1876-6102 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license [610134]

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer
-review under responsibility of the organizing committee EENVIRO 2015
doi: 10.1016/j.egypro.2015.12.265 Energy Procedia 85 (2016) 383 – 389 ScienceDirect
Sustainable Solutions for Energy and Environment, EENVIRO – YRC 2015, 18 -20 November
2015, B ucharest, Romania
Breakup of Liquid Jets
Ioana Laura Omoceaa*, Claudiu Patrascua, Mih aela Turcanua, Corneliu Balana
aREO ROM Group, Hydraulics Departament, University "Politehnica" of Bucharest, 313 Splaiul Independentei sector 6,
060042 Bucharest, Romania
Abstract
The present paper investigates breakup of immersed jets of water and water – glycerol solutions in a hydrophobic environment.
Organic oil was used as the surrounding medi um . Experimental setup allowed the investigation of jet behavior, respectively the
exact moment when perturbations appear. The phenomenon of jet breakup was quantified by measuring the breakup length.
Max
imum breakup length, normalized with the nozzle diameter, wa s plotted and analyzed function of dimensionless numbers.
Results showed that normalized breakup length has a linear dependence with Reynolds and Capillary, respectively.
©2015 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the org anizing committee EENVIRO 2015.
Keywords: Immersed jet; Rayleigh instability; interfacial tension; breakup length
1. Introduction
Oil spilling pollution is one of the most important ecological problem s of the century. Breakup of liquid jets is a
phenomenon related to this problem. When oil is spilled in the ocean, generall y it spreads at the water surface and,
depending on its density and composition it might migrate into the water or form a slick at the surface [1]. This oil –
water interaction leads to a process in which sea water drop lets become suspended in the oil to form a water -in-oil
e
mulsion. This physical mixing is promoted by turbulence at the sea surface and it increa ses the volume of pollutant
between 3 and 4 times [2]. This affects drastica lly the evolution of the marine biosystem and it is a tremendous
challe
nging problem for bioresearchers [3].

* Corresponding author.
E-mail address : [anonimizat]
Available online at www.sciencedirect.com
© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer
-review under responsibility of the organizing committee EENVIRO 2015

384 Ioana Laura Omocea et al. / Energy Procedia 85 (2016) 383 – 389
In the environmental context of nowadays, understanding how pollutants are acting provides the main knowledge
for finding optimal solutions to counteract their action. In this framework we are interes ted to see how droplets are
formed when water penetrates a hydrophobic fluid, such as oil.
Along with the emulsification, other multiphase processes i n which breakup of jets is of huge interest are widely
encountered in nature, technology and basic science, such as medical diagnostics, DNA sampling, cosmetics, sprays,
j
et engine technology and combustion processes [4] .
A liquid jet emerging from a nozzle will experience in sta bility and breakup into drops. This phenomenon is
known as Rayleigh instability. This instability is due to th e interaction between the fluid discharging from the nozzle
and the surrounding medium properties. The resulting shape of the interface can be a subject of Fourier analysis, and
it can be showed that there is a certain wave length at which jet breakup occurs [4] –[6].
Until now, breakup of both Newtonian and non -Newtonian jets into droplets was extensively studied in the
literatu re, covering mostly their evolution in the air [7] –[9]. Both theoretical and experimental aspects regarding the
in
jection of a liquid jet in a gaseous medium were first studied by Lord Rayleigh [4], [10] .
The aim of this work was to investigate instabilities and br eak up of different immersed jets into an oil phase. The
influence of physical properties, such as viscosity, on the dynamics of breakup, especially the breakup length was
discussed . Startin g from Tomotika ’s work [5], a theoretical predictio n for the breakup length was achieved, in good
agreement with the experimental work.

Nomenclature
ࢽ interfacial tension [ܰȀ ݉ ]
࣋ density [݃݇Ȁ݉ଷ]
ࢍ constant of gravity [ ݉Ȁݏଶ]
η viscosity of water and water – glycerol [ݏܽܲ]
࢒࢏࢕ࣁ viscosity of the surrounding medium [ݏܽܲ]
ࢇ capillary length [݉]
ࡰ needle inner diameter [ ݉]
ࡾ needle inner radius [ ݉]
ࡸ breakup length of the jet [݉]
࢜ single jet velocity [݉Ȁ ݏ ]
࢑ wave number [ ͳȀ݉ ]
ࣅ wavelength [݉]
࣓ perturbation frequency (growth rate of disturbance [ͳȀ ݏ]
࢚ breakup time [ݏ]
2. Materials and methods
The experiments involved in this study used organic oil as hy drophobic medium. Mixtures of water and glycerol
were used for studying jet formation and breakup in to oil. Pure water jet was used as reference.
By adding glycerol in water we increased the viscosity and density of the mixture.
Interfacial tension between the two phases was measured w ith the pendant drop method. Densities are evaluated
by weighting a volume of liquid using a Hamilton microsyringe (Gastight #1725 ͲǤʹͷŽ) and a microscale balance
(Radwag AS 82/220.R2). Viscosity was measured with a rotational rheometer (Anton Parr Physica MCR301), using
a cone –plate geometry ( CP 50/1°). Fluids properties are presented in Table 1, along with the capillary length, ܽ ,
v
alues. All fluids were tested at ʹͷǏܥ .
ܽൌටఊ
ఘ௚ (1)

Ioana Laura Omocea et al. / Energy Procedia 85 (2016) 383 – 389 385
Table 1. Liquids’ Properties at ʹͷǏܥ
Glycerol concentration
[%] η [Pas] ߛ [N/m] ρ [kg/m3] a [mm]
0 1.00E -03 0.03 1004 1.75
40 0.00412 0.032 1117 1.71
50 0.00845 0.028 1149 1.58
60 0.0131 0.029 1177 1.58
Oil 0.055 – 877.5 –
Experimental setup, sketched in Fig. 1 consists of a glass cell filled with organic oil, a syringe pump and a high –
speed camera (Nikon J5). Two differ ent n eedles with th e interior diameters ଵൌͲ Ǥͺ͵ͺ (code) and ଶൌ
ͲǤͷͳͶ were connected to the syringe pump, as indicated.
Jets of water in oil were created injecting water thr ough out the needle at different flow rates. Flow rate was
chosen from ͷ݈݉Ȁ݊݅݉ to ͵Ͳ݈݉Ȁ݊݅݉ ,li mited by the syringe pump to prevent the motor to stall.

Fig. 1 – Sketch of the experimental setup. Exemple of water jet in oil and measurement of breakup length L
The progressive thinning of the thread is driven by capillarity and resisted by inertia and viscosity. The velocity
between the jet and the surrounding liquid (oil) is different. Thus, the oil – water (or glycerol – water mixture) is
u
nstable [4].When the jet column shape becomes unstable it eventually breaks into drops. Breakup length, defined
by
Eggers and Villermaux, represents the minimum distance from the nozzle over which the liquid jet is still
connected [4]. In our studies we measured the maximum breakup length, ܮ ,as indicated in Fig.1. All experiments
w
ere performed at ʹͷǏܥ in triplicate and representative imag es wer e chosen for analysis.
3. Resul ts and discussion
3.1. Image analysis
Movies at normal and high speed were recorded from a perpendicular direction to the jets plane. Fig. 2 shows a
set of ph
otos of water jet in oil. Rayleigh instabilities of the water jet were observed. Wavelength can be
distingu
ished in the images. The jet’s lead has a round shape, prior to dr o p formation. The volume of this drop in
increasing, then breakup occurs. The same behaviour and response was also observed in the case of glycerol –
water mixtures.
Dimensionless numbers, Reynolds and Capillary numbers, w ere calculated using of jet velocity throw the needle.
These numbers were used for further determination of the jet breakup dynamics.
ܴ݁ – ratio of inertia and viscous forces:
ܴ݁ൌఘ௩஽
ఎ (2)

386 Ioana Laura Omocea et al. / Energy Procedia 85 (2016) 383 – 389
ƒ – ratio of viscous forces to interfacial tension:
ܽܥൌఎ௩
ఊ (3)

Fig. 2 – Breakup of water jet in oil; velocity ͳͲ݈݉Ȁ݊݅݉ ; needle diameter ͲǤͺ͵ͺ; e ach two frames are separated by ͶͲݏ݉
3.2. Parameter L/D dependence
Maximum breakup length, ܮ ,was measured from image data. It was normalized with the needle diameter, D. ܴ݁
and ܽܥ number were calculated for three different glycerol concentration in water, ͶͲΨ , ͷͲΨ and ͸ͲΨ ,
respectiv
ely. Experimental data for ܮȀܦ parameter, normalized breakup length, were plotted function of ܴ݁ and ܽܥ
number (Fig. 3 and Fig. 4.). Normalized breakup length has a linear dependence with these two dimensionless
n
umbers.
Viscosity was increased by adding glycerol in water. Th e exact i mpact on breakup length was analysed for
different jet’s flow r ate. Fig. 5 represents the variation of parameter L/D with increasing viscosity. A decreasing
no
nlinear effect on liquid breakup length can be noted.
Results presented were for the same nozzle diameter . Fi g. 6 represents the normalized length function on Re
n
umber for two different nozzles interior diameters ( ͲǤͺ͵ͺ݉݉ and ͲǤͷͳͶ݉݉ .)Jet breakup shows similar
behaviou
r for certain ܴ݁ .Same behaviour was noticed for other glycerol concentrations.
40 80 120 16010203040
40% glycerol conc.
50% glycerol conc.
60% glycerol conc.L/D1 (-)
Reynolds number (-)
Fig. 3 – Dependence ܮȀܦଵሺܴ݁ሻ for three different glycerol concentration s in water

Ioana Laura Omocea et al. / Energy Procedia 85 (2016) 383 – 389 387
0.1 0.2153045 40% glycerol conc.
50% glycerol conc.
60% glycerol conc.L/D1 (-)
Capillary number, Ca (-)
Fig. 4 – Dependence ܮȀܦଵሺܽܥሻ for three different glycerol concentration s in water
048 12204060
11ml/min
14ml/min
17ml/min
20ml/minL/D2 (-)
K(mPas)
Fig. 5 – Parameter L/ D2 dependence with viscosity at constant flow rate
(viscosity increasing with increasing glycerol concentration in water )
100 2002040
glycerol 40% L/D1
L/D2L/D (-)
Reynolds number (-)
Fig. 6 – Dependence ܮȀܦሺܴ݁ሻ for two different needle diameters (ܦଵൌͲ Ǥͺ͵ͺ݉݉ and ܦଶൌͲ ǤͷͳͶ݉݉ 😉
glycerol 40 % concentration in water

388 Ioana Laura Omocea et al. / Energy Procedia 85 (2016) 383 – 389
3.3. Theoretical prediction of breakup length, L
The breakup phenomenon is characterized by the breakup length, ܮ ,and the dominant wavelength, λ, th at causes
formation of droplets. One of the hypotheses that Tomotika considered was a cylindrical thread of viscous fluid
sur
rounded by another viscous liquid [5]. Considering that inertial effects are small against the viscosity, he derived a
dispersion relation that captures the dependence of perturbation frequency (growth rate of disturbance [5]), ߱ሾͳȀݏሿ , on
the
wave number:

߱ ൌ ߛሺͳെ݇2ܴ2ሻܨሺܴ݇ሻȀሺʹߟܴ ௢௜௟ሻ (4)
where the wave number, ݇ൌଶగ
ఒ, and ܨሺܴ݇ሻis a function of ܴ݇ resulting from the equation of motion.
As described in [5] , Tomotika’s dispersion relation (4) was an alyzed. Breakup occurs for the maximum
wavelength. The wavelength, ߣ , that theoretically predicts breakup, can be determined. For that, ܨሺܴ݇ሻ needs to be
plotted. In
Fig. 7 values of ሺͳെ݇2ܴ2ሻܨሺܴ݇ሻ were plotted for different water -glycerol solutions in order to extract
inf
ormation regarding the curve shape for these specific cases.
Incre asing viscosity shifts the maximum growth rate of breakup to lo wer values and to shorter wavelengths. The
next step was to determine a relation that predicts the breakup length, considering that:
ܮൌݐݒ
ݐൌ
ܥ Ȁ ߱௠௔௫
ܮൌݒܥȀ߱௠௔௫ (5)
0.0 0.5 1.00.00.20.4(1-k2R2)F(kR)
kR water 100%
40% glycerol conc.
50% glycerol conc.
60% glycerol conc.

Fig. 7 – Tomotika’s dispersion relation for three different glycerol concentrations in water and water, respectively
0.3 0.6102030
glycerol concentration 40%Experimental and theoretical length (mm)
velocity v (m/s) L experimental
L theoretical

Fig. 8 – Experimental and theoretical prediction of length L for 40% glycerol concentration in water

Ioana Laura Omocea et al. / Energy Procedia 85 (2016) 383 – 389 389
Instability occurs for values of ܴ݇൏ͳ. Wavelength that produces breakup corresponds to the maximum value of
ሺͳെ݇2ܴ2ሻܨሺܴ݇ሻ, predicted in Fig. 7. Maximum wavelength ɘ୫ୟ୶was determined from (4) and applied for jet
break
up theoretical prediction (5). Experimental data were compared with t heoretical predictions for solutions with
40% glycerol (Fig. 8). The value of the constant ܥ [5] is found to be ͵ǤͶͻ. This constant depends on both initial and
maximum amplitude of perturbation.
4. Conclusion and future work
An experimental work has been performed in order to study viscosity influence, ratio between jet viscosity and
su
rrounded fluid viscosity, respectively, on the dynamics and breakup of jets. Organic oil was used as a surrounding
medium. Jets of water in oil were created. Viscosity of the jets was increased by adding glycerol in water ( ͶͲΨ,
ͷͲΨ and ͸ͲΨ).
As ex pected, increasing viscosity and density of the jet h as a decreasing effect on breakup length. Parameter ܮȀܦ ,
rep
resenting normalized breakup length with the diameter of the nozzle, was analysed function of dimensionless
n
umbers, Re and Ca.
Dispersion relation derived by Tomotika [5] was the input in theoretical prediction for breakup length. Further
in
vestigation of ܥ constant has to be made, the precise variation of ܥ with increasing viscosity. The manner in
w
hich this constant varies from one solution to another needs further investigation. For a lower glycerol
co
ncentration, for example, 50%, ܥ was found to be ͶǤ͹Ͷ. Ex perimental data and theoretical predictions were found
to be in good agreement for the first jet investigated ( ͶͲΨ glycerol concentration in water).
Atomization of immersed jets in oil, transition from Raylei g h regime to atomization, is another subject of our
future work.
Acknowledgements
The work has been funded by the Sectoral Oper ation al Programme Human Resources Development 2007 -2013
of
the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/134398 and
POSDRU/159/1.5/S/132395.
The authors acknowledge the financial support from the grant CNCS -UEFISCDI: PN -II-PT-PCCA -2011- 3.1-
0052 and PN -II-ID-PCE-2012 -4-0245.
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