, for example, than the hydrodynamic time, is required to havea steady-state cone–jet structure (Gan&an-Calvo, D&avila, & Barrero, 1997). If the electrical relaxationtime of the outer liquid is much smaller than that of the inner one, charges are located at the outer

Fig. 3. Downstream detail of the dyed EG–Somos coaxial jet structure. QEG =0:3 ml=h; Qsomos =12 ml=h; voltage 7500 V;needles to plate distance 2:5 cm; outer needle: ID = 1:1 mm, OD = 1:5 mm; inner needle: OD = 0:9 mm, ID = 0:5 mm.The diameter of the jet is approximately 40 �m.


100

120

140

160

180

200

220

1 3 5 7 9 11 13

Qsomos (ml/hr)

I(n

A)

QEG=0.05 ml/hr

QEG = 2ml/hr

Regression line

Fig. 4. Current transported by an EG jet coated by Somos as a function of the Somos <ow rate for two di;erent valuesof the EG <ow rate. The corresponding regression line [I = 34:4 (Qsomos)1=2 + 70:13] has been also plotted. The electricalconductivity of the EG was in this case KEG = 1:1× 10−5 S=m (Sample EG-1).

interface and they are supplied to the outer interface much more eLciently from the outer liquidbulk than from the inner one. This is the case of the experimental data shown in Fig. 4a, wherethe electrical relaxation of Somos is smaller than that of EG; the ratio being 0.057 (�Somos ∼= 13:5,KSomos ∼= 6:3× 10−5 S=m, �EG ∼= 41:1, KEG ∼= 1:1× 10−5 S=m, �o = 8:85× 10−12 C2 N−1 m−2).The driving character of one of the liquids can lost be in favor of the other if the electrical

conductivity of the latter is enhanced suLciently by adding a suitable additive to it. In e;ect, datain Fig. 5 show that when the electrical conductivity of the EG was increased by a factor of 1800,the current through an EG jet coated with Somos remains almost independent of the Somos <owrate while it varies appreciably with the EG <ow rate; note that the current doubled when the EG<ow rate was increased by a factor of almost four. Therefore, one concludes that, charges are mainlytransported through the more conductive liquid and EG is the driver in this case.When charges are located at the outer interface, the tangential electrical stresses which point

towards the vertex of the conical interface must be eLciently transmitted throughout the liquid bulkby viscous di;usion. This requires that the viscosity of the outer liquid be high enough to play animportant role in the liquid motion. Moreover, the use of less viscous liquids outside would giverise to intense re-circulations in the electri ed meniscus (Barrero, Gan&an-Calvo, D&avila, Palacio, &G&omez-Gonz&alez, 1998). These re-circulatory motions are incompatible with steady compound jetsESs.However, liquids with low viscosity can be used as drivers in compound ESs when they are

located inside. That is the case shown in the picture in Figs. 6A and B, where a Taylor cone ofde-ionized water is formed inside a meniscus of a non-conducting liquid such as olive oil. By varyingappropriately the oil <ow rate one can obtain good control of the coating thickness as shown inFig. 6 where a water cone is coated with a thin (A) or a thick (B) sheath of olive oil. Note thatolive oil (or any other liquid insulator) cannot be electrosprayed on its own in the cone–jet mode,since the lack of surface charge density prevents the formation of a steady Taylor cone. The two


1

1.2

1.4

1.6

1.8

2

2.2

0 0.05 0.150.1

QEG(ml/h)

I (µA

.)

V=7 kV. Qsomos=1.5 ml/h

V=7 kV. Qsomos=3 ml/h

Regression line

Fig. 5. Current through an EG jet coated by Somos as a function of the EG <ow rate for two di;erent values of Somos<ow rate. The corresponding regression line [I = 5:95 (QEG)1=2 − 0:11] has been also plotted. The electrical conductivityof the EG was in this case KEG = 2× 10−2 S=m (Sample EG-2).

Fig. 6. Water Taylor cones coated by a thin sheath of olive oil (A) and by a thick sheath of olive oil (B). The needlediameters in (A) and (B) were: outer needle, OD = 1 mm, ID = 0:8 mm; inner needle, OD = 0:5 mm, ID = 0:35 mm.

ways of electrospraying liquid insulators in the cone–jet mode are by increasing arti cially theirelectrical conductivity via additives or by compound ESs.In the experiments shown in Fig. 6, the electrical relaxation time for oil is much longer than

that for water, so that charges are located at the water–oil interface. The water meniscus adopts aconical shape for appropriate values of the water <ow rate and the applied voltage. Viscous di;usiontransmits the action of the tangential stresses at the water–oil interface towards the olive bulk andsets the oil into a motion that is quasi-parallel to the water–oil interface. These two co-<owingstreams eventually give rise to a coaxial jet of water coated by oil. Note that, as in regular ESs,the motion of the driving liquid in this second con guration (water) does not need to be dominatedby viscosity. Observe also that the concept of driving interface, de ned as the one on which thetangential electrical stresses are non-zero, can be used instead of the driving liquid concept.


3.2. Current scaling law

We have carried out a set of experiments to investigate the current transported throughout coaxialliquid jets generated via ES, and their dependence on both the <ow rate and the properties of theliquids. Our aim was to explore whether magnitudes such as the emitted current or the jet size incompound ESs can be predicted in dimensionless form by relatively simple laws as in regular ESs.In particular, the possible dependence of the current on the square root of the <ow rate of the drivingliquid should be investigated.We have used several couples of liquids in which one of them is an insulator, i.e. sun<ower oil and

the other one is a semi-conductor, i.e. EG in one case and de-ionized water in other. Measurementsof the current transported through both a jet of EG coated with sun<ower oil and a jet of sun<oweroil coated with EG have been carried out in three sets of experiments. In two of them, the EG was<owing inside and each set was characterized for di;erent values of the sun<ower <ow rate: Qoil =1and 15 ml=h, respectively. The current transported by a jet of de-ionized water with sun<ower oilco-<owing outside has been also measured.For a more complete understanding of the phenomenon under consideration it proves convenient

to make dimensionless the obtained data by using reference characteristic values of the <ow rate,Qo, and the current, Io. We have used the reference values given by Gan&an-Calvo et al. (1997):

Qo =�e; �oK

and Io =(�2e; �o

)1=2; (1)

where , and K are, the density and electrical conductivity of the considered <uid, respectively. �ois the permittivity of vacuum, and �e; is an e;ective value of the surface tension. In situations whenthe outer liquid is the driving one �e; = �01. However, in those situations in which the driving liquidis coated with a lm of the insulator liquid of very small thickness, �e; =�01+�12; �01 and �12 are thesurface tensions of the gas–liquid insulator and the conducting liquid–insulator liquid, respectively.In e;ect, the normal balance across the outer and the inner interfaces yields, respectively,

�01R+ �

≈ p1 − p0 + 12�o[E

2n0 − �E2

n1];�12R

≈ p2 − p1 + 12��oE

2n1 (2)

where � is the thickness of the layer oil, R is the radius of the inner interface, p is the pressure, Enis the normal component of the electric eld, and subscripts 0, 1, and 2 refer to air, oil and drivingliquid, respectively. In Eqs. (2), we have assumed that En2 is much smaller than En0 and En1. Byadding the two equations in Eq. (2), and neglecting � as compared to R, one arrives at,

�12 + �01R

≈ p2 − p0 +12�oE2

n0 (3)

which shows that the driving liquid feels an e;ective surface tension �e;=�01+�12. Clearly, expression(3) is not valid when the coating thickness is not small enough compared to the characteristic radiusof the inner meniscus but the value �e; = �01 + �12 may still be used as a characteristic value ofreference (Chauhan, Maldarelli, Papagiorgiu, & Rumschitzki, 2000).


I/Io=6.2[Q/(β 1/2Qo)]1/2-2.0

0

10

20

30

40

50

0 2 3 5 6 8 9

[Q/(β1/2 Qo)]1/2

I/I o

EG-1 inner Oil outer: Qoil=1 ml/hr

EG-1 inner Oil outer: Qoil=15 ml/hr

EG-3 outer Oil inner: Qoil=1 mL/hr

Water int Oil ext: Qoil= 0.2 ml/hr

After Gañan-Calvo et al.(1997)

Fig. 7. Dimensionless current versus dimensionless <ow rate for di;erent experimental sets. Current scaling law given byGan&an-Calvo et al. (1997) is plotted for comparison.

In accordance with the current scaling law for regular ESs, we have plotted the dimensionlessvalue of the current as a function of the square root of the value of the dimensionless <ow rateof the driving liquid. Data of the three experimental sets collapse very close to a straight line, seeFig. 7. This fact indicates that the current follows very closely a power law of the Q1=2 type. Notethat the values of the dimensionless current of the experiments with EG are almost independentof whether the EG <owed either through the inner or the outer part of the jet. Observe also thatthe current is practically independent of the sun<ower oil <ow rate. In particular, the increase ofthe current was smaller than a 15% when the <ow rate increased by a factor of 15. This increaseof the charge transported through the jet is not probably due to an increase of the charge transportedby the sun<ower oil but due to the higher values of the applied voltage required to obtain steadycone jets when the sun<ower oil <ow rate was increased.One of the existing current scaling laws for regular ESs given in the literature (solid line) has been

also plotted in Fig. 7 for comparison. Note the remarkable agreement between the EG–sun<oweroil data and the current scaling law for regular ESs given by Gan&an-Calvo et al. (1997); � is therelative dielectric constant, which in this case is � = �EG=�oil.Unexpected values in the current transported through electri ed coaxial jets were found in the

case of electri ed water jets coated with sun<ower oil. In e;ect, although the measured values tclosely the Q1=2 power law since they lie on a line parallel to the Gan&an-Calvo et al. law, theypractically doubled the expected values, see Fig. 7. In the absence of a satisfactory explanation ofthis behavior, we limit ourselves to report here that we have found an abrupt increase of the emittedcurrent in the transition from dripping to jetting in electri ed menisci of water–sun<ower oil. Asfar as we know such a particular behavior has not been observed, neither when di;erent couples ofliquids are used nor in regular ESs.Let us now discuss the main sources of uncertainty in our measurements. The <ow rate delivered

by the syringe pump is known within an error of the order of ±1%. However, the current measured


by the picoammeter experienced a background low frequency oscillation of the order of 5% ofthe average current, well above the device measuring error. Other sources of error come from themeasurements of the liquid properties, mainly viscosity, surface tension and electrical conductivitywhose values are determined with an error below 1%. Therefore, our experimental uncertaintiesallow the knowledge of the values of I=Io and Q=Qo within an error of 6% and 3%, respectively.

3.3. Jet diameter scaling law

The break up of electri ed coaxial jets due to varicose instabilities is an extremely complicatedelectro-hydrodynamic process which depends on several dimensionless numbers, Reynolds, Weber,Ohnesorge, and electrical Bond numbers, which account for the relative importance on the processof the inertial, viscous, aerodynamic, capillary, and electrical forces.We present here preliminary results of an experimental research aimed to gain insight on the

scaling laws of the diameters of the electri ed coaxial jets and the droplets resulting from theirbreak up. The mean droplet diameter, d50 resulting from the break up of electri ed coaxial jetshave been measured with a non-intrusive system SYMPATEC-HELOS/BF-MAGIC. Diameter, d50,corresponds to a drop diameter such that 50% of the total liquid volume of the spray is containedin droplets of smaller diameters.Let us point out that although the compound ES technique has proved its ability to generate

coaxial jets with diameters well below the micrometric range (Loscertales et al., 2002), here, for thesake of an easy jet measurement, we limit ourselves to generate jets with diameters well abovethe micrometric range. In our experiments, we have used the couple sun<ower oil–EG. In one casethe oil which <owed inside was coated with a co-<owing charged EG layer. The opposite situation(the electri ed EG <owed inside and the oil outside) has also been investigated.Fig. 8 shows the size droplet histograms corresponding to the break up of three di;erent jets of

sun<ower oil coated with electri ed co-<owing EG layers. The geometrical standard deviation of thethree distributions is practically the same and equal to 1.2, so that, the diameter d of the 95% ofthe droplets are within the range 0:7d506d6 1:44d50.The mean diameter of the droplets, d50, resulting from the jet break up as a function of the EG

<ow rate for several values of the oil <ow rate is plotted in Fig. 9. Note that for a given value ofthe oil <ow rate, the droplet size increases linearly with the value of the EG <ow rate. For a xedvalue of the EG <ow rate, the droplet diameter also increases linearly with the oil <ow rate. Thislinear behavior of the compound droplet size di;ers from the non-linear ones Q1=3 and Q1=2 givenin the literature for regular ESs (Fern&andez de la Mora & Loscertales, 1994; Gan&an-Calvo et al.,1997; Gan&an-Calvo, 1997). This discrepancy may be due to the fact that in regular ESs, the sizeof droplets is a result of the capillary break up of a charged jet while in this case, the size of theresulting compound droplets is governed by the capillary break-up of the inner uncharged viscousoil jet. In addition, in regular ESs operating in air at atmospheric pressure, the jet is accelerateddownstream by the electrical tangential stress acting on the surface; the e;ect of the surround-ing medium on the jet dynamics being negligible. On the contrary, non-negligible viscous stressesact at the liquid–liquid interface of a coaxial jet. The dependence of the diameter and velocity ofthe jet on the electrosprayed <ow rate is a result of the balance between accelerating and dragforces.


Fig. 8. Volumetric droplet size distribution, d50, of three di;erent compound sprays for three di;erent couples of valuesof the EG and oil <ow rates. The geometric standard deviation is 1.2 in the three cases, while the mean droplet diametersare 25, 32 and 36 m for QEG =1 ml=h and Qoil =1 ml=h; QEG =1 ml=h and Qoil =2 ml=h; QEG =5 ml=h and Qoil =3 ml=h,respectively.

20

30

40

50

60

70

0 2 4 6 8 10QEG (ml/hr)

d 50

(µm

)

Qoil= 1 ml/hr

Qoil= 2 ml/hr

Qoil= 3 ml/hr

Qoil= 5 ml/hr

Fig. 9. Mean outer diameter, d50, of a spray of compound droplets of sun<ower oil coated with EG as a function of theEG <ow rate and di;erent values of the oil <ow rate (sample EG-4).

Data from Fig. 9 t very closely the following algebraic dimensionless expression:

d50do

= 0:0750Qoil

Qo+ 0:035

QEG

Qo+ 5:15; (4)


Fig. 10. Volumetric size distribution corresponding to types A and B of the sketched jet break up. For the distributioncorresponding to QEG = 1 ml=h and Qoil = 8 ml=h, the standard geometric deviation is 1.20 and the mean diameter is52 �m. For the distribution corresponding to QEG = 8 ml=h and Qoil = 8 ml=h, the standard geometric deviation is 1.24and the mean diameter is 50 �m.

where the characteristic values Qo = ��o=(K) and do = (Qo�o=K)1=3 have been obtained using thephysical properties of the EG and the EG–air surface tension. Eq. (4) allows for the prediction ofthe mean outer diameter d50 as a function of the EG <ow rate, the oil <ow rate and some of theliquid properties. The volume of oil enclosed in the EG droplets can be estimated from the followingrelationship:

d3oild350 − d3oil

=Qoil

QEG; doil =

d50(1 + QEG

Qoil)1=3

: (5)

Measurements of the mean droplet diameter in sprays resulting from the break-up of electri edcoaxial jets of EG coated with a layer of co-<owing sun<ower oil exhibit quite a di;erent behaviorfrom that of the above case. In e;ect, in this case and because of the di;erent viscosities of theEG and the oil, we have identi ed three di;erent patterns of the break-up process depending on theratio of the <ow rates of the two liquids. For oil <ow rates much larger than the EG <ow rates,the droplet diameter distribution is that of the type called A, see Fig. 10. In this case, the breakup wavelength of the EG jet is much shorter than the wavelength break up of the oil. The EGjet break-up precedes the oil jet one and the EG droplets are so small that they hardly contributeto the total drop volume, see histogram A in Fig. 10. As shown in the gure, the spray is rathermonodisperse with a geometric standard deviation of 1.2. For larger values of the EG <ow rate,the found histogram is that of type B, see Figs. 10 and 11. In these cases, as shown in sketch B,both break up wavelengths are comparable and both break-up processes become coupled (the two


Fig. 11. Volumetric size distribution corresponding to types B and C of the sketched jet break up. For the distributioncorresponding to QEG = 8 ml=h and Qoil = 1 ml=h, the standard geometric deviation is 1.20 and the mean diameter is40:5 �m. For the distribution corresponding to QEG = 1 ml=h and Qoil = 1 ml=h, the standard geometric deviation is 1.27and the mean diameter is 24 �m.

break-up characteristic times are comparable). As a result, the EG to oil volume ratio of dropletsis less uniform and, consequently, broader droplet size distributions than in case A are found; thestandard deviation being 1.24 and 1.27 for the cases shown in Figs. 10 and 11, respectively. Thetail of type B histogram in Fig. 10 shows a non-negligible amount of small satellite droplets whichare absent in the same type histogram in Fig. 11. Although the ratio QEG=Qoil is the same in bothexperiments, a plausible explanation lies in the di;erence in the Ohnesorge number of the two Bbreak up processes of Figs. 10 and 11. The Ohnesorge number, Oh = �=(�d)1=2, accounts for therelative importance of the viscous to capillary forces. As is well known, the larger the Ohnesorgenumber the smaller the size of the satellites (L&opez-Herrera, Gan&an-Calvo, & P&erez-Saborid, 1999;Chaudhary & Maxworthy, 1980). Since the jet diameter is larger in the case in Fig. 10, Qoil=8 ml=h,than in the case in Fig. 11, Qoil=1 ml=h, the in<uence of viscosity in the break-up process is smallerand, consequently, the number of satellites and their sizes must be considerable larger in the formercase than in the latter one.The narrowest size distributions are found when the EG <ow rate is much larger than the oil one.

In this case a thin layer of oil coats the EG jet, see sketch C in Fig. 11, and the droplet volumeis completely governed by the EG jet break-up. Data of the mean droplet diameter, d50, of thesecompound jets as a function of the EG <ow rate for di;erent values of the oil <ow rate are plotted inFig. 12. Two limit behaviors are found. In one case, for the larger oil <ow rates, the mean diameteris almost independent of the EG <ow rate while for lower oil <ow rates the mean diameter exhibitsa marked linear dependence on the EG <ow rate. For the larger oil <ow rates, Qoil = 8 ml=h, thebreak-up process is mainly of type A, although some histograms corresponding to type B are foundfor increasing values of the EG <ow rate. Consequently, the mean diameter is almost independentof the EG <ow rate. On the contrary, for smaller values of the oil <ow rate, Qoil = 5 ml=h andQoil = 1 ml=h, the break process corresponds mainly to type C, although some of type B are foundfor decreasing values of the EG <ow rate. The regularity of the break-up process indicated by the


0

20

40

60

0 2 4 6 8 10

QEG (ml/hr)

d 50

(mm

)

Qoil= 1 ml/hr

Qoil= 5 ml/hr

Qoil= 8 ml/hr

Fig. 12. Diameter of the compound droplet as a function of the inner EG <ow rate for several values of the outer oil<ow rate (sample EG-5).

narrowness of the histograms obtained for these set of experiments (geometric standard deviation lessthan 1.2) allows for an indirect calculation of the volume of the EG contained inside the droplets.We assume that this volume forms a drop of diameter dEG given by

d3EGd350 − d3EG

=QEG

Qoil→ dEG =

d50(1 + Qoil

QEG)1=3

: (6)

Fig. 13 shows dimensionless EG diameter dEG=do as a function of dimensionless <ow rate(QEG=Qo)1=3 for several values of the oil <ow rate. Note that the calculated data collapse rela-tively close to a straight line obtained from an average on an ample set of regular ESs experimentsreported in Gan&an-Calvo et al. (1997). The scaling law for the size slightly underrated the exper-imental values. This may be explained by the e;ect of the oil layer which slows down the EGjet much more eLciently than the air does in regular ESs and, consequently, its diameter becomeslarger for the same value of the <ow rate. In any case, the relative error between the measured andcalculated jet diameters is below 20%.Finally, it is worthy of noting that the experimental data plotted in Fig. 13 not only t well the

(QEG=Qo)1=3 scaling law reported by Fern&andez de la Mora and Loscertales (1994) and Gan&an-Calvoet al. (1997), but also exhibit a good agreement with the other competing (QEG=Qo)1=2 scaling lawjet size derived analytically by Gan&an-Calvo (1997). Unfortunately, the small di;erences betweenthe jet diameters predicted by the two models are comparable to the accuracy with which can beexperimentally sized. Therefore, our measurements do not provide a de nitive proof for ruling outthe wrong model.


0

5

10

15

20

1 2 3 4 5 6 7 8 9

(QEG/Qo)1/3

dE

G/d

o

Qoil= 1 ml/hr

Qoil= 5 ml/hr

After Gañán-Calvo et al(1997)

Fig. 13. Dimensionless diameter of the compound droplets as a function of the EG dimensionless <ow rate for severalvalues of the oil <ow rate. The scaling law for the droplets of a regular EG ES is also given for comparison.

4. Summary and conclusions

An experimental investigation on the current transported by ESs coaxial jets and the size ofthe compound droplets resulting from the jet break-up has been carried out for several couples ofliquids. The e;ects of the liquid <ow rates as well as the liquid properties (electrical conductivity,permittivity, density, and surface tension of both liquid–liquid and gas–liquid interfaces) on thecurrent and size have been investigated.The role of the driving liquid has been investigated using the Somos–EG couple. We have found

that if the electrical relaxation time of the outer liquid is smaller than (or comparable to) that ofthe inner one, charges are located at the outer interface; the outer liquid being the driving one. Onthe contrary, if the electrical relaxation time of the outer liquid is much larger than that of the innerliquid (the case of insulators as outer liquids), the free charges are disposed at the inner liquidinterface; the inner liquid being in this case the driving one. In any case, the current mainly dependson the <ow rate of the driving liquid.Current measurements show that the dependence of the current on the driving <ow rate t well the

Q1=2 law. This fact indicates that the current transport mechanisms in these coaxial jets are entirelysimilar to those in regular ESs. Moreover, we have found that the value of the current transportedby coaxial jets of conducting-insulator liquid couples hardly depends on whether the conductingliquid <ows outside or inside but on the conducting liquid <ow rate. Using appropriate referencemagnitudes, we found that the dimensionless current of EG–oil coaxial jets agrees satisfactorilywith the current law for regular ESs given by Gan&an-Calvo et al. (1997). Dimensionless currenttransported by jets of de-ionized water coated by oil exhibit also the same parametric dependenceon the liquid properties and <ow rate than that in regular ESs. Nonetheless the measured current is,in this case, higher than that predicted by the current law for regular ESs.Data of the mean diameter of droplets resulting from the break-up of EG–oil coaxial jets have been

obtained using a SYMPATEC non-intrusive system. We have found that the results are completely


di;erent depending on whether the driving liquid is <owing outside or inside. In any case, thesize distributions of the compound droplets are, in general, relatively narrow (geometric standarddeviation of the order of 1.2). When the oil is <owing inside, the coaxial jet break-up process andthe size of the resulting droplets are governed by the break-up of the oil jet which, due to its higherviscosity, is more stable than the EG jet and prevents its break-up. In this case, we must considerthe break-up of an uncharged jet (the EG–oil interface is uncharged) surrounded by a co-<owingcharged EG jet. Dimensionless experimental diameters d50=do scales linearly with both QEG=Qo andQoil=Qo. When the oil <ows outside, we have found di;erent break-up process depending mainly onthe Qoil=QEG ratio. For larger values of this ratio, the break-up processes of both jets are uncoupled.Small EG droplets are contained in the uncharged oil jet which eventually breaks up in oil dropletsof much larger size than the EG droplets which are contained inside. The resulting spray is rathermonodisperse with a typical standard deviation of 1.2. For decreasing values of Qoil=QEG, bothbreak-up processes become more and more coupled: the less monodisperse compound droplets arefor values of the <ow rate ratio of order of unity. Finally, for small values of Qoil=QEG, the resultingspray of EG droplets covered by a thin oil layer is very monodisperse in size. In our experiments,we have obtained histograms with geometric standard deviation of 1.15, although, as is well known,sprays with smaller values of the standard deviation can be obtained if the system is operated at<ow rates near the minimum one.

Acknowledgements

This work has been supported by the Spanish Ministry of Science and Technology under ProjectBFM2001-3860-C02-01. The authors are also indebted to Mr. Ismael Guerrero and Mr. Robert Perezfor their useful contributions to the preliminary steps of this work. The valuable assistance of Mr.Manuel Gonz&alez is also acknowledged.

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CoaxialjetsgeneratedfromelectriedTaylorcones. Scalinglaws · 2007-04-23 · 536 J.M.Lopez-Herreraetal./AerosolScience34(2003)535–552& 1. Introduction Theproductionofveryhighqualityspraysofstructureddropletsorparticlessuchthateachparticle