Particle separator utilizing ultrasonic standing waves in

microfluidic channels

Andreas Sandin Experimental Biophysics

Lund University May 30, 2006

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CONTENTS 1 Abstract .................................................................................................................................. 2 2 Purpose of this project............................................................................................................ 3 3 Basic theory............................................................................................................................ 3 4 Particle separator designs ....................................................................................................... 4 5 Band formation....................................................................................................................... 6 6 Experimental setup................................................................................................................. 6 7 Measurements: Separation of blood and fat lipids in cream .................................................. 6

7.1 Results and conclusions .................................................................................................. 7 8 Lateral movement of a particle in the flow ............................................................................ 9 9 Measurements: Separation of plastic particles of different size........................................... 10

9.1 Results and conclusions ................................................................................................ 10 10 Acknowledgements ............................................................................................................ 13 11 References .......................................................................................................................... 13

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1 Abstract Separation science is a wide and well investigated area. Techniques such as many kind of filters, centrifugation or dielectrophoresis has been developed during the years. Many of these applications are used in the medical area which demands high performance and polite devices. Blood washing is an important application where it is desirable to separate red blood cells (erythrocytes) from the carrier medium, the blood plasma. This could be the case when the plasma contains high levels of drugs, inflammatory or coagulation. Blood washing is also necessary during very complicated surgeries, such as cardic surgery where the blood loss is evident. This is a better alternative than transfusion of new blood to the patient in such matter to eliminate transfusion transmitted disease and immunologic reactions to allogenic blood. Another thing to advocate blood washing is that fresh blood is today an article in short supply. Currently, centrifuge-based methods are utilized for blood washing. But this technique suffers from two major drawbacks. First it can not remove lipids sufficiently enough which will leak out in the blood from surrounding fat tissue. Lipid micro emboli can affect different organs such as the brain and kidney by obstruct the capillary system in the body[1]. Secondly the centrifuges expose the red blood cells to strong deformation forces which lead to the cells to break up and cause a hemoglobin leakage in the plasma. The department of electrical measurement at Lund institute of technology has developed a new technique which is free from these problems. This technique uses an ultrasonic standing wave in a micro fluidic channel to separate different particles from each other. Particles that are exposed to an ultrasonic standing wave field are affected by an acoustic radiation force and will be collected depending on its acoustic properties.

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2 Purpose of this project The aim of this project was first to simulate a blood wash of bovine blood contaminated with fat globules from cream by using an ultrasonic wave in a micro fluidic channel. This was made to get a view of the application and to get a clear understanding in the basic theory and idea of this technique. In the second part the separation efficiency of particles of different sizes by changing the amplitude of the wave, was investigated.

3 Basic theory All waves can be reflected. If a wave is reflected back onto itself it will interfere with itself. This creates an interference pattern both constructive and destructive which will occur as antinodes and nodes respectively. A sound wave is a longitudinal wave. It is called longitudinal because the molecules in the medium are moving back and forth in the same direction as the wave. The molecules are vibrating sinusoidal and it is useful to see them as they are connected by springs with a displacement from equilibrium of the individual air molecules. At a node the molecular displacement has its maximum value and at the anti node it has its minimum value.

Fig 1. A model of the molecules in which the wave is traveling through. An acoustic standing wave can mathematically be described as:

⎟⎠⎞

⎜⎝⎛ +⋅⎟

⎠⎞

⎜⎝⎛ +⋅=

22sin

22cos φπφλπ

TtxAy (1)

Where (y) describes the displacement to a certain position (x) at the time (t). A is the amplitude of the wave and λ is the wavelength. T is the period time and the phase shift between two traveling waves is expressed with Φ. The cosine part describes the wave in space and the sinus part describes the time dependence. If we have the case of a standing wave the phase shift is fixed, by looking at the cosine part it is easy to see that the distance between two consecutive nodes is λ/2. Formula 1 can then be rewritten in terms of pressure:

⎟⎠⎞

⎜⎝⎛⋅⎟

⎠⎞

⎜⎝⎛⋅=

Ttxpp π

λπ 2cos2sin0 (2)

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A standing sound wave can create an acoustic force on particles in the x direction. This force has been theoretically expressed by Yosioka and Kawasima[2]:

( ) ⎟⎠⎞

⎜⎝⎛⋅⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

λπρβφ

λβπ xVp

F wcr

4sin,2

20 (3)

w

c

wc

wc

ββ

ρρρρ

φ −+−

=2

25 (4)

wβ = Compressibility of medium cβ = Compressibility of the particles

wρ = Density of medium cρ = Density of the particles

cV = Volume of the particle

The direction of the force is dependent on the sign of the Φ-factor. To separate two types of particles they need to have opposite signs of the Φ-factor. One particle type will end up in the pressure node and the other type in the pressure anti node. This effect can be used to separate different particles in a continuously and laminar flow. A flow is laminar if there is no turbulence in the liquid. Particles will keep their lateral position even after leaving the acoustic force field. For example if the particles are erythrocytes with Φ ≈ 0.3 and lipid particles with Φ ≈ -0.3, the erythrocytes will be dragged to the centre node while the lipid particles are forced out to the anti nodes. However, Φ can not be zero thus there will be no net force on the particle.

Figure 2. (a)The wave profile in a micro fluidic channel with two different particles positioned, one in the pressure node and the other one in the pressure anti node. (b) Top view of the continues separation [3]. It is important to have a sufficiently strong force to separate many particles in a short time. According to formula 3 the force is increased with increased pressure amplitude. This works well but only to a certain critical limit. The increased power dissipation will heat up the surrounding medium to a critical temperature and even create gas bubbles. There is also a risk for acoustic streaming to occur if the pressure amplitude is high.

4 Particle separator designs The micro fluidic channel was made in Silicon. Silicon is preferable because of its good acoustic properties. The fabrication process is well known and by using photolithography and

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anisotropic wet etching, perfectly vertical walls can be obtained with a hydrophilic surface. The channel was 375 μm wide and 125 μm deep.

Figure 3. Cross section of the micro fluidic channel with an ultrasonic standing wave in fundamental resonance mode orthogonal to the flow direction [4]. The ultrasonic waves were generated by a standard 2 Mhz resonant piezoelectric crystal, PZT (PZ26 Ferroperm Piezoceramics AS, Kvistgard, Denmark). This PZT must be attached to the channel without preventing the waves to propagate into the channel. By using an ultrasonic gel which is used in mammography investigation this problem can be minimized. To enclose the channel a boron-silicate glass lid was bonded to the silicon wafer. The device had two inlets and two outlets but only one inlet was used so one of them was plugged with piece of metal to avoid leakage. a) b)

Fig. 4 a) Top view of the separator chip. b) Bottom view of the separation chip.

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5 Band formation To create a stable standing wave in the micro fluidic channel it is important to choose frequency which fits well to the dimension of the cross section of the channel. The choice of ultrasonic frequency is given by:

λc

f = (5)

Where c is the speed of sound in the liquid. In these experiments the fundamental resonance mode (λ/2) was used. This will create a single band formation in the middle of the channel. It is also possible to operate at even higher harmonics with the possibility to generate multiple bands.

Fig. 5 Different modes of standing pressure waves in a micro fluidic channel[5].

6 Experimental setup The outlets and the inlet of the chip were connected with Teflon tubes with an inner diameter of 0.8 mm. The two outlet tubes were used to collect the sample after the separation and the length was varied depending on how much of the sample that was needed for further investigations. To create a stable flow in the channel, an under-pressure was created by two syringe pumps (SP260P, World Precision Instruments Inc, Sarasota, FL, USA) connected to the outlet tubes. The PZT was supplied via a high frequency power amplifier (Model 75A250, Amplifier Research, Southerton, PA, USA) and the frequency was set by a function generator (Model HP 3325B, Hewlett-Packard Inc, Palo Alto, CA, USA). The signal amplitude was controlled by a digital oscilloscope (Model HP 54503A). Finally the separator was placed under a bright field microscope connected to a CCD-camera to study the process in real time.

7 Measurements: Separation of blood and fat lipids in cream By separating bovine blood and cream in an ultrasonic particle separator, a realistic simulation of blood washing can be made. The cream that was used was coffee cream with a fat content of 12 %. The frequency was 2 MHz which was the resonance frequency of the PZT, to get a standing wave of the first order in the channel. The signal voltage was varied from 0 to 20 Vpp and the flow rate was 50 μl/min. To measure the separated samples in the outlet tubes a centrifuge (Haematokrit 2010, Hettich Zentrifugen, D-78532 Tuttlingen, Germany) was used. The

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sample was put in to a thin glass pipe with the top of the pipe directed to the centre of the centrifuge. A centrifuge separates the particles by density. The erythrocytes in the blood have a larger density than the fat in the milk so they were collected in the bottom of the pipe. In the middle, water and other particles in the milk and the blood was collected and at the top the lipid vesicles with the lowest density. Each sample was centrifuged for two minutes at 13000 rpm after which of the participation of blood and fat could easy been read out in the pipe. Assume that: A = relative particle fraction collected from the centre outlet B= relative particle fraction collected from the side outlets Then the separation efficiency of the blood was determined as the ratio of the percentage fraction blood from the centre outlet to the percentage total fraction blood in the fluid at all three outlets:

Separation efficiency = BA

A+

⋅100 (6)

This was made in the same way for the cream but with the B as numerator in formula 6.

7.1 Results and conclusions The result showed that the separation process was successful for both the mixtures with an efficiency of at least 83 %. Bovine blood has almost the same properties of human blood and the consistency is quite inert. So was the cream and to avoid clogging it was necessary dilute the sample. They were diluted with common NaCl solution because that is a natural medium in the body and will not affect the red blood cells. Both of the mixtures were tested without any acoustic wave and the side- and centre outlet tubes then had the same fraction blood and cream. This shows clearly that erythrocytes and lipids behave in the same way in a laminar flow and that the acoustic radiation force is the only thing that will give rise to separation. The voltage can be seen as proportional to the amplitude of the standing wave. The 25 Volume % sample needed a voltage of 17 Vpp to get the best and most stable flow while the more diluted sample only needed 10 Vpp. This shows that a higher concentration of particles needs a stronger acoustic force to separate them. High concentrations will disturb the standing wave because the speed of sound is different in the particles than in the liquid medium which will affect the resonance frequency according to formula 5. If the Voltage was increased to even more than 17 Vpp, the flow became unstable and the separated blood in the middle started to show fluctuations. This was due to that the PZT quickly became hot because of the increased power dissipation. The gel which attaches the PZT to the channel became dry and sticky and it lost its acoustic properties.

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(a) (b)

Figure 6. (a) A mixture of 25% blood and 25% cream flowing through the chip without ultrasonic wave. (b) The same mixture with the ultrasonic wave turned on. The flow rate was 50 μl/min and a Voltage of 17 Vpp. (a) (b)

Figure 7. (a) A mixture of 12.5% blood and 12.5% cream flowing through the chip without ultrasonic wave. (b) The same mixture with the ultrasonic wave turned on. The flow rate was 50 μl/min and a Voltage of 10 Vpp. Content of

the volume before separation

frequency amplitude Flow rate Content of the volume after separation, in the centre outlet

Content of the volume after separation, in the side outlets

Separation efficiency

Blood 25 % 21 % 2 % 91 % Cream 25 % 2 Mhz 17 Vpp

50 μl/min 3 % 20 % 87 %

Blood 12,5 % 12 % 0,5 % 96 % Cream 12,5 %

2 MHz 10 Vpp50

μl/min 1 % 5 % 83 % Table 1. Separation efficiency for two different diluted mixture of blood and cream.

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8 Lateral movement of a particle in the flow The primary force acting on a particle in a laminar flow is, according to equation 2, the acoustic radiation force, Fr. It is also a viscous drag force, Fd which is directed in the opposite direction. These forces acts perpendicular to the direction of the flow. Assume that the channel flow is along the y-axis and the position over the width of the channel is denoted x. The drag force is described by [5]:

xdFd ′−= μπ3 (7) Where d is the particle diameter, is the velocity perpendicular to the flow and μ is the dynamic viscosity of the fluid.

x′

This is the same force which prevents a body from falling faster than a certain maximum velocity when falling out from an air plane. Or when falling into a river, the viscous drag force will accelerate the body to make it follow the stream. The resulting movement of the particle along the x-axis is then governed by this equation:

( ) xdxVpFFxm wp

dr ′−⎟⎠⎞

⎜⎝⎛⋅⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛−=+=′′ μπ

λπρβφ

λβπ

34sin,2

20 (8)

The Volume of a spherical particle is given by

63

4 33 dr ππ =

Expressing the mass of the particle in terms of the volume times the density, ρp, the equation becomes:

( ) xdxdpdx

w

p ′−⎟⎠⎞

⎜⎝⎛⋅⋅

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−=⋅′′ μπλπρβφ

λ

βππρπ 34sin,

26

6

3203

(9)

With some rearrangement, the acceleration of the particle is given by the following equation.

( ) xd

xpx

pp

w ′−⎟⎠⎞

⎜⎝⎛⋅⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛−=′′ 2

20 184sin,

2 ρμ

λπρβφ

λρβπ (10)

p

wpC

λρβπ

2

20

1 = , p

Cρμ18

2 = (11)

04sin221 =⎟

⎠⎞

⎜⎝⎛+′+′′λπxCx

dCx (12)

This differential equation describes a typically expression for a damped free vibration model [6] where C1/d2 is the damping factor. The damping factor shows that larger particles are damped less then smaller particles.

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9 Measurements: Separation of plastic particles of different size In this part of the experiments the separation efficiency of different large particles at different applied voltage was measured. The major aim was to see if the efficiency can be related to the size of the particles in the same way as the theoretical measurements. The measurements were made at a Voltage 0f 0 Vpp, 2 Vpp, 4 Vpp, 6 Vpp and 8 Vpp. At even higher the flow became unstable. The particles had the size of 1, 3, 5 and 8 μm in diameter. They were made of Polystyrene mixed in distillated water. Furthermore the separation efficiency was determined in the same way as in experiment 1 according to formula 6. Afterward the separation the medium was collected and analyzed using a multisizer ( model 3, Beckman Coulter) to determine the concentration of the particles. 150 ml of all the samples were collected by using two 0.15 m long Teflon tubes connected to the syringe pumps. The flow rate was 50 μl/min so all the separations lasted for at least 3 minutes, after the flow had been stabilized. Between the separations the system was rinsed with NaCl for cleaning and to remove air bubbles.

9.1 Results and conclusions The Voltage is proportional to p0 and in theory the acoustic force is changed by the square of the amplitude of the wave. This appearance can roughly be seen for the 3 micron and 5 micron particles (fig. 8). According to figure 8 the separation efficiency is increasing with increased Voltage apart from the 1 micron particles. Its efficiency is even higher without the any acoustic wave. This can be explained by the fact that small particles have a propensity to be collected in the middle of the channel in a laminar flow. This is because the flow profile is parabolic with a slower flow in the periphery. Why they are not affected by increasing amplitude is probably due to that the acoustic radiation force is not sufficient to attract them. The results indicate that 1 μm particles are simply too small to separate with this chip. A limitation of the particle separation has been reported by Augustsson [5] where the critical particle was estimated to approximately 1,8 μm. 1 μm 3 μm 5 μm 8 μm

0Vpp 58.29 46.80 47.11 45.28 2Vpp 56.35 60.95 65.90 72.37 4Vpp 51.63 65.04 76.57 94.93 6Vpp 52.76 62.59 72.46 85.70 8Vpp 55.80 91.00 97.96 95.95

Table 2. Separation efficiency in percentage for different diameter of the particles at different applied voltage.

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Fig. 8 Separation efficiency of different size of the particles as a function of the Voltage∝ p0. Constant frequency of 2 Mhz and a flow rate of 50 μl/min The best efficiency was found at a voltage of 8V (figure 9a) for particles of 5 and 8 μm. Equation 12 describes the lateral movement of the particles which shows that large particles are less damped and therefore they can move easier to the centre of the channel. At an applied voltage of 2V, 4V and 6V the efficiency shows a linear relationship for the particle size. One theory has been estimated by simulations which support this linear relationship[5].

dy 1∝Δ (13)

where Δy is defined to be the distance along the y-axis that a liquid element travels when moving 80% of the distance from the channel wall to the center of the channel. This Δy can approximately been related to the separation efficiency by a converted relationship because with a high efficiency only a short distance in the flow direction (y-axis) is needed for the particles to be separated. This approximation which gives this linear relation:

efficiencydefficiencyd

∝⇒∝11 (14)

However, this particle separation technique demonstrated in this project offers not only the ability to wash cells, but also to sort particles by there size which can be useful for instance in biomedical and chemical applications. For example it could be used to manipulate and control different reaction by moving certain particles over bands in the channel for a given period of time.

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a) b)

c) d)

e)

Fig 9. Graphs over separation efficiency depending the on the size of the particles at a) 0V, b) 2V, c) 4V, d) 6V and e) 8V

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10 Acknowledgements I wish to express my gratitude to doctoral student Per Augustsson for all his kind help and guidance during my work. His engagement and expertise in this area of research made it possible for me to complete this project in an enjoyable way. I also want to thank the Electric Department of Measurement at Lund Institute of Technology for letting me use all the necessary equipment.

11 References [1] F Petersson, A. Nilsson, H. Jönsson and T. Laurell, Carrier Medium Exchange through Ultrasonic Particle Switching in Microfluidic Channels, Anal. Chem, 77, 1216-1221 (2005). [2] K. Yosioka and Y. Kawasima, Acoustic radiation pressure on a compressible sphere, Acustica, 5, 167-173 (1955). [3] F Petersson, A. Nilsson, C. Holm, H. Jönsson and T. Laurell, Separation of lipids from blood utilizing ultrasonic standing waves in microfluidic channels, Analyst, 129, 938-943, (2004) [4] A. Nilsson et al. Acoustic control of suspended particles in micro fluidic chips, Lab Chip, 4, 131-135 (2004). [5] P Augustsson, Ultrasonic Control of Particles in Microfluidic Channels, Master’s thesis, Department of Measurement at Lund Institute of Technology, 27/01 (2006). [6] J.L. Meriam, L.G. Kraige, Engineering Mechanics, Dynamics, Fourth Ediditon (1998).

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