The effect of a nanoparticles and surfactant
on the water drops evaporation
Terekhov V.I., Shishkin N.E.
Kutateladze Institute of Thermophysics SB RAS
Novosibirsk, Russia
terekhov@itp.nsc.ru, shishkin@itp.nsc.ru
Abstract — Experimental researches of flow rate drops
evaporation have shown, that addition carbon nano- tubes in
base a liquid (water) practically does not affect laws heat and
mass transfer. That addition of superficially active substance
renders essential influence on mass transfer. Laws of change
surface temperature of a drop and flow rate evaporation at
change of thermal and dynamic conditions are submitted.
Keywords- heat and mass transfer, evaporation, drops, nanoliquid,
carbon nanotubes, surfactant
INTRODUCTION
Evaporation of droplets consisting of multicomponent
mixtures and including suspended inclusions of solid particles
has significant practical importance for design of various
power installations [1, 2]. Great attention to evaporation of
liquid films and droplets with surfactants is caused by possible
control of surface tension at the interface and, hence, control
of heat transfer intensity. According to the opinion of the
authors of [3], the effect of surfactant addition on the growth
of heat transfer coefficients during the fall of liquid films over
a vertical wall relates to foaming, but not to surface tension
Recently the interest to heat transfer processes in
nanofluids becomes more intensive [4, 5]. Many papers deal
with investigation of nanofluid boiling. The modern state of
this problem is shown in monograph [6]. Simultaneously
evaporation of nanofluid droplets is studied insufficiently.
Publications [7, 8] are the exclusions: the rate of evaporation
into the ambient stationary air medium of nanofluid droplets
suspended on a capillary and their surface tension were
measured there. Water was used as the basic fluid, and
particles were presented by laponite, Ag and Fe2O3, whose
concentration was 0.05 %, and only for laponite it was 0.5 %.
The main conclusion of these works is the weak effect of
nanoparticles on surface tension of liquid droplets and the rate
of their evaporation at the initial moments of time. When some
critical size is achieved, the evaporation rate of nanofluid
droplets decreases, and this effect is especially strong for
silver particles. For laponite the changes in the rate of droplet
evaporation were not observed, and nanofluids with Fe2O3
particles occupy some intermediate position.
Li H.-X.
State Key Laboratory of Multiphase Flow at Xi’an Jiotong
University, Xi’an, China
huixiong@mail.xjtu.edu.cn
Evaporation of fuel droplets (ethanol, n-decane, etc.)
under the conditions of free and forced convection with
addition of aluminum nanoparticles is studied experimentally
in [9]. The main conclusion of this work is reduction of
evaporation rate for nanofluid, what contradicts investigation
results on evaporation of nanofluids with distilled water as the
basic liquid medium [7].
It becomes obvious from the abovementioned that the
problem of heat and mass transfer at evaporation of liquid
droplets in the presence of nanoparticles and surfactants is far
from its solution. This paper presents the first experimental
results on evaporation rate of water droplets with
nanoparticles of carbon nanotubes and surfactants in the flow
of dry air with varying temperature and velocity.
In literature great attention is paid to investigation of heat
and mass transfer at evaporation of liquid films. As for the
liquid droplets the situation is more complex in comparison
with the film flow. The fact is that the size of droplet at
evaporation decreases causing a change in the character of
circulating flow inside the droplet, its composition and surface
tension. At this, a monolayer of insoluble substances of
surfactant and substances absorbed from the ambient air can
be formed on the droplet surface. This was mentioned in some
papers [10-15], where experimental and theoretical works
prove a significant decrease in the rate of evaporation in
comparison with pure fluid. A change in the surface
temperature of droplet with surfactant addition is qualitatively
different [14, 15].
Surfactant composition as well as gas temperature,
corresponding to droplets evaporation, effect significantly
regularities of heat and mass transfer. Thus, according to [7],
if polyvidone (PVP) is added to water droplets, heat and mass
transfer as well as evaporation rate become more intensive.
The authors explain this phenomenon mainly by a change in
surface tension of droplets [8]. Surfactant concentration also
effects significantly the evaporation rate, what is proved by
many scenarios of development of heat and mass transfer
processes at variation of surfactant composition [14].
Despite long history and applied importance of this
problem, the studies in this field are far from completion. The
current work presents the results of experimental investigation
of evaporation of droplets with surfactant addition (sodium
dodecyl sulfate) in the flow of dry air with varying
temperature and velocity.
I.
EXPERIMENTAL SETUP
0
T s, C
50
o
t0 = 175 C
40
30
86
20
23
10
t, sec
0
0
25
TEMPERATURE OF DROPLET SURFACE
75
100
125
150
175
the character of temperature alteration in time is shown. For the
droplets of pure water the average temperature and its minimal
values became stable fast and almost coincided with the values
at adiabatic evaporation of liquid [17], but in the presence of
surfactant the surface temperature decreased initially, and when
the minimal value was achieved, it increased by the factor of
1.5 – 2 in comparison with pure water (Fig.2). This tendency of
temperature alteration in time at evaporation of droplets with
surfactant was also observed in experiments [14]. It can be
assumed that with a rise of particle concentration on the surface
liquid evaporation becomes slower and as a sequence, the
temperature increases.
13
12
11
Тmiddle
10
II.
50
Figure 1. Surface temperature of evaporating droplets: dark points – pure
water, light points – nanofluid.
0
TS , C
In experiments liquid droplets were suspended in the
center of the air jet flowing from a channel of the 52-mm
diameter. Air with low humidity (below 2 %) was supplied
with the velocity of 0 ÷ 6 m/s, turbulence degree was ~ 5.5 %,
and the jet temperature changed in the range of ~ 20 ÷ 200 0С.
To compensate the gravity force and avoid droplet separation,
the flow was directed vertically upwards.
Droplets of distilled water with the diameter of ~ 2 ÷ 3
мм and droplets of nanofluid, where carbon nanotubes were
used as the solid admixture, were the targets of research.
Single-wall nanotubes were made by “Carbolex” company.
They were of a random length, less than 1 m, and diameter of
1.3 nm. The initial mass content of carbon particles in a
droplet was constant K0 ~ 0.1 %. In these experiments the
droplets were located on a wire ring (wire diameter was 50
m).
In the next experiments we added surfactant to distilled
water. Sodium dodecyl sulfate, also called sodium lauryl
sulfate, attributed to the class of anion surfactants, was used as
the surfactant in these experiments [16]. Its chemical formula
is С12Н25OSO3- Na+. This surfactant is a good penetrating and
foaming agent. It is nontoxic, used in tooth pastes, food
industry and cleaning solutions. We used the solution with
mass concentration of surfactant of 0.15 %. In some
experiments at sir jet heating mass concentration of surfactant
was 0.07 %. Liquids by means of a syringe were fed to the tip
of asbestos thread; the size of this thread did not exceed 25
m, what minimized significantly conductive heat supply to
the studied object through the supporting thread.
The temperature of droplet surface and their size were
measured both for pure fluid and for fluid with carbon
nanotubes or surfactants by thermographic camera Thermo
Tracer TH7102MV at a change in the velocity and
temperature of the streamlining air jet. The detailed
description of experimental method and measurement errors is
shown in [17, 18].
9
Tmin
8
Measurement results on surface temperature of
evaporating droplets are shown in Fig. 1 for different
temperatures of the air flow. It can be seen that the surface
temperature becomes stable fast and takes the equilibrium
value with consideration of heat losses to the wire supporting
this droplet [19, 20]. At this, the temperature of nanofluid
almost coincides with the temperature of pure water in the
studied range of ambient air temperatures, what proves the
absence of nanoparticle addition influence on thermodynamic
parameters of evaporation process. The temperature of
droplets was not measured in [7], and this excludes the
possibility of their even qualitative comparison with data of
the current study.
Simultaneously the presence of surfactant leads to
significant changes in temperature of evaporating surface.
This can be seen from Fig. 2, where the effect of surfactant on
7
t , sec
6
0
30
60
90
120
150
180
Figure 2. Surface temperature of evaporating droplets: dark points – pure
water, light points – water and 0.15 % of surfactant; Тс = 19.8 0С, U0 = 3.2 m/s.
III. INTENSITY OF DROPLET EVAPORATION
Experimental data on the rate of liquid droplet evaporation
were generalized using the method presented in [17]. From the
equation of heat balance on the surface of evaporating droplet
T 

   Ж    T0  TЖ   jW L
r 

7
d
3/2
at adiabatic evaporation
j w L = α∙(T0 – Tl)
6
and from the use of relationship for its heat transfer coefficient
[21]
Nu = 2 + 0,53∙Re 0.5∙Pr1/3
where Fo = t ∙ao / d02 is Fourier number, Ku = r / [cpo
∙(To - Ts)] is Kutateladze criterion of phase transformation, r
and cpo are latent heat of vaporization and heat capacity of gas,
and Ts and T0 are the temperature of vapor-gas mixture on the
droplet surface (saturation line) and in the ambient air flow,
respectively.
In contrast to the known square law of evaporation (d2
law) [22], valid for the low values of Reynolds number (Re0→
0 and Nu = 2); at high values of Re as it follows from (2), law
(d / d0)2 works.
In this manner a change in droplet diameter at evaporation
was considered. The change in size of pure water droplets and
droplets with 0.15 % of nanotubes is shown in Fig. 3 for the jet
temperature of 23 0С; in Fig. 4 the jet temperature is 175 0С.
According to both figures, the addition of solid admixture did
not effect evaporation intensity (the angle of inclination,
characterizing evaporation rate, was kept almost in all
experiments).
t, sec
3
0
10
20
30
40
50
60
Figure 4. Evaporation regularity for water and nanofluid droplets at То =
1750С, U0 = 4 m/s.
Generalization of experimental data shows that results of
experiments with water and nanofluid droplets are described
by linear empirical dependence
(d / d 0)3/2 = 1 – 0.676∙K.
(3)
These data are shown in Fig. 5. It is obvious that in this form
all experimental data have a tendency to generalization. At
this, calculation by formula (3) almost coincides with
calculation of evaporation of water droplets at their convective
streamlining [17], with consideration of additional heat supply
through thermocouple wires supporting the droplet [19 - 20].
1.5
(2)
Nanofluid
4
(d/do)
Re 0  Fo
,
Ku
0.. 5
(d / d 0)3/2 = 1 – A∙
5
(1)
with prevalence of convective transfer (Re >> 1, in
experiments the Reynolds number was varied within Re0 =
500 ÷ 2000) we can derive the following dependence for the
droplet diameter
Water
1.0
0.9
1 - 0.676 K
0.8
0.7
0.6
8
0.5
23
80
0
175 С
3/2
9
d
Water
droplets
nanofluid
0.4
7
0.0
Nanofluid
0.2
0.4
0.6
K = Re
0.5
0.8
Fo / Ku
6
Figure 5. Generalization of experimental data on evaporation of water
and nanofluid droplets
5
4
t, sec
Water
0
50
100
150
200
Figure 3. A change in size of water and nanofluid droplets at air
temperature То = 23 0С, U0 = 4 m/s.
If a surfactant is added, the rate of droplet evaporation
decreases. This can be seen from Fig. 6, where measurements
of droplet diameter alteration in time are shown. The angle of
experimental data inclination is significantly lower in the
presence of surfactant as compared to pure fluid, what proves
the suppression of evaporation processes.
REFERENCES
d
1.5
3,5
2,5
2,0
water
1,5
1,0
t , sec
-20
0
20
40
60
80
100
120
140
160
180
200
220
Figure 6 Evaporation intensity for water droplets and water droplets with
surfactant additions at air temperatures of 19 and ~ 80 0C, the flow velocity is
4.3 m/s.
Experimental data on evaporation of water droplets with
surfactant shown by expression (2) are presented in Fig. 7. In
this form experimental results are generalized and described
satisfactorily by linear correlation dependence
(d / d 0)3/2 = 1 – 0.552∙K.
(4)
1,0
( d / d0 )
1.5
S.S. Sazhin, “Advanced models of fuel droplet heating and evaporation,”
Progress in Energy and Combustion Sciense, vol. 32, 2006, pp. 162214.
[2] P.L.C. Lage., R.H. Rangel., C.M. Hackenberg,. “Multicomponent heat
and mass transfer for flow over a droplet,” Int. J. Heat and Mass
Transfer, vol. 34, 1993, pp. 3573-3581.
[3] B.H. Shan, R. Darby, “The effect of evaporative heat transfer in vertical
film flow,” Int. J. Heat and Mass Transfer, vol. 16, 1973, pp. 1889 –
1903.
[4] S.U.S. Choi, “Nanofluids: A new field of scientific research and
innovative applications, ”Heat Transfer Eng., vol. 29, 2008, pp. 429 441.
[5] V.I. Terekhov, S.V. Kalinina, V.V. Lemanov, “The mechanism of heat
transfer in nanofluids: state of the art (review). Part 2. Convective heat
transfer”. Thermophysics and Aeromechanics, vol. 17, 2010, pp. 157171.
[6] S.K. Das, S.U.S. Choi, W. Yu, T. Pradeep, ”Nanofluids. Science and
Technology.” Jone Wiley & Sons Inc., Publication. 2008. -572 P.
[7] R.-H. Chen, T. X. Phuoc, D. Martello, “Effect of nanoparticles on
nanofluid droplet evaporation,” Int. J. Heat and Mass Transfer, vol. 53,
2010, pp. 3677 - 3682.
[8] R.-H. Chen, T. X. Phuoc, D. Martello, “Surface tension of evaporating
nanofluid droplets,” Int. J. Heat and Mass Transfer, vol.54, 2011, pp.
2459 - 2466.
[9] Y. Gan, L. Qiao, “Evaporation characteristics of fuel droplets with the
addition of nanoparticles unde natural and forced convection,” Int. J.
Heat and Mass Transfer, vol. 54, 2011, pp. 4913-4922.
[10] R.S. Bradley, “The rate of evaporation of micro-drops in the presence of
insoluble monolayers,” J. Colloid. Sci., vol. 10, 1955, pp. 571-575.
[11] B.V. Deryagin, Yu.S. Yu.S. Kurgin, S.P. Bakanov, "About effects of
monolayers on a drop evaporation,” Doklady Akademii Nauk, 1960,
Vol. 135, pp. 1417- 1420 (in Russian).
[12] V.A. Borzilov, N.V. Klepikova, V. M. Merkulovich “Effect of a
surfactants on growth and evaporation drops,” Meteorology and
Gidrology, 1979, № 5, pp. 41 – 48 (in Russian).
[13] B.V. Deryagin, Yu.S. Kurgin, “Unsteady drop evaporation with adsorbed
layer,” Doklady Akademii Nauk, 1964, Vol. 155. pp. 644 – 646 (in
Russian).
[14] P.A. Sadd, J.A. Lamb, R.Clift, “The effect of surfactants on heat and
mass transfer to water drops in air,” Chemical Engineering Science, vol.
47, No 17/18, 1992, pp. 4415-4424.
[15] A.M. Hashem, “Effect of surfactants on mass transfer coefficients of
single liquid drops,” Alexandria Engineering Journal, vol. 44, 2005, pp.
477 – 486.
[16] Surfactants and washing-up liquids // Handbook. Ed. Abramzon A.A.Moscow. 1993 (in Russian).
[17] V.I. Terekhov, V.V. Terekhov, N.E. Shishkin, K.Ch. Bi, “Heat and mass
transfer in disperse and porous media experimental and numerical
investigations of nonstationary evaporation of liquid droplets”, J. Eng.
Physics and Thermophysics, vol. 83, 2010, pp. 883-890.
[18] V.I. Terekhov, N.E. Shishkin, “Adiabatic evaporation of binary liquid
mixtures on the poous ball surface,”
Thermophysics and
Aeromechanics. 2009, Vol. 16, pp. 239-245.
[19] N.A. Fuhcs, Evaporation and droplet growth in gaseous media. The
Pergamon Press, Oxford. 1959. 72 pp.
[20] T. Harada, H. Watanabe, Y. Suzuki, H. Kamata, Y. Matsuhita, H. Aoki,
T. Miura, “A numerical investigation of evaporation characteristics of
fuel droplets suspensed from a thermocouple,” Int. J. Heat and Mass
Transfer, vol. 54, 2011, pp. 649 - 655.
[21] W.E. Ranz and W.R. Marshall, “Evaporation from drops,” Chem. Eng.
Prog., vol. 48, 1952,pp. 141-146 and 173 - 180.
[22] D.B. Spalding, Some fundamentals of combustion. London, Butterworth’s. - 1955.
[1]
3,0
0,9
0,8
0,7
0,6
1 - 0.552 К
0,5
0,4
К
0,3
0,0
0,2
0,4
0,6
0,8
1,0
Figure 7. Generalization of experimental data on evaporation of droplets
with surfactant.
If we compared data in Fig.7 with results obtained for
pure water (Fig.5) or linear relationship (3) with (4), we can
made the important conclusion that surfactant addition leads to
a significant decrease in the rate of evaporation. A decrease in
inclination angle of linear approximation is ~ 35%, what
finally gives the same difference between the values of
transverse matter flux on the surface of evaporating droplet as
well as between the coefficients of heat and mass transfer.
Results of the current study coincide qualitatively with data of
[14,15], where a decrease in evaporation rate of droplets with
surfactant additions in the stationary gas medium was also
determined.
The work was financially supported by the Russian
Foundation for Basic Research (project-11-08-91156-GFEN).