Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 13.2.1 - Droplet internal recirculation measurement by micro-PIV
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 Material Information
Title: 13.2.1 - Droplet internal recirculation measurement by micro-PIV Micro and Nano-Scale Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Vetrano, M.R.
Lebeau, F.
Parente, A.
Riethmuller, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: droplet formation
micro-PIV
 Notes
Abstract: This communications aims to study the feasibility of micro-PIV measurements inside bodies having a curved shape. In particular the effect of optical aberration, as astigmatism and measurement plane deformation, is analyzed. Measurements of the flow within a jet resulting from a capillary tube with piezoelectric control are carried out. The liquid recirculation inside a droplet detached from this jet is also observed. Sub-micrometric fluorescent particles are employed in low concentration as seeding in order to have good signal to noise ratios and the ensemble averaging method is used to increase the height of the correlation peaks. Preliminary numerical simulation conducted to validate the experimental measurements are also presented.
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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Volume ID: VID00319
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1321-Vetrano-ICMF2010.pdf

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


Droplet internal recirculation measurement by micro-PIV


M.R.Vetrano* F. Lebeau! A. Parente* and M. Riethmuller*

*von Karman Institute for Fluid Dynamics, Chauss6e de Waterloo 72, B 1640, Rhode Saint Genbse, Belgium
SFacult6 Universitaire des Sciences Agronomiques de Gembloux -UMC, 2 passage des d6port6s, 5030 Gembloux, Belgium
vetrano@vki.ac.be, f.lebeau@ulg.ac.be, parente@vki.ac.be and riethmuller@tvki.ac.be
Keywords: Droplet formation, micro-PIV




Abstract

The abstract goes here. This communications aims to study the feasibility of micro-PIV measurements inside bodies
having a curved shape. In particular the effect of optical aberration, as astigmatism and measurement plane defor-
mation, is analyzed. Measurements of the flow within a jet resulting from a capillary tube with piezoelectric control
are carried out. The liquid recirculation inside a droplet detached from this jet is also observed. Sub-micrometric
fluorescent particles are employed in low concentration as seeding in order to have good signal to noise ratios and the
ensemble averaging method is used to increase the height of the correlation peaks. Preliminary numerical simulation
conducted to validate the experimental measurements are also presented.


Introduction


The micro-PIV consists in an extension of the standard
Particle Image Velocimetry technique to the study of
flows at micrometric scale. This technique has been
presented the first time by Santiago et al. at the end
of nineties [Santiago & Wereley & Meinhart & Beebe
& Adrian (1998), Meinhart & Werely & J. G. San-
tiago ( 1999)]. In his first tests, Santiago where us-
ing 300 nm fluorescent particles to observe an Hele-
Shaw flow around a cylindrical obstacle of 30 pm diam-
eter. Since its first application the micro-PIV technique
shown his huge capabilities in the study of microscale
fluidics as flows behavior in inkjet printhead [Meinhart
& Zhang (2000)]or turbulent flows in squared channels
[Li & Olsen (2006)].Micro-PIV is also used to study
microfluidic systems of different shapes, as an example
studies of flows in cylindrical channels or in embryonic
avian heart [Venneman et al. (2006)].While many stud-
ies have been conducted to analyze the advantages and
the disadvantages of the micro-PIV technique in squared
channels [Meinhart & Zhang & Werely & Gray (2000)
Meinhart & Werely & Santiago (2000)], a feasibility
study of the microPIV technique applied to curved body
is still missing. In this paper it is not pretended to give
an general answer on the feasibility of the technique ap-
plied to all the possible shapes. The paper focuses on
the analysis of the optical aberrations encountered in the
measurements of flow field inside a droplet during its


formation through the breakup of a liquid jet. This com-
munication is structured in six sections. The first one
concerns the introduction to the micro-PIV technique.
The second chapter describes in details the micro-PIV
measurement technique with its advantages and its lim-
itations. The introduction of the ensemble average con-
cept is also given. The third chapter is related to op-
tical aberration problems, namely astigmatism and of
measurement plane deformation. The fourth and fifth
chapters concern respectively the experimental condi-
tions and the measurement results. The sixth chapter
introduced the methodology used for the numerical sim-
ulations conducted to validate the measurement results.
The paper ends with the conclusion, the perspectives and
the future plans.


The measurement technique

The micro-PIV technique can be described as a stan-
dard PIV technique in which the measurement plane is
not defined anymore by a laser sheet but by the mea-
surement plane of an epifluorescent microscope system.
The seeding used is very often constituted by polyester
sub-micron fluorescent particle possessing a Stoke shift
larger than 40 nm. A simplified sketch of the optical
configuration of a micro-PIV system is shown on Fig. 1.

A Nd-Yag pulsed laser beam, with a wavelength of
A=532 nm, is enlarged by lenses system and passes,
















Inlet Outlet
I Microchannel
-..._ I ::;:


Microscope objective
Nd:Yag laser Filter

-3 nmPrism
Beam expander ( Filter
Light emitted at 610 nm

piv camera





Figure 1: Sketch of the optical configuration for a
micro-PIV system


through an epifluorescent prism and a microscope objec-
tive. The light coming out of the objective illuminates
a specified volume of a micro-channel in which liquid
seeded with fluorescent particles is flowing. The parti-
cles are excited by the laser light and emit in a different
spectral band (see Fig. 2).











400 450 500 550 600 650 700 750
Wavelength (nm)

Figure 2: Example of Stoke shift

The light emitted is collected by the microscope
objective, passes through an epifluorescent prism and is
directed on a synchronized PIV camera that acquire the
particle images.

Depth of field and particle concentration The main
difference between a standard PIV optical configuration
and a micro PIV one is that a full volume of seeded
flow is illuminated and the measurement plane is de-
fined by the microscope optical configuration. Due to
the volume illumination the signal-to-noise ratio for in-
stantaneous velocity field measurement can strongly de-
crease if some precautions are not taken into account.
Indeed being the particles out of measurement plane il-


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


luminated they still emit light that is collected by the
microscope. This light does not contribute to the cross-
correlation resulting in an increase of the noise. Studies
show that in order to reduce this problem or low concen-
tration of seeding particles has to be used or the channel
depth has to be reducedMeinhart & Zhang & Werely &
Gray (2000). In some applications, where the channel
size is fixed, the seeding particle concentration has to be
extremely reduced. This leads to situations in which the
number of seeding particle per interrogation window be-
come insufficient for standard correlation algorithms.
Since the flows encountered in micro-fluidics are in gen-
eral laminar and either steady or periodic a study of the
mean flow field can be sufficient to understand the dy-
namic of the flow. The ensemble average method, de-
scribed in Sec. overcome the problem of poor seeding
without affecting the signal to noise ratio and the corre-
lation peak shape.
Ensemble average The ensemble average method has
been introduced by Meinhart et al. Meinhart & Werely
& Santiago (2000). It is based on the consideration that,
differently from the image average method, the peak cor-
relation function was constituted only by the correlation
function of cross-correlated images. This method indeed
calculates the average correlation function as the sum of
the correlation function of the single cross correlated im-
ages:


RAB (s)


if A (X) B(X+s) -d2X

SJ A(X) B(X + s) .d2X


S Ai- Bi- dX,
i i


where N,, is the number of correlation function used
for the average. The correlation function is strongly
improved by the averaged ensemble method and flows
poorly seeded can be still measured providing a suffi-
cient number of coupled images. Figure 3 shows three
correlation peaks obtained increasing the number of im-
ages used by the average ensemble method. These cor-
relations peaks have been calculated using experimen-
tal PIV measurements performed inside a squared mi-
crochannel with a very low seeding (0.02 % by volume).
The signal to noise ratio increases with the number of
images, in the case presented it grows from a value of
S/N=1.1 for a single couple of PIV images to a value of
S/N=7.8 for 25 couples of PIV images (see Table 1).
Unfortunately in the experiment we have performed
only 5 couples of PIV images have been acquired with a
very low seeding and this will give a smaller S/N.




























1 Image


50 50 25 (pixels
-50 -50 A (pixels)


(a)
5 Images


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



Table 1: Signal to noise ratio improvement with ensem-
ble average method

Number of images S/N.

1 1.1.
5 4.5.
25 7.8.



Optical aberrations

Astigmatism Astigmatism occurs when a lens (in this
case the droplet behaves as a lens) does not present a
P' symmetrical front to the incident light rays. Indeed two
planes can be defined as tangential (containing the object
50
25 and the axis of symmetry) and the sagittal plane perpen-
dicular to the tangential plane. This two planes form
their foci at two different distances form the lens. So,
in the presence of astigmatism, an off-axis point appears
as a sharp line oriented along the sagittal and tangential
plane (see Fig. 4).


Prim


0
'7--
-25 _-25
-50 -50 A. (pixels)

(b)

25 Images


Circle of least confusion


Optical axis


ary image





Secondary image


Figure 3: Signal to noise ratio improvement by means
of the correlation peak ensemble average.


Figure 4: Schematic drawing of the astigmatic aberra-
tion.


In between these two foci, a round but blurry image
is formed. This is called circle of least confusion. This
o plane often represents the best compromise image lo-
cation in a system with astigmatism. It is not the pur-
pose of this communication to detail the astigmatism
phenomenon, more details can be found in fundamen-
tal optics books as Born & Wolf (1959). Astigmatism
is clearly present in the droplets images as can be seen
in Fig.5 where an image of droplet formation taken at
40x magnification is shown. The horizontal and vertical
strips correspond to the primary and secondary images
of Fig. 4.
The astigmatism cannot be corrected in the experi-
mental configuration under study, nevertheless tests have
been performed to evaluate the possibility of using the
cross correlation method on lines instead of points. An
example of these tests is shown in Fig. 6, where two
synthetic images, respectively with and without astig-


o
A (pixels)
Y


0.8-
0.6-
0.4-
0.2-
0
50
0
A (pixels)
Y












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


Figure 5: Image of a detaching drop at 40xMagnifica-
tion. The horizontal and vertical strips are
images of the particles distorted by astigmatic
aberration.


matism, of a Poiseuille flow are presented. In the image
with astigmatism the strips have a length going from 2
to 6 pixels. These two images have been separately pro-
cessed with the same PIV processing parameters as the
window size (8x8 pixels) and the overlapping (50%).
The results of the PIV processing are presented in 7
and show that using an interrogation window size larger
than the strip and providing that the strips do not change
shape between the PIV images the cross correlation re-
mains good and is suitable to contribute to the ensemble
average.


Figure 6: Synthetic PIV image of a Poiseuille flow
without (a) and with (b) astigmatism


Figure 7: Vector field computation of the Poiseuille
flow without (a) and with (b) astigmatism




Measurement plane deformation In a typical mi-
croPIV configuration the measurement plane is defined
by the focal plane of the microscope. If this focal plane
is sited inside a curved transparent object it can be de-
formed as it was passing through a lens. Geometric op-
tics calculations have been performed in order to eval-
uate such a deformation. In Fig.8 an example of focal
plane distortion due to the passage of the light rays in-
side the droplet is shown. This example corresponds
to the deformation of a 20X microscope objective plane
due to the passage through a water droplet (real refrac-
tive index n=1.33) of 100 pm diameter. The objective
aperture NA is equal to 0.3, the working distance WD is
7.3 mm and a depth of field DOF is equal to 8.65 pm.
In this configuration the deformed plane differs from the
straight one of about A=8 pm which is smaller than the
DOF the plane deformation does not affect the measure-
ments. It can also be observed that the difference be-
tween the deformed and the undeformed plane decreases
with the droplet diameter. The plane deformation is a
drawback of the microPIV technique when experiments
as the one presented in this paper are conducted.















.......... Focal plane * Distorted Focal plane












Figure 8: Example of focal plane deformation due to the
passage of the light rays through a droplet.


Experimental conditions

A 70 microns internal diameter capillary tube, driven by
an annular piezoelectric element, has been used to gen-
erate liquid droplets in air (non confined flow). The sig-
nal used to drive the piezoelectric element is sinusoidal
with a frequency of 8 kHz. A mixture of 50% glycerin
and 50% water is used as testing fluid. This liquid has
been seeded with submicronic fluorescent tracer parti-
cles possessing a mean size of 0.86 pm. In Fig. 9 a
picture of the capillary tube under the microscope ob-
jective is shown. The methodology used to perform the












Figure 9: Image of the piezoelectric capillary tube.

measurements is the following. A pushing syringe sys-
tem is used to drive the flow at constant flow rate into the
capillary tube. The piezoelectric element is driven by a
sinusoidal wave at frequency fc. To perform the image
acquisition, two synchronized signals are generated by
an analog output card. The first signal is amplified to
drive the piezoelectric control. The second one is used
to trigger the PIV laser system. The trigger signal fre-
quency is less than 5 Hz to be compatible to the PIV
camera maximum acquisition rate. The trigger signal
frequency is chosen to perform a stroboscopic sequence
of nl acquisition to cover a piezoelectric control signal
cycle. As a result, a sequence of images with regular
phase shift is obtained. The same signal sequence is re-
peated n2 times successively to get n2 synchronized rep-


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


etitions for each phase step (nl x n2 being limited by the
maximum number of images taken from the PIV cam-
era). In such a way the breakup of the liquid jet coming
out from the nozzle can be divided in several time steps
up to the droplet formation. This technique allows the
analysis of the droplet generation event in time. In Fig.
10 an example of micro-PIV image obtained during the
experiments is shown.


Figure 10: Example of micro-PIV image.


0.1 Post-processing

The micro-PIV image post processing is done using the
ensemble average method with only 5 couples of im-
ages; the time separation between the two PIV frames
is 2ps. Despite the small amount of images and of trac-
ers the S/N ratios remain higher than 1.7. A dynamic
mask, is used to mask the zones of the image in which
the liquid is absent.This masks are computed from the
raw PIV images using a threshold filter on the image
intensity. The velocity of the jet at the exit of the capil-
lary tube is measured by micro-PIV and compared with
the one obtained by the ratio between the liquid flow rate
and the capillary tube section. The value obtained is sub-
tracted to the velocity field of the liquid jet, measured by
micro-PIV, in order to obtain the internal movements of
the fluid (relative motion). The window size used for the
cross-correlation is kept quite large (64x64 pixels) in or-
der to do not affect the measurement by the presence of
the strips created by the astigmatism and 50% overlap is
used.

Results

In this section the first result obtained during the mea-
surement campaign is shown. This result shows the rela-
tive vector field inside a detaching droplet, zone 1 of Fig.
10, moreover a first attempt to validate such measure-
ments is presented. Fig. 11 shows the internal relative
velocity pattern, two recirculation zones on the border
of the drop are clearly visible(red zones in which the ve-
locity become positive). These recirculation zones cor-
respond to the stretching of the liquid jet which will give
place to a liquid detachment and then to the droplet for-
mation. The micro-PIV velocity flow field has been used
















Zone I


a


0.05 0.1 0.15 0.2
position (mm)


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


volved in the domain, ca. For the qth phase, a continuity
equation is solved for aq:


2,4
vx rs
2.2

IeA
1.6
0.8
0.6
OA
0.2


atQg + V (qpqgVq) E (T p[q
p-1


,,.), (2)


where p, is the density of phase q, mqp and mp, are the
mass transfers from phase q to phase p and vice versa.
The volume fraction equation is not solved for the pri-
mary phase involved in the simulation; being its volume
fraction computed to respect the constraint:


Figure 11: Relative velocity pattern corresponding to
Zone 1 of Fig. 10.


to calculate the evolution of the mean flow rate in time.
This quantity has been compared with the impulse signal
given to the piezoelectric capillary tube. This compari-
son is shown in Fig. 12, where the sinusoidal shape of
the input signal is retrieved. The mean flow rate cal-
Flow ratevuiaon


Time (ps)


100


150


Figure 12: Mean flow variation calculated from the mi-
croPIV velocity profile (dot line) and its fit-
ting sinusoidal function (solid line).

culated by means of micro-PIV velocities and the one
imposed differs of about 8%. This is due to statistic er-
ror performed during the flow rate measurement using
the pushing syringe system. On the other hand also the
detection of the drop contour, which is essential for the
calculation of the flow rate by means of micro-PIV ve-
locities is very delicate and can affect the results.


Preliminary numerical simulations

Preliminary numerical simulations have been performed
using the commercial code FLUENT by Ansys Inc.
Being the flow laminar at the investigate conditions;
the continuity and the momentum equation are solved.
The liquid surface is tracked using the Volume of Fluid
(VOF) model (Fluent Inc., 2006). The method is based
on the definition of volume fractions for the phases in-


Saq 1.
q=l


The surface of the jet is reconstructed using the geomet-
rical reconstruction scheme of Youngs (1982), using a
piecewise-linear approach. The effect of surface tension
on the volume fraction distribution is modeled follow-
ing Brackbill & Kothe & Zemach (1992), with the addi-
tion of a source term to the VOF equation, based on the
continuum surface force (CSF) model. A 2-dimensional
(2D) axy-symmetric model is adopted for the current in-
vestigation. The grid consists of 68035 hexahedrons,
with a particular refinement at the nozzle exit. The com-
putational domain and the main boundary conditions are
shown in figure 13.

-.-- oazzle outlet


axis

Figure 13: Computational domain and main boundary
conditions

A velocity inlet boundary condition is applied to
the domain inlet, whereas pressure outlet conditions
are used for the boundaries which define the enclosure
where the jet is discharged. As far as the wall boundary
condition is concerned, a no-slip condition is employed.
Moreover, a User Defined Function (UDF) is coupled to
the solver to emulate the wall displacement induced by
a piezoelectric. In particular, the following velocity is
applied to the jet nozzle in the longitudinal direction:

v, A f cos (f t), (4)

where A is the amplitude of the displacement induced
by the piezoelectric, f is the frequency and t is the time.
In the present study A and f were set to 1 pm and 8000
Hz, respectively. Transient simulations are performed
by specifying a very small time step, i.e. le-07. This is
necessary to follow the variation of the volume fraction












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


during the drop formation process and to ensure numer- J. U. Brackbill, D. B. Kothe, and C. Zemach. A Contin-
ical stability. Preliminary results of the volume fraction uum Method for Modeling Surface Tension. J. Comput.
during the drop formation process are shown in figure Phys., 354, 1992.
14.
D. L. Youngs. Time-Dependent Multi-Material Flow
with Large Fluid Distortion. In K. W. Morton and M. J.
Baines, editors, Numerical Methods for Fluid Dynam-
ics. Academic Press, 1982.




0 02 04 06 08 1

Contous of Volume fraction phasee) (Time-2 7247e03) Mar 24, 2010

Figure 14: Volume fraction during the drop formation
process



Conclusions

In this paper it has been shown that, even in presence of
optical aberrations it is possible to measure the flow field
inside a droplet during its detachment from a capillary
piezoelectric tube. These measurements have been vali-
dated comparing the mean flow-rate measured by micro-
PIV to the one imposed by the pushing syringe system.
This measurement campaign is largely promising and
gives many perspectives. New tests are planned to see
the effect of fluid viscosity on the internal droplet flow
field and non-isothermal tests are also envisaged.


References

J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J.
Beebe and R. J. Adrian, Exp. Fluids 13, 105-116 (1998)

C. D. Meinhart, S. T. Werely and J. G. Santiago, Exp.
Fluids 27 (199

C.D. Meinhart and H.S. Zhang, Journal of MEMS 9
(2000) 679) 414

H. Li and M. G. Olsen, Int. Jou. of Heat and Fluid Flow
27 (2006) 123

P. Vennemann et al.,J. ofbiomechanics 39(2006) 1191

C. D. Meinhart, S. T Werely and M. H. B. Gray, Meas.
Sci. Technol. 11(2000) 809

C. D. Meinhart, S. T. Werely and J. G. Santiago, Jour.of
Flu. Eng. 122 (2000) 285

M.Born and E. Wolf, Principle of Optics, Pergamon
Press 1959.




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