Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 10.2.2 - Microbubble dynamics in a simple shear flow under the effect of ultrasound. Coupling of Saffman Lift with bubble volume oscillations and Bjerknes Force
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Title: 10.2.2 - Microbubble dynamics in a simple shear flow under the effect of ultrasound. Coupling of Saffman Lift with bubble volume oscillations and Bjerknes Force Particle Bubble and Drop Dynamics
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Aliseda, A.
Engebrecht, C.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Notes
Abstract: The dynamics of microbubbles under the effect of ultrasonic pressure waves presents many open questions in multiphase flow that are relevant to the field of interventional radiology and targeted drug delivery. The possibility of manipulating bubbles non-intrusively was predicted in the seminal work by Bjerknes (1906) and demonstrated by (Eller 1968; Crum and Eller 1970). These studies focused their attention on arresting the motion of a bubble, keeping it stationary. It has recently been shown however that the Bjerknes force can be coupled with hydrodynamic forces to produce very rich behaviour (Rensen et al. 2001). To manipulate the trajectory of microbubbles immersed in a unsteady, sheared flow, such as the one found in the human circulation, it is necessary to understand this complex coupling between hydrodynamic forces acting on the bubble and the ultrasound-induced volume oscillations. We have performed experiments on microbubbles (4 m < d < 14 m) immersed in low Reynolds steady flow in a round tube. The microbubbles are subject to hydrodynamic forces, and are under the effect of external ultrasound forcing propagating downwards, that is, normal to the horizontal flow direction. Under this configuration there are only three forces acting on the bubbles in the vertical direction: buoyancy, Bjerknes force and Saffman Lift, due to the presence of the sheared velocity profile in the carrier flow (Saffman 1965). The velocity measurements, averaged over bubbles of the same size and in the same region of the flow are shown in the figure below. The change in behaviour of bubbles in areas with opposite sign of the shear indicates a rich mechanism for the coupling between these two forces. In the absence of ultrasound excitation, Saffman’s lift forces the microbubbles towards the wall. The volume oscillations induced on the microbubble by the propagating ultrasonic pressure waves significantly modify the lift, reversing its direction and making it away from the wall.
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: 1022-Aliseda-ICMF2010.pdf

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


Microbubble dynamics in a simple shear flow under the effect of ultrasound.
Coupling of Saffman Lift with bubble volume oscillations and Bjerknes Force


A. Aliseda and C. Engebrecht

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195, USA
aaliseda@uw.edu
Keywords:




Abstract

The dynamics of microbubbles under the effect of ultrasonic pressure waves presents many open questions in mul-
tiphase flow that are relevant to the field of interventional radiology and targeted drug delivery. The possibility of
manipulating bubbles non-intrusively was predicted in the seminal work by Bjerknes (1906) and demonstrated by
(Eller 1968; Crum and Eller 1970). These studies focused their attention on arresting the motion of a bubble, keeping
it stationary. It has recently been shown however that the Bjerknes force can be coupled with hydrodynamic forces
to produce very rich behaviour (Rensen et al. 2001). To manipulate the trajectory of microbubbles immersed in a
unsteady, sheared flow, such as the one found in the human circulation, it is necessary to understand this complex
coupling between hydrodynamic forces acting on the bubble and the ultrasound-induced volume oscillations.
We have performed experiments on microbubbles (4pm < d < 14um) immersed in low Reynolds steady flow in a
round tube. The microbubbles are subject to hydrodynamic forces, and are under the effect of external ultrasound
forcing propagating downwards, that is, normal to the horizontal flow direction. Under this configuration there are
only three forces acting on the bubbles in the vertical direction: buoyancy, Bjerknes force and Saffman Lift, due to the
presence of the sheared velocity profile in the carrier flow (Saffman 1965). The velocity measurements, averaged over
bubbles of the same size and in the same region of the flow are shown in the figure below. The change in behaviour
of bubbles in areas with opposite sign of the shear indicates a rich mechanism for the coupling between these two
forces. In the absence of ultrasound excitation, Saffman's lift forces the microbubbles towards the wall. The volume
oscillations induced on the microbubble by the propagating ultrasonic pressure waves significantly modify the lift,
reversing its direction and making it away from the wall.


Introduction

Ultrasound Contrast Agents (UCAs) are gas bubbles
coated with a lipid bilayer with a diameter between
1 10 pm that are injected in the human circulation to
enhance the contrast of Ultrasound (US) medical imag-
ing. These microbubbles are comparable in size and
deformability to a single red blood cell. As such, they
travel through the human vasculature and eventually, af-
ter multiple passages through the lungs, the gases are
exhaled and the lipid are degraded in the organism. The
use of microbubbles in diagnostic ultrasound has raised
several Ihl pl',dsis, to incorporate them into treatment,
giving them a more active role in the medical proce-
dure. One of this proposed therapeutical uses consists
of loading the lipid shell with specific drugs and direct-
ing them to the treatment site through an ultrasound in-
duced force. The possibility that an external force can
be applied to the microbubbles by the ultrasound pres-


sure waves is based on the physical observation that a
fluctuating pressure field exerts a net force on a bub-
ble due to its compressibility, and it goes back all the
way to Bjerknes (1906). Although Bjerknes conducted
his analysis in the context of meteorological fronts of dif-
ferent densities responding to a variable pressure field,
it is clearly applicable to the case of bubbles in ul-
trasonic pressure wavesYosioka and Kawasima (1955);
Eller (1968); Crum and Eller (1970); Crum (1975). This
force can be used to manipulate the microbubbles unin-
trusively, and move them towards certain regions of the
vasculature. Briefly, the Bjerknes force is the net result
of the pressure acting on the variable cross section of
the bubble as it oscillates in volume under the pressure
wave. When integrated over a whole cycle of the ex-
citation, the phase lag between the volume oscillations
of the bubble and the forcing pressure wave results in
a non-canceling component in the direction of propaga-











tion (or in the direction of the antinodes in a stationary
wave), see figure 1.

The possibility of manipulating the bubbles with
a safe, non-intrusive mechanism, such as ultrasound
through the Bjerknes force, has open the way for many
different potential therapeutic techniques. But the appli-
cation that has attracted the most attention in medical
circles is ni iliii' inb i1sis the destruction of throm-
bus by a combination of US, UCAs and anticoagulant
drugs (Tsutsui et al. 2004; Stroick et al. 2006; Alexan-
drov 2007; ter Haar 2004; Soltani and Soliday 2007; Me-
unier et al. 2007). To avoid repeating previous mistakes
(Daffertshofer et al. 2005) where the application of this
phenomenon was pushed forward without a clear fun-
damental understanding of the underlying physics, the
dynamics of microbubbles under pulsatile flow in a com-
plex geometry need to be studied. In particular, we focus
our attention to the coupling of the ultrasound-induced
oscillations, and the resulting Bjerknes force on the bub-
bles, with the hydrodynamic forces on the bubble.


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


Theoretical Background

In order to improve our understanding and modeling
capability of the interaction of bubbles with an ultra-
sound field, including the Bjerknes force and the ef-
fect of volume oscillations on the hydrodynamic forces
(drag, lift, added mass, history), it is useful to first study
the non linear oscillation of the bubbles under a har-
monic excitation close to its resonance frequency. The
bubble volume oscillations under a fluctuating pressure
field can be described by the Rayleigh-Plesset equation
(Eq. 1). Significant contributions Rayleigh (1917); Min-
naert (1933); Pfriem (1940); Devin (1959); Plesset and
Hsieh (1960); Plesset (1964); Prosperetti (1977); Pros-
peretti et al. (1988) have extended this formulation to
include the effect of surface tension, viscosity, thermal
and radiation losses.


p RR + R2


SR
--- R -
R R


Poo PAsin(wt)


(1)


Figure 1: Schematic of the bubble volume oscilla-
tions,represented by the instantaneous bubble
radius, Rb(t), in response to an ultrasonic
pressure field, P(Zb, t). Note that Bjerknes
force exists because of the phase lag between
the bubble volume and the pressure fluctua-
tions, irrespective of attenuation of the pres-
sure wave amplitude.


Here, R is the bubble radius, Ro is the initial equilib-
rium radius, P90 is the initial equilibrium pressure inside
the bubble, K is the polytropic constant for the gas evo-
lution (its value ranges from 1 for an isothermal process
to 1.4 for an adiabatic process), Poo is the hydrostatic
pressure in the absence of an ultrasound field, PA is the
amplitude of the ultrasound excitation, p is the liquid
viscosity, and a is the surface tension between the liquid
and the gas.
Because of the interest in inertial cavitation and sono-
luminescence, the validity and accuracy of this equation
has been thoroughly studiedProsperetti (1974, 1982);
Crum and Prosperetti (1983); Matula et al. (1997); Mat-
ula (2003); Chen et al. (2003). Interestingly, many of
these studies used the Bjerknes force to trap isolated
microbubbles against buoyancy (but not hydrodynamic
forces), exciting their oscillations while keeping them
stationary to facilitate their study.
Recent interest in Ultrasound Contrast Agents has
led to the extension of the Rayleigh -Plesset equation
to describe the dynamics of bubbles encapsulated by a
viscoelastic shell deJong (1993); Church (1995); Hoff
(2001); Morgan et al. (2000); Chatterjee and Sarkar
(2003). Although different models are optimized for dif-
ferent shell rheologies, they all reproduce well the bub-
ble volume oscillations in a quiescent medium. In most
cases, the theological properties of the shell cannot be
measured directly, and they need to be extracted from
the fit of the model to the experimental measurements of
the bubble behaviour. These studies of UCAs oscillating
under steady state excitation, and the growing interest in
the use of Bjerknes force as a microbubble manipulation







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


tool, has led to a growing understanding of the effect of
ultrasound on microbubbles in a quiescent environment
Stride and Saffari (2003); Rychak et al. (2005).
To understand the mathematical modeling of the
Bjerknes force and its parametric dependency, we can
solve the linearized Rayleigh-Plesset equation under
harmonic excitation. Assuming small amplitude pres-
sure waves propagating through the liquid medium:

P(z,t) = PAcos(wt kz) (2)

where PA is the amplitude of the ultrasound pressure
wave, c = 247f is the angular frequency, k = is the
wavenumber and c is the speed of sound in the liquid.
The gradient of the pressure is then:

VP(z, t) = kPAsin(ct kz) (3)

If the radius oscillations of the bubble correspond to
the peaks and valleys of the pressure wave, and the ra-
dius oscillations are small in comparison to the equilib-
rium radius, then the equation for the bubble radius as a
whole can be expressed as:

R Ro + R,(t) = Ro R,,iwot (4)

where R is the bubble radius, R,,ocio0 represents the
small amplitude oscillations that the bubble wall follows
about the mean radius Ro, and ,o = 27FR is the reso-
nant angular frequency. The negative sign in equation 4
corresponds to the decreasing size of the bubble experi-
enced when the pressure wave amplitude is positive.
If R, << Ro, and vapor pressure and viscosity are
negligible, the simplified solution of equation 1 gives the
volume as a function of time:


A bubble with volume V that lies in a pressure gradi-
ent VP will experience a downward force that is equal
to VVP. In this case, the pressure oscillates in time and
therefore the force is a function of time as well. The av-
erage net force however, is the time average of the total
forces:
(FBjrk) = (V(t)VP(z,t)) (8)
where z is the distance between the transducer source
and the bubble. Substituting equations 3 and 5 into equa-
tion 8 gives:


(FBjk) (= VokPA (1


3Rmax \
-_ )cos(wt
R( T


kz 0))


(sin(kz ct)))
=VokPA ((sin(kz ct)))

-VkPA 3 iax(((sin2 (ct- kz)sin())

+VPA ((cos( ct kz)sin(wt kz))cos(0))


(9)


In this case, the average of both the (sin(kz-wt)) and
(cos(wct-kz)sin(cwt-kz))cos(O) terms go to zero. The
((sin2(wt kz)) goes to 1/2 and the force is simplified
to be:
(FBjrk) = VokPA 3 sin(O) (10)
2R,
Substituting equations 6 and 7 into equation 10 and sim-
plifying, we obtain the average Bjerknes force.


V(t) v o (1


3TRmax
S)-cos(wt
(O TI


kz- 0)) (5)


where Vo = 7R3 is the equilibrium bubble volume,
Rmax is the maximum bubble radius, and 0 is the phase
lag between the acoustic pressure wave and the volume
oscillations. Rmax is described by the equation below:


Rmax


A (6)
p2 +(( ) 2 1)2 t


where wo 27fo is the resonant frequency for a bubble
with the equilibrium radius of Ro and 3tot is the dis-
sipative constant that takes into consideration all of the
factors that effect the bubble damping (such as viscous
and thermal losses) Leighton (1994). The 0 in equation
5 corresponds to the phase lag which is related to the
dissipative constant and angular frequencies present.

0 sin 1( c%2 ) (7)
S/(2 _2)2 + (2/3t,_,)2


3V0kP2 ( 2dtt)
O~oK-^ ^W


(FBjrk)


RT(pc(2 2)
0


1)W2 ) 2]


Experimental Setup


Experiments were conducted by injecting the microbub-
bles into a small diameter tube immersed in a large ob-
servation tank field with water. The US excitation is ap-
plied on the free surface by a water-coupled transducer
oriented vertically looking down. The water in the tank
is an ideal propagation media for the US, it has a low
impedance of about 1.5 MRayls (similar to human tis-
sue), and is well matched to the acoustic impedance of
the tube, avoiding scattering of the US waves. A sketch
of e iuos Iw iWar eynolds number of 200
is created in the test section by a computer controlled
pump that recirculates DI water with the microbubbles







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


Figure 2: Experimental setup sketch. The Microbub-
bles are injected from the syringe pump
into the flow phantom and convected into
the test section where they are subjected to
Ultrasound-induced Bjerknes force perpen-
dicular to the direction of the mean Poiseuille
flow.

dispersed into it. The ultrasound contrast agents are cre-
ated by controlled shaking of a lipid/buffer solution in
the presence of gas (air or perfluorobutane). These mi-
crobubbles are diluted into DI water in a syringe and in-
jected into the flow phantom with a syringe pump. Fig-
ure 3 shows the difference between the concentration of
the UCA solution by itself and the concentration when
70% water is added. The diluted solution shows a large
decrease in the concentration of the bubbles. However,
it also shows that the bubbles can exist in low concen-
tration in deionized water without dissolving, the UCAs
are injected at the entrance of the tube to the observation
tank, about 100 diameters upstream from the location of
the image acquisition. The microbubbles have accom-
modated to the flow and their behaviour is not influenced
by the injection conditions.
We collect the backlighted images of the microbub-
bles inside the flow phantom with a Phantom V12 high
speed camera (Vision Researc, Inc., Wayne, NJ) At the
maximum resolution of 1280 x 800 (200 pm x 125 pm),
the camera is capable of taking pictures at frame rates
just over 6,000 frames per second. To obtain the high
spatial resolution necessary to capture the microbubble
dynamics, we couple the high speed camera with a K2
long distance microscope (Infinity Photo-Optical Co.,
Boulder, CO). We achieved a ii.igiini ..ii ilii of over 20X
at a distance of 95 mm, with a depth of field of about 20
microns. This allowed us to physically filter the bubble
data we captured by positioning the focal plane collo-
cated with the maximum cross sectional area of the flow
phantom to ensure that all the microbubbles analyzed
are flowing on a plane that cuts diametrically through
the tube and therefore the distance from the bubble to


(a) Concentrated UCA solution


(b) Diluted with 70% filtered water


Figure 3: Difference between concentrated UCA for-
mula and diluted UCA formula











the tube's walls is that measured in the images, without
uncertainty about out of plane effects.
To excite the microbubbles, we use a Panametrics-
NDT V303 1MHz transducer. It is a 2.54 cm di-
ameter, unfocused, water-coupled transducer with a
near field effect region between 1.524 and 2.032 cm.
In this application, well beyond its near field region,
it produces a uniform pressure waves propagating in
the far field. The transducer is controlled by an
Olympus Panametrics-NDT Model 5077PR Squarewave
Pulser/Receiver whose lowest and highest pulsing fre-
quency settings are 100 kHz and 20 MHz respectively.
To determine the exact pressure field generated by the
transducer, a hydrophone and hydrophone positioning
system are used. The hydrophone is from Onda Cor-
poration model HNC-1000 S/N 1061. To determine the
impedance through the tube that will channel the mi-
crobubbles in a unidirectional flow field, the pressure
amplitude was sensed by the hydrophone both with and
without the tube.



-- -.....*..
*>
-<-------i i =


.-


Figure 4: Shear resulting from Poiseuille flow in tube.
The shear which imposes the Saffman force is
always largest near the walls.



Results and Discussion

The trajectories of the microbubbles in the flow phantom
were extracted by image processing from the high speed
video. The horizontal (along the flow phantom's axis)
and vertical (normal to the phantom's wall and along the
direction of propagation of the US) velocity components
were measured from the trajectories by particle track-
ing. The concentration of microbubble in the flow was
diluted enough that there were only a few bubbles in any
given frame, making the tracking possible.


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


The vertical velocity of the microbubbles was aver-
aged based on the diameter of the microbubbles. The
result of this measurement is shown in figures 5 and 6
as the overall average. We observe that the microbubble
velocity is reduced by the effect of the US excitation.
In the absence of US, buoyancy dominates to establish
a positive rise velocity for all bubbles. The US excita-
tion induces a Bjerknes force downwards that counter-
acts buoyancy and establishes a new equilibrium veloc-
ity in the direction perpendicular to the wall.
When the bubble velocity is averaged conditioned on
both their diameter and their location within the flow
phantom, the behaviour of the bubbles is found to de-
pend strongly on their position. This is true for both
cases, with and without US excitation. In the absence
of US pressure fluctuations, the bubbles subject to pos-
itive shear, that is those close to the lower wall, have a
reduced vertical velocity, while those subject to nega-
tive shear near the upper wall, see their vertical velocity
increased. The effect of Saffman Lift for this very low
Reynolds number bubbles is to drive them towards the
wall. In the experiments where the bubbles were under
the effect of the ultrasonic pressure waves, the behaviour
is reversed. Bubbles near the bottom of the phantom,
where shear is maximum, see their vertical velocity in-
creased compared to the overall average with US. The
bubbles near the top, where the shear is minimum (max-
imum in value but negative in sign), the vertical veloc-
ity is reduced. We hypothesize that the volume oscilla-
tions induced by the US excitation on the microbubbles,
shifts the sign of Saffman's Lift, modifying the balance
between Bjerknes force and other hydrodynamic forces
(buoyancy and lift) and resulting in a modified trajec-
tory where bubbles are driven away from the walls (the
net velocity in the upper region is negative and the net
velocity in the lower region is positive).


Conclusions

We investigate the dynamics of microbubbles (UCAs)
under the effect of shear flow and US. The balance and
coupling between hydrodynamic forces and Bjerknes
force has been studied experimentally. Lipid coated mi-
crobubbles with diameters between 1 and 15 pm were
injected in a flow phantom under steady flow and ob-
served with high speed microscopy imaging. The trajec-
tories of the bubbles in the flow, with and without the
effect of ultrasound pressure waves propagating perpen-
dicular to the direction of the carrier flow were extracted
from the images and the velocity of the microbubbles de-
termined by Particle Tracking Velocimetry (PTV). The
results show a reduction in the vertical velocity of all
microbubbles due to the downward force exerted by the
US as it propagates in that direction. This reduces the








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


Cross streamwlse velocity of mlcrobubbles No Ultrasound exctallon
02

015


| oos ^^ /
-0 1


-005-


6 8 10 12
Bubble diameter (rm)


14 16


Cross streammuse velocity of microbubbles 1 MHz, 200 kPa Ultrasound excitation

- 208 pm

. r<208 pm


- 208 pm

> 01
005
0
E 005
-01
-015-


6 er
GbX "e 1,e j D


02-
2 4 6 8 10 12
Bubble diameter (pm)


14 16


-208 pmro 625 pm









- .-8pmr 625 pm


Figure 5: Vertical velocity of bubbles in the absence of
US excitation. The vertical velocity is only a
balance between buoyancy and Saffman Lift.
The bubbles are grouped depending on their
position within the flow phantom and there-
fore based on the shear they are subject to
from the Poiseuille flow.



net upwards velocity of the microbubbles induced by
their buoyancy. The effect of Lift on these low Reynolds
number bubbles is observed for bubbles near the walls,
where shear is maximum in magnitude. In the absence
of US excitation, Saffman lift pushes bubbles towards
the walls. In the presence of ultrasonic pressure waves,
however, the sign of the lift is reversed. We attribute this
reversal to the volume oscillations induced on the bub-
bles by the US pressure fluctuations. Efforts to under-
stand and model this effect from a theoretical standpoint
are currently underway,


Acknowledgements

The authors would like the thank Alejandro Algora for
his help in the early stages of the experimental setup
and Tom Matula and Jonathan Lundt for their help in
the manufacturing of the coated microbubbles. Funding
for this work was provided by NSF through CAREER
award CBET-0748133 from Particulate and Multiphase
Processes/Biomedical Engineering.


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Figure 6: Vertical velocity of bubbles under the influ-
ence of the 1 MHz transducer. The direction
of propagation of the US waves is downwards.
The bubbles are grouped depending on their
position within the flow phantom and there-
fore based on the shear they are subject to
from the Poiseuille flow



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


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