Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 6.2.2 - Flow instabilities in ethanol sessile drops
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 Material Information
Title: 6.2.2 - Flow instabilities in ethanol sessile drops Particle Bubble and Drop Dynamics
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Sobac, B.
Brutin, D.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: drop evaporation
flow motion
instabilities
infrared visualization
 Notes
Abstract: Thanks to a recent increase in space resolution and temperature accuracy of infrared (IR) camera device, it is now possible to perform thermal visualizations of sessile drops under evaporation. Using infrared techniques, we can access local thermal motions inside millimetric drops without perturbing the internal mechanisms. In the full paper, we will provide a literature review of experimental, numerical simulation and theoretical work recently perform on sessile drop evaporation. We will also detail the experimental setup which has been elaborated to realize these thermal observations. Using infrared and visible video recording, we can follow respectively the evolution of the motion inside the drop and the drop shape during evaporation. Using a heat fluxmeter placed below the drop, we can analyze the heat transfer between the substrate and the drop. We will completely describe the evaporation process based on a reference experiment and evidence the existence of several phases during this process. Then, we will focus on thermal-convective instabilities with notably the evolution law of the number of cells. We will evidence the influence of substrate temperature and drop size on these instabilities. Finally, we will present a scaling law which will allow us to better understand the drop evaporation and to determine the cell disappearance criteria, and to obtain an acceptable agreement with the IR visualization.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Resource Identifier: 622-Sobac-ICMF2010.pdf

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


Flow instabilities in an ethanol sessile drop


B. Sobac and D. Brutin

IUSTI Laboratory Ecole Polytechnique Universitaire de Marseille
Aix-Marseille University, Marseille, 13453, FRANCE
benjamin.sobac@polytech.univ-mrs.fr


Keywords: drop evaporation, flow motion, instabilities, infrared visualization




Abstract

Thanks to a recent increase in space resolution and temperature accuracy of infrared (IR) camera device, it is now
possible to perform thermal visualizations of sessile drops under evaporation. Using infrared techniques, we can
access local thermal motions inside millimetric drops without perturbing the internal mechanisms. In the full paper,
we will provide a literature review of experimental, numerical simulation and theoretical work recently perform on
sessile drop evaporation. We will also detail the experimental setup which has been elaborated to realize these thermal
observations. Using infrared and visible video recording, we can follow respectively the evolution of the motion
inside the drop and the drop shape during evaporation. Using a heat fluxmeter placed below the drop, we can analyze
the heat transfer between the substrate and the drop. We will completely describe the evaporation process based on
a reference experiment and evidence the existence of several phases during this process. Then, we will focus on
thermal-convective instabilities with notably the evolution law of the number of cells. We will evidence the influence
of substrate temperature and drop size on these instabilities. Finally, we will present a scaling law which will allow us
to better understand the drop evaporation and to determine the cell disappearance criteria, and to obtain an acceptable
agreement with the IR visualization.


Nomenclature


Roman symbols
Cp heat capacity (J.kg 1.K 1)
d drop diameter (m)
h drop height (m)
m drop mass (kg)
Nc number of thermal-convective cells (-)
Lc capillary length (m)
L, latent heat of vaporization (J.kg 1)
P power (W)
Pr Prandtl number (-)
Qw heat flux density (W.m 2)
t time (s)
T temperature ( C)
V drop volume (L)
Greek symbols
e emissivity (-)
p viscosity (Pa.s)
A heat conductivity (W.m- .K 1)
a surface tension (N.m 1)


0 contact angle (o)
g density (kg.m 3)
Subscripts
a atmospheric
evap evaporation
1 liquid
s substrate
sat saturation
v vapor


Introduction

Drop evaporation is a simple phenomenon but still
unclear concerning the mechanisms of evaporation.
A common agreement of the scientific community
based on experimental and numerical work evidences
that most of the evaporation occurs at the triple line.
However, the evaporation mass flow rate is still em-
pirically predicted due to the lack of knowledge on
the convection cells which develop inside the drop.
In the present paper, we present recent experimental











results obtained using a FLIR SC-6000 infrared camera
coupled with a microscopic lens giving 10 pm of spatial
resolution to observe the evaporation of sessile drops.
For the present study, we use ethanol which has the
particularity to be semi-transparent in the infrared
notably in the range of the camera which is 3 to 5
pm. It is then possible to follow the thermal motion
inside the drop and the evaporation heat flux using a
heat flux-meter placed below the drop. This experiment
allows us to underline the general existence of four
steps during the evaporating process according to the
presence of convective cells or a lack of. We evidence an
evolution law for convective cells and influences of ge-
ometrical and energetic parameters on these instabilities.

In spite of a lack of knowledge in mechanisms of
evaporation, it's today a common agreement in the
scientific community that most of evaporation appears
at the triple line and that evaporation of a sessile drop is
the coupling between various mechanisms :

the conduction heat transfer into the wall,

the convective heat transfer induced by the surface
tension gradients and the natural convection due to
the temperature gradients in the liquid drop,

the liquid/wall molecular interactions, coupled with
the substrate surface roughness, which tend to mod-
ify the droplet wettability, and then, the wetting sur-
face area for identical drop volume,

the vapor mass diffusion around the drop.

First studies about evaporation observed the profile
and mass evolution of an evaporating sessile drop. Pick-
nett & Bexon (1977) (1) distinguished then different
modes of evaporation: constant contact angle mode with
the receding of the contact line at constant contact angle,
constant contact area mode with reducing of the contact
angle at a fixed contact line or mix mode. Birdi et al.
(1989) (2) tried to obtained the evaporation rate and
the residual mass function of geometrical parameters.
These studies showed then the narrow link between
evaporation and triple line, contact angle dynamics.
Whereas some authors (3) looked at the influence of
contact angle on evaporation, other like Bourges &
NIi.ii.ili.,in (1995) (4) examined the influence of evapo-
ration on contact angle. Generally, previous works were
carried out using the spherical cap geometry. However,
when the gravity effect becomes predominant, the shape
is distorted. Erbil & Meric (1997) (5) took account of
this and developed a model for ellipsoidal cap geometry.
In 2002, Hu & Larson (6) investigated numerically the
evaporation of a pinned contact line droplet. Using
Laplace equation, they obtained the vapor concentration


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


around the drop and checked that the evaporation flux
becomes more strongly singular at the edge. Stodtke at
al. (2008) (7) developed a model including the effects of
surface tension, evaporation, thermocapillarity, gravity,
disjoining pressure, as well as heat transfer with the
substrate in order to describe the dynamics of volatile
liquid droplets on heated surfaces. There is a good
agreement with experiments as long as the lubrification
assumption is valid. However, thermal aspects of the
phenomenon have never really been approached in a
systematic way. Ristenpart & al. (2007) (8) investigated
theoretically and experimentally the thermal Marangoni
flow and established that the direction of the flow
depends on the relative thermal conductivities of the
substrate as well as the contact angle. Dunn & al. (2009)
(9) demonstrated that the evaporation of a droplet is
strongly influenced by the thermal conductivity of the
substrate.

The first observation of an internal flow motion in
an evaporating drop was realized by Hegseth (1996)
(10). Using 2pm diameters particles of polystyrene
as tracers, the author showed that natural convection
can appear in an evaporating drop of methanol due to
surface tension gradient. In 2002, a new laser shad-
owgraphy method, permitting to measure the dynamic
contact angle of a sessile drop on a non transparent
metal substrate and simultaneously to visualize flow
motions inside the drop, was presented by Zhang &
Chao (11). Thanks to their method, the authors clearly
observe convective flow during drop evaporation in
some cases (for n-pentane and freon 113). Deegan & al.
(2000) (12) explained mechanisms to the origin of the
"coffee ring" effect by the particles migration to the
edge of the drop due to the creation of an outward flow,
the evaporation flux been more important close to the
triple line. They also used particule tracking in order
to measure the height-average radial velocity. This is
also confirmed by the theoretical and numerical work
of Petsi & Burganos (2006) (13) which showed, in the
case of kinetical controlled evaporation, for hydrophilic
substrates, the flow inside the evaporating liquid is
directed towards the edges for pinned contact lines,
thus, promoting a coffee stain effect. The opposite
flow direction is however observed for depinned contact
lines.

Other kinds of experimental visualizations can be
done using IR thermography. In fact, infrared mea-
surements are a non intrusive thermal measurement
that have the advantage to allow the observation of
thermal phenomenon during drop evaporation without
disturbing it. The difficulty is then to correctly interpret
the infrared flux measured by the camera with respect








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010



Table 1: Publications related to sessile drop evaporation [numerical simulation (num.), experiments (exp.) or theoret-
ical investigations (th.)]


Authors
Piknett
Birdi
Bourges-Monnier
Hegseth
Erbil
Deegan
Erbil
Hu
Zhang
Savino
Petsi
Ristenpart
Tarozzi
Sefiane
Sodtke
Dunn


Approach
Exp.
Exp.
Num. and Exp.
Exp.
Exp. and Th.
Exp. and Th.
Exp.
Num. and Exp.
Exp.
Exp. and Num.
Th
Exp.
Exp.
Exp.
Exp. and Th.
Exp.


Fluid Substrate
Methyl-acetoacetate PTFE
Water PTFE
Water, N-decane PTFE, Glass, Epoxy
Ethanol
Water PMMA
Acetone, Methanol, Toluene, Ethanol Glass, Metal, Polyethylene, Teflon, Mica, Ceramic, Silicon
N-butanol, Toluene, N-nonane PTFE
Water Glass
Silicon Oil, R113, Ethanol Anodized glass
Silicon oil, Hydrocarbones, Water Several metals


Several volatile liquids
Water
Water, Ethanol, Methanol, FC-72
Water
Acetone, Methanol, Deionized water


PDMS
Black paint on infared materials
PTFE, Ceramic, Titanium, Copper
Stainless steel
Aluminium, Titanium, Ceramic, PTFE


to the radiative properties of the observed fluid. Indeed,
the liquid sample may be semi-transparent in some
spectral measurement ranges, making it difficult to
convert the measured luminance into surface temper-
ature. Some authors (14), (15) choose not to observe
directly the fluid but prefer observing the rear face of
the plate on which the drop is laying. The 'drop side'
of this transparent BaF2 plate is coated with an opaque
emissive paint, making it possible to measure its surface
temperature that is also the temperature of the drop
base. In other publications, authors observe directly
the fluid (16), (17), (18). Assuming the opacity of the
various observed fluids (water, ethanol, n-pentane) in
the long wave spectral range of the camera (around
9-10pm) they only need the fluid emissivity to deduce
the surface temperature of the liquid. This kind of
method allows for example to Savino & al. (2004) to
carry out the study of Marangoni effects during the
evaporation of pendant droplets. They showed that
marangoni effects have a large influence on velocity and
temperature distributions on the heat transfer between
the drop and the plate whereas, in generally, previous
works neglected thermocapillary effects. In 2008,
Sefiane & al. (19) observed at the free surface of sessile
drops under evaporation (water, ethanol, methanol and
FC 72), the presence of patterns which were interpreted,
in some case, as hydrothermal waves (methanol and
ethanol). The evolution of these waves and the influ-
ence of temperature and thermal conductivity of the
substrate on HTWs were observed (20). The number of
HTWs seems to decrease with a linear variation during
evaporation. However, as we will present later, ethanol
and methanol are semi-transparent fluids in IR field.


The information obtained from the IR visualization are
consequently volumic and do not only come from the
surface.

The goal of our experiment is to gain a better un-
derstanding of sessile drop evaporation and particularly
to understand the influence of thermal-convectives
instabilities on the evaporation process.



Experimental set-up

An experimental device was designed in order to
follow and characterize the drop evolution during its
evaporation from 3 points of view, namely: kinetics,
heat transfers and flow motion associated with this
phenomenon. This device includes a heating control
support where the drop is deposed. The entire device is
placed in an experimental cell so as not to be perturbed
by natural external convection and comprising an
instrumentation dedicated to thermal measurements
(temperature, density flux). Pressure conditions are not
imposed and the experiment weas designed in order to
not be in a saturated vapor condition. The environmental
conditions (temperature, pressure, moisture) are mea-
sured permanently. A schematic diagram illustrating the
experimental set-up is shown in Figure 1.

The heater is a cylinder block of aluminum of 10 mm
in diameter by 8 mm long. A heating resistance is stuck
in between the Acetal cylinder and the aluminium. The
latter is coupled with a regulator PID in order to main-
tain a constant imposed temperature (between 25 C and








7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


25 ml ethanol syringe


FLIR SC6000
infrared camera
with 10pm lens



PTFE
substrate
/


70 mm


Aluminum W

- Acetal -
P


JAI BM500GE
visible camera
with 4iw m lens


Valve for Pressure Degasing
air refilling transducer valve

Figure 1: Experimental setup made of a test cell, a syringe pump and two cameras (visible and IR).


450C) of the substrate. A flux-meter, located at the top
of the aluminium cylinder, allows us to obtain the heat
flux transmitted to the drop. It is painted in black using
a black metal paint mast in order to have an emissivity
close to 1. A PTFE sheet of 200 pm is attached to the
flux-meter, this surface will receive the posed drop.
The PTFE sheet is regularly changed to avoid any
cleaning issues and to guarantee the reproducibility of
the surface quality. Also, a cleaning procedureusing
optical paper and compressed air is performed between
each experiment in order to remove any residual de-
position that can occur after an evaporation. Finally,
the reproductibility of the experimental results has
been checked by realizing the same experiment several
times. This also attests the cleanliness of the experiment.

The liquid investigated using the infrared camera is pure
ethanol. Ethanol has been used for its semi-transparency
properties in the infrared wavelength of the SC6000
infrared camera. Measurements have been performed
using a FTIR NICOLET Nexus 560 spectrophotometer
to access the monochromatic transmitivity of a given
thickness of fluid in the spectral range of 2.5 to 14 /m.
We analyse and extract only the data in the range of
3 to 5 pm which correspond to our infrared camera
wavelength band. The transmitivity measurements
are performed three times. For each measurement, a
background measurement is first carried out consisting
in measuring the radiative power that is transmitted by
the empty cell. The three independent measurements
enable us to provide the ordinate error bar which is the
standard deviation. On Figure 2, we provide the global
emissivity in the infrared wavelength range of 3 to 5 /m.
The optical fluid thickness investigated are in the range
0.2 to 2.0 mm which correspond to the starting range
of drop height encountered. The emissivity variation
evidenced with this figure can be fitted by an decreasing


exponential law given below c = 1 exp(-A x)
where x is the fluid optical thickness and c is the global
fluid emissivity. The constant 'A' for ethanol is 1.85
mm 1nn 2.1'.

Physical properties of the ethanol at 25 C and 1
atm are the following : L = 789 kg.m 3; v 1, 50
kg.m 3; Cp 2845 J.kg 1.K 1; Lv 841 kJ.kg 1;
lambda 0,140 W.m .K 1; = 1,095 mPa.s;
a 22, 0 mN.m 1; Tst 78, 0C; L 1, 69 mm &
Pr = 22, 3.


1,1
1,0-
0,9-
0,8-
-
0,7-
-
i 0,6-
T
E 0,5-
E
5 0,4-
o -
0,3-
CD'~


0,5 1,0 1,5 2,0 2,5 3,0
Optical Fluid Thickness (mm)


Figure 2: Ethanol infrared properties in between wave-
lengthes of 3 to 5 pm.


An optical diagnosis allowing video acquisition is
obtained using a camera JAI BM500GE 2456 by 2058
pixels with a maximum full frame rate of 15 frame/sec
coupled with a microscope lens VZM100i. This optical
diagnosis allows a visualization of the drop at the side


--@-


Test cell


-----------------


N_


I- k











with a spatial resolution of 4 pm. After having selected
an area of interest on the image, an analysis is carried
out in order using a commercial software (Kruss -
DSA3) to determine the contact angles left and right,
the height and the diameter of damping. Surfaces and
volume are calculated by carrying out an integration
with the axisymmetric assumption of the drop.

The infrared diagnosis is carried out using a camera
FLIR SC6000 (640 by 512 pixels) coupled to a mi-
croscope making it possible to reach a resolution of
10 pm so a field of view of 6.4 mm x 5.12 mm. The
infrared camera is vertically assembled at the top of the
drop to visualize. The copper fluxmeter is painted in
black in order to obtain an almost null reflectivity and a
homogeneity of the temperature of the support from the
start to the finish of the evaporation lower by 1 C.
The image thus obtained on the level of the camera is
calibrated in order to validate the thermal environment
around the drop and the exact emissivity of the support.

A T-type thermocouple allows us to get the exper-
imental cell temperature. It is recorded at 1 Hz. The
heat fluxmeter with tangential gradient, made by
CAPTEC, has a diameter of 10 mm, a thickness of
0.8 mm and a sensitivity of 0.725 pV.W .m2. It is
attached at the top of the aluminum cylinder and it is
instrumented in its center by a T-type thermocouple.
This last device permits us to obtain simultaneously the
substrate temperature and the heat flux transmitted to
the substrate. All delivered signals are recorded on an
acquisition station HP34970A.

The IR observations of a semi-transparent fluid
give us for now only qualitative informations i.e a better
understanding of the thermal and fluid motion behavior
inside a drop doing evaporation. The IR heat-flux
transmitted to the IR camera depends on the form factor
and the emissivity (which depend on the thickness of
the drop). All these parameters are changing due to the
mass transfer.


Reference experiment

In this section, we will completely describe and ana-
lyze the evaporation of a sessile drop of ethanol using
visible information, infrared visualization, heat-flux and
temperature measurements from the heat fluxmeter. In
this experiment, the substrate temperature is imposed
at Ts 34,5 C and we have a temperature gradient be-
tween the substrate and the air AT 16 C. The infrared
camera allows us to check thermal homogeneity of our
substrate before the experiment. If the maximum tem-
perature difference is below 1 C, we can carry out the


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


experiment. Figure 3 shows the evolution of different
informations obtained: geometrical parameters from the
visible video, fluid motion from infrared measurements,
the temperature of the substrate and the power from the
fluxmeter. The considered power is the power absorbed
by the evaporating drop at constant temperature. It is ob-
tained by removing the natural convection contribution
which is transferred from the flux meter to the air (since
the drop diameter is below the flux meter diameter).
According to this information, we can observe that the
process of evaporation is composed by four phases ac-
cording to the presence or lack of thermal-convective in-
stabilities:

Phase 0 Drop warming up The start of the
experiment is defined as the initial contact of the
drop on the substrate. The first two seconds of
this experiment are characterized by a transition
phenomena; the drop which was initially at room
temperature is posed on a warm surface; the
drop is first heated to reach almost the substrate
temperature, that is the first step of the phenomena
is mainly driven by the fluid heat capacity.


Phase 1 Drop evaporation The power reaches a
maximum value which corresponds to the begin-
ning of our evaporation investigation. At the same
time, we can observe using infrared visualization
the appearance of thermal-convective instabilities
that we have decided to call in a general way
'convection cells'. The drop is formed by a colder
center surrounded by these convection cells. It
is then possible to follow clearly its evolution.
We observe during this period that the number of
convective cells is decreasing overtime like the
power. The evolution of the convection cells will
be tackled later.


Phase 2 Transition This phase begins with
the destabilization of the center of the drop and
finishes with the complete disappearance of the
convection cells. It is difficult to follow precisely
the number of these cells during this phase.


Phase 3 Film evaporation The last phase of
evaporation is characterized by the non-presence
of the convection cells. The evaporation process is
then mainly driven by conduction. The shape of
the drop seems to be more a film.


In this reference experiment, we can also observe
different modes of evaporation. During the first 40












seconds, the evaporation occurs at constant diameter
with a decreasing of the height and the contact angle
(il'iiilcd drop) and during the second phase we observe
an evaporation with height constant, the drop recedes.
In phase 3, both the contact angle and the contact area
are decreasing.

The perturbations observed in the power measure-
ment curves are simultaneous with variation of the
temperature imposed. So, this is due to the PID regula-
tion.


0 20 40 60 80 100 120 140 160 180
46,5 "
31,0 Phase3
5 Phase Phase 2

35
30
25 A
20 "%-|



23
1


0,8
0,6 ^ ~~-~- -L _"
0,4 3
0,2 3
0,0



0,0 i . I i i i i . .
1,0
0,6 3
0,4
0,2
0,0
35,0
34,5
34,0 -
33,5 . .
0 20 40 60 80 100 120 140 160 180
time (s)


Figure 3: Evaporation of
T, 34, 5C.
mm, V 7 iL,
0L 37, 6,R


an ethanol sessile drop at
[d 4,7 mm, h = 0,75
AT 16C, tevap 187 s,
= 38, 3 and 0YL 36, 6].


Thermal-convectives instabilities

In the first phase of evaporation, we can clearly observe
thermal-convective instabilities and follow the number
of these cells. Fig 4 a) shows an evolution of the number
of convective cells versus dimensionless time. The error
bars signify uncertainties in the visual observation of the
number of convection cells. The figure reveals that the


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


number of convection cells is decreasing and that can
be understood by the geometrical variation of the drop
due to evaporation. This evolution seems to follow a
power trend that is confirmed by the linear trend of the
evolution presented with a log-log scale in fig.4 b). In
all experiments, the evolution of the these instabilities is
decreasing with a power law Nc(t) atb.
In the second phase of evaporation, the decreasing of
the drop volume causes the destabilization of the center
of the drop. It appears difficult to follow the instabilities
in this phase. However, when it's possible, the decline
does not follow the same law and seems sharper.


a)

35.
0
a(D
-Q 30.
E
t-


0
S25.
0

0
S20
C


0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40
Dimensionless time t/tevap(-)


Figure 4: Convective cells number variation observed
during the evaporation of an ethanol drop with
an initial diameter of 4,67 mm, posed on a
PTFE substrate at 39, 6C. a) Normal scale.
b) Log-log scale.


An experimental campaign varying two parameters:
the initial drop diameter and the substrate temperature
has been performed. This allows to understand the in-
fluence of geometrical and energetic parameters on the
evaporation of a drop. Even if the convection cells num-
ber trend evolution appears to be the same in all cases,
we can remark:


at a fixed imposed temperature, the number of cells
increases as it is shown on the Fig. 5 in log- log
scale.


at a fixed diameter, the number of cells increase
with an increasing temperature gradient.


SExperimental data
j Power law fit y=ax"







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


E
J-
C
a)

Z


0,05 0,1
Dimensionless time t/t eva(-)


Figure 5: Convective cells number variation observed
during the evaporation of an ethanol drop
posed on a PTFE substrate at 30 C with dif-
ferent initial diameters (Log-log scale).


Scaling law analysis

The typical results obtained in Fig. 3 have been also per-
formed for several drop diameters and substrate temper-
atures. By plotting the power transferred to the drop as
a function of the non-dimensional evaporation time, we
observe similar behaviors. Using the infrared camera,
we observed that the drop is at first driven by convection,
then later by conduction. The use of the Nusselt number
to scale all the data is possible. We define the following
Nusselt number for our case based on Equation 1 given
below:

h.d Q d 2P
Nu AT 7dAT (1)

Our reference surface is the drop interface, assuming
for our small drops the capillary length is a spherical
cap (Set = d), where d is the initial drop diameter.

On Figure 6, we plot only the data of phases 1 to 3.
We remove that of phase 0 which does not correspond
to the drop evaporation. We can observe a good scaling
agreement of all the data with a single evolution, see
the dashed line. The transition at Nusselt equals to 1
corresponds to about 55-60% of the total evaporation
time. In IR visualization of our experiments, the dis-
appearance of convection cells is observed between 40
and 55'. according to the situation. More investigations
are required to enforce this point. Regarding the first
part of the evaporation, the Nusselt number is greater


2,5- mm
AT=11C&d=4,Omm
SAT=16C & d=3,3mm
SAT=16C & d=3.4mm
2,0, AT=16oC & d=4,8mm
AT=20C & d=2,7mm
AT=20C & d=4,4mm
1,5- AT=20C & d=4,7mm
-- Mean linear fit

1,0onvt


0,5

convective conductive
0,0 1 -


0,0 0,2 0,4 0,6 0,
Dimensionless time t/tevap (-)


8 1,0


Figure 6: Nusselt number evolution for different sub-
strates temperatures and drops diameters.


than 1 which corresponds to the heat transfer driven
by convection; while for the second step, the Nusselt
number is below 1. This last situation corresponds to
the observed disappearance of the convective cells and
the heat transfer is driven by conduction.



Conclusion and on-going-work

In this paper, we provide a literature introduction of ex-
perimental, numerical simulation and theoretical work
recently performed on sessile drop evaporation. We also
detail the experimental setup which has been elaborated
to realize thermal and fluid motion observations. Using
infrared and visible video recording, we follow respec-
tively the evolution of the motion inside the drop and
the drop shape during evaporation. Using a heat fluxme-
ter placed below the drop, we analyze the heat trans-
fer between the substrate and the drop. We completely
describe the evaporation process based on a reference
experiment and evidence the existence of four phases
during this process. We evidence for all experiments a
power law on the convective cells evolution with coeffi-
cients related to the experimental conditions. Moreover,
we show that the evaporation is characterized by a Nus-
selt number which evidences the competition between
the convective and conductive heat transfers. Conse-
quently, the first stage of the drop evaporation is driven
by the internal convection of the drop since the Nusselt
number is greater than one, whereas for Nusselt num-
bers below one, the heat transfer is only conductive. This
analysis allow us to obtain transition criteria which is in
acceptable agreement with the transition observed using











the IR camera. In a second step, to improve the thermal
measurements accuracy and to avoid the influence of the
PID regulation, we are going to study the influence of
the aluminum cylinder volume on the drop evaporation
dynamics when the cylinder is placed below the drop.

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7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 -June 4, 2010


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