Evaluation of OSTE-hybrid materials for acoustophoresis applications
ELIN FORSS
KTH
SKOLAN FÖR KEMI, BIOTEKNOLOGI OCH HÄLSA
applications
ELIN FORSS
Master in Medical Engineering Date: June 23, 2020
Supervisor: Karl Olofsson Examiner: Matilda Larsson
KTH Royal Institute of Technology
Swedish title: Utvärdering av OSTE-hybrid-material för applikationer inom akustofores
This project aimed at exploring new hybrid materials to be used for acousto- phoresis applications. Acoustophoresis can be used to manipulate particles inside a microfluidic channel by creating ultrasound standing waves within the channel [1]. This can be used for cell separation [2] or trapping of particles [3].
The intent of this project was to create materials for use in microfluidic channels that would be cheaper and easier to manufacture than those tradi- tionally used, while still having adequate acoustic properties to allow for use in acoustopheresis. This was done by investigating whether the addition of glass-beads or glass-bubbles could increase the acoustic properties of an off- stoichiometry-thiol-enes (OSTE) based polymer.
Hybrid samples with different volume fractions of glass-beads or glass- bubbles added to the OSTE polymer were manufactured and characterised ac- cording to their acoustic properties using the pulse-echo buffer-rod method.
The acoustic properties measured were the density, attenuation, acoustic imp- edance and the reflection coefficient between water and the material. The ad- dition of glass-beads was found to increase the acoustic impedance while the inverse was found for the addition of glass-bubbles. Both the addition of glass- beads and glass-bubbles were found to increase the attenuation.
The hybrid material that was found to have the most suitable acoustic prop- erties was OSTE/Glass-beads 40%, whose acoustic impedance had been in- creased ∼60% compared to pure OSTE. Consequently, the OSTE/Glass-beads 40% material was used to manufacture a microfluidic channel.
A particle trapping experiment showed that the OSTE/Glass-beads 40%
microfluidic channel was able to obtain bead trapping. This means that a standing wave was able to be generated within the channel and that it was strong enough to trap particles in the centre of the channel. However, evalua- tion of the particle trapping efficiency of the channel showed that it was not as effective as those using traditional materials. Therefore, future work is recom- mended to optimise a channel design for the OSTE/Glass-beads 40% material to increase the particle trapping efficiency.
Sammanfattning
I detta projekt undersöktes ett nytt hybridmaterial för användning i applikatio- ner inom akustofores. Akustofores kan användas till att manipulera partiklar inuti mikrofluidkkanaler genom att generera ståendevågor i kanalen med hjälp av ultraljud [1]. Detta kan användas till cellseparation [2] eller till att fånga partiklar [3].
Målet i detta projekt var att skapa material som skulle bli billigare och möjliggöra enklare fabricering av kanalerna som används inom akustofores än de material som traditionellt används, med bibehållande av tillräckliga akus- tiska egenskaper. Detta genomfördes genom att undersöka om tillsättning av glaspärlor eller glasbubblor kunde förbättra de akustiska egenskaperna av en off-stoichiometry-thiol-enes (OSTE) baserad polymer.
Hybridprover gjorda på OSTE-polymeren med olika volymandelar av glas- pärlor och glasbubblor tillverkades och kategoriserades med avseende på deras akustiska egenskaper med hjälp av pulseeko buffertstång metoden. De akustis- ka egenskaperna som uppmättes var densitet, attenuering, akustisk impedans och reflektions koefficienten mellan vatten och materialet. Resultatet av pro- jektet visade att tillsättning av glaspärlor ökade den akustiska impedansen i motsatts till glasbubblorna som visade sig minska den. Vidare visade det sig att både tillsättningen av glaspärlor och glasbubblor ökade attenueringen.
Det hybridmaterial som visade sig ha de mest lämpliga akustiska egen- skaperna var OSTE/glaspärlor med en 40% volymandel av glaspärlor. Den akustiska impedansen hade förhöjts med cirka 60% jämfört med vanlig OS- TE. Därför valdes det hybrid-materialet till att tillverka en mikrofluidikkanal.
Därefter genomfördes ett partikelfångstexperiment som visade att, OS- TE/glaspärlor med en 40% volymandel av glaspärlor, kunde erhålla partikel- fångst i kanalen. Detta innebär att en stående våg kunde genereras i kanalen och att den var tillräckligt stark för att kunna fånga partiklarna i mitten av kanalen.
Däremot visade utvärdering av kanalens partikelfångsteffektivitet att den inte var lika effektiv som kanaler gjorda av traditionellt använda material. Därför rekommenderas framtida arbete till att designa en optimerad kanaldesign med OSTE/Glas-pärlor 40% materialets egenskaper i åtanke för att förhoppnings- vis kunna öka partikelfångst effektivitet.
Acoustophoresis; off-stoichiometry-thiol-enes; OSTE; microfluidics
Acknowledgements
First, I would like to thank Martin Viklund and Karl Olofsson for giving me the opportunity to do this project. I especially want to thank Karl for all the help and guidance he as given me in the project as my supervisor. I also want to thank Björn Hammarström for his help with the MATLAB code. Furthermore, I want to thank everyone at SciLife Lab for being so welcoming. Lastly, I want to thank my family and partner for always supporting me throughout my education.
1 Introduction 1
1.1 Objectives . . . 2
2 Methods 3 2.1 OSTE hybrid samples . . . 3
2.1.1 Sample production . . . 3
2.1.2 Density measurements . . . 5
2.2 Sample characterisation . . . 6
2.2.1 Buffer-rod Pulse-echo Experiment (BPE) . . . 6
2.2.2 System of equations . . . 7
2.2.3 Frequency-based Amplitude Ratio (FAR) method . . . 9
2.2.4 Time of flight (TOF) method . . . 10
2.2.5 Reflection Coefficient . . . 11
2.2.6 Verification . . . 11
2.3 Microfluidic channel . . . 12
2.3.1 Manufacturing process . . . 12
2.3.2 Channel evaluation . . . 14
3 Results 17 3.1 Verification . . . 17
3.1.1 Sample manufacturing verification . . . 17
3.1.2 Pulse-echo buffer-rod experiment verification . . . 19
3.2 Sample characterisation . . . 19
3.3 Channel evaluation . . . 23
3.3.1 Particle trapping . . . 23
3.3.2 PIV-analysis . . . 26
4 Discussion 28 4.1 Characterisation methods . . . 28
4.2 Manufacturing verification . . . 29
vii
4.3 The OSTE-hybrid materials . . . 29
4.3.1 OSTE/Glass-beads . . . 29
4.3.2 OSTE/Glass-bubbles . . . 31
4.4 Microfluidic channel . . . 31
5 Conclusions 33 A State of the Art 37 A.1 Ultrasound . . . 37
A.1.1 Ultrasound basics . . . 37
A.1.2 Standing waves . . . 41
A.2 Acoustophoresis . . . 43
A.2.1 Design . . . 44
A.2.2 Polymers used in acoustophoresis . . . 46
A.3 Off-stoichiometry thiol-enes (OSTE) polymer platforms . . . . 48
A.3.1 OSTE . . . 48
A.3.2 OSTE+ . . . 48
A.4 Pulse-echo method . . . 50
A.4.1 Pulse-echo set up . . . 50
A.4.2 Trailing echoes in buffer rods . . . 51
B Additional acoustic property data 53 B.1 Manufacturing verification . . . 53
B.2 Sample characterisation . . . 55
C MATLAB scripts 57 C.1 Echo analysis - Frequency-based Amplitude Ratio (FAR) method 57 C.2 Echo analysis - Time of flight (TOF) method . . . 60
C.3 PIVlab analysis . . . 64
D Microfluidic channel design 67 D.1 Design considerations . . . 67
D.2 Detail drawing of channel mould . . . 68
Ultrasound, defined as sound with a frequency above 20 kHz [4], is utilised in many fields of science, one of which is acoustophoresis. Acoustophoresis involves the use of ultrasound to generate standing waves within channels that enables particle manipulation [1]. It can be used for acoustic trapping [3, 5]
and particle separation [2, 6, 7, 8]. Where particle separation can be used for blood cell purification [8] and acoustic trapping can be used to create 3D cell cultures [5].
The materials commonly used for acoustophoresis applications are silicon and glass due to their well-suited acoustic properties [1]. However, these mate- rials are expensive and require laborious manufacturing techniques [2]. Con- sequently, this is a potential hindrance in the commercialisation of acousto- phoresis applications. Therefore, there is a need for a material better suited for mass production.
Polymers, on the other hand, are inexpensive and easy to use in mass pro- duction, however, they do not possess appropriate acoustic properties. Com- pared to glass and silicon, the acoustic impedance is lower and the attenuation is higher. This leads to an inefficient standing wave [1]. Nevertheless, if these properties were able to be enhanced, polymers could be a viable choice in commercial acoustophoresis devices.
In this project, it is investigated whether the acoustic properties of off- stoichiometry thiol-enes (OSTE) based polymers can be enhanced by the ad- dition of glass-beads or glass-bubbles. The project is a continuation of a master thesis project conducted by Yassin where it was shown that acoustic proper-
1
ties of OSTE based polymers could be improved through the addition of glass- beads [9].
Two hybrid materials were investigated: OSTE/Glass-beads and OSTE/- Glass-bubbles, with different volume fractions of beads/bubbles. The intent of adding glass-beads was to give the OSTE-material glass-like acoustic prop- erties, increasing the acoustic impedance, bringing the reflection coefficient as close to 1 as possible to create a rigid wall scenario. The addition of glass- bubbles, on the other hand, aimed to give the OSTE-material air-like acous- tic properties and therefore decrease the acoustic impedance to an extent that brought the reflection coefficient close to -1 to create a free boundary scenario (See section A.1.2 for explanations of rigid and free boundary).
1.1 Objectives
The first objective of the project was to determine the ratio of OSTE to Glass- beads or Glass-bubbles that results in the best acoustic properties for acousto- pheresis. This was conducted by producing samples of two hybrid materi- als (OSTE/Glass-beads and OSTE/Glass-bubbles), with different volume frac- tions of glass-beads/glass-bubbles and characterising their acoustic properties (attenuation, acoustic impedance, density and reflection cooefficient).
The second objective of the project was to determine whether a microflu- idic channel made using the best performing hybrid material could obtain par- ticle trapping , and if so, evaluate its efficiency.
2.1 OSTE hybrid samples
2.1.1 Sample production
To produce both the OSTE/Glass-beads and OSTE/Glass-bubbles samples, the commercial polymer platform Ostemer 322 crystal clear (OSTE) was used. It has epoxy added to it making it an OSTE+ polymer. The OSTE polymer plat- form components are stored as two separate parts in bottles labelled part A and part B respectively. These are combined at the time of manufacturing to produce the OSTE polymer at a ratio of 1.09:1(A:B).
In the OSTE/Glass-beads samples, silica glass-beads (SiLibeads Type S, SiLi) with a diameter of 40-70 µm and a density of 2500 mkg3 were used. For the OSTE/Glass-bubbles samples, air-filled glass-bubbles (Glass Bubbles K20, 3M) were used with a median diameter of 60 µm and a density of 200 mkg3.
Before producing the OSTE/Glass-beads and OSTE/Glass-bubbles sam- ples, a sample containing only OSTE was produced. This sample was needed to determine the density of OSTE and to be used as a reference.
To produce the samples, a scale was placed inside a fume hood and a stand- ing tube was placed on it. OSTE part B was then poured into the tube and weighed. The necessary weight of part A could then be calculated and added.
The OSTE mixture was then mixed using a vortex mixer until visibly ho- mogenously combined. The mixture was then degassed in a desiccator to re-
3
move air bubbles.
A calculation of the mass (mb) of glass-beads or glass-bubbles needed to produce a sample with a certain volume fraction (F ) was performed using equations 2.1 and 2.2.
Vb= moF
ρo(1 − F ) (2.1)
mb= Vbρb (2.2)
Where mo and ρo are the mass and density of the OSTE respectively and ρbis the density of either the glass-beads or glass-bubbles.
To produce the OSTE/Glass-beads samples, the glass-beads were added to the OSTE mixture and mixed using a vortex. This mixture was then degassed in a dessicator and injected into a PDMS mould of dimensions 34 x 34 x 3.76 mm with a glass slide top using a syringe (Figure 2.1). The glass slide was placed on top to ensure that the surface would be smooth and parallel to the bottom.
Figure 2.1: Image showing the mould used to produce the samples. In the bottom corners of the mould there are channels. One acts as an inlet and is used to insert a syringe and inject the mixture and the other acts as the outlet, allowing air to escape. The dimensions of the mould are 34 x 34 x 3.76 mm.
light for approximately 3 minutes on one side and 1 minute on the other side.
The sample was then demoulded and placed inside an analogue heat block for the second cure step at a temperature of 110◦Cfor approximately 1 hour.
Immediately after removing a sample from the heat block, it was placed under a heavy object to make sure the bottom and the top of the sample were parallel. The OSTE/Glass-beads samples were produced with different vol- ume fractions of glass-beads with increments from 8% up to 40%.
The OSTE/Glass-bubbles samples were produced in the same way except for two of the steps. The mixture was not degassed in a dessicator after the addition of glass-bubbles due to the risk of the glass-bubbles rupturing. Since the OSTE/Glass-bubbles mixture could not be degassed, the mixture was not mixed using a vortex as this introduced too many air bubbles. Instead, the tube was turned slowly around by hand until mixed. OSTE/Glass-bubbles samples were produced with volume fractions of glass-bubbles in increments from 10%
up to 30%.
2.1.2 Density measurements
To determine the density of the samples, the Archimedes density method was used. The samples were first weighed on a scale to obtain the mass. They were then submerged into a cylinder of distilled and degassed water with a temper- ature of 20◦C. Since density is temperature dependent, the temperature of the water needed to be the same as in the room where the proceeding pulse-echo experiments were conducted (see section 2.2.1).
The mass of the samples when submerged in water was then measured using the hook option of the scale. When the mass of the samples (m) and their mass when submerged (msub) were obtained, their density could be de- termined using equation 2.3.
ρs= mρw
m − msub (2.3)
Where ρsis the density of the sample and ρwis the density of distilled wa- ter at 20◦C.
2.2 Sample characterisation
2.2.1 Buffer-rod Pulse-echo Experiment (BPE)
To measure the acoustic properties of the samples, a buffer-rod pulse-echo method was used (Section A.4.1). A transducer was coupled to an aluminium buffer-rod with a pentagon cross section. The buffer-rod was then coupled to the sample. The different parts were all coupled together with glycerine to aid in the transmission of ultrasonic waves. To make sure that the different parts of the set-up did not move and were firmly pressed against each other, a holder was used (Figure 2.2).
An Olympus 5072PR pulser/receiver was used to excite the transducer and to receive the returning echoes. The pulser/receiver was set to a pulse repe- tition frequency of 100 Hz, 128 averaging, an energy setting of 3, a damping setting of 2 and zero gain. To view and capture the echoes, an oscilloscope was used. The data from the echoes were then stored in excel and analysed us- ing MATLAB (R2019a, Version 9.6.01072779, MathWorks Inc., Natick, MA, USA, 2019) (see appendix C.1-C.2 for the code used).
To ensure that the results were consistent, the pulse-echo method was per- formed 5 times for each sample. From this, a mean value and standard devia- tion for the acoustic properties were obtained.
(a) (b)
Figure 2.2: Image (a) shows the holder used in the pulse-echo experiment, where the hole creates a sample/air interface. Image (b) shows the whole set- up with the holder (1), transducer (2), buffer-rod (3) and sample (4).
2.2.2 System of equations
To determine the acoustic impedance, speed of sound and the attenuation of the samples, a system of equations was derived for the first three echoes recorded (Equations 2.4-2.6).
A1 = A0R12e−αa2da (2.4) A2 = A0T12R23T21e−αa2dae−αs2ds (2.5) A3 = A0T12R223R21T21e−αa2dae−αs4ds (2.6)
Where A1, A2and A3 are the amplitudes of the returning echoes 1, 2 and 3 respectively (See section A.4.1 for further explanation on how the echoes are generated). αais the attenuation of aluminium, αsis the attenuation of the
sample, dais the length of the aluminium buffer rod and dsis the thickness of the sample (Figure 2.3).
Lastly, R and T are the pressure reflection and transmission coefficients respectively, where the subscript numbers pertain to a specific interface. The buffer rod is denoted with 1, the sample with 2 and air with 3. So, for example, R12is the pressure reflection coefficient for the Buffer-rod/Sample interface.
Figure 2.3: Represenation of how the three echoes A1, A2and A3 were gener- ated. The echoes have been spread apart in the image for clarity, however, in reality they will all travel the same path.
The expressions for the reflection and transmission coefficients are shown in equations 2.7-2.11 where Z is acoustic impedance and the associated sub- script number refers to the medium.
R12 = Z2− Z1
Z2+ Z1 (2.7)
R21 = Z1− Z2
Z1+ Z2 = −R12 (2.8)
R23 = Z3− Z2
Z3+ Z2 (2.9)
T12 = 1 + R12 (2.10)
T21= 1 + R21 = 1 − R12 (2.11)
The first method used to determine the acoustic properties of the samples is a method using the ratios of the first three echoes detected by the receiver. This method determines all the acoustic properties as a function of frequency by Fourier transforming the amplitudes of the echoes.
From the system of equations (2.4-2.6), the reflection coefficient (R12) of the interface between the buffer rod and the sample can be derived.
R12 = −
s A1A3
A3A1 − A22 (2.12)
By using equation 2.7, the acoustic impedance of the sample (Z2) can then be found.
Z2 = Z11 + R12
1 − R12 (2.13)
Using the acoustic impedance (Z2) and density (ρs) of the sample, the speed of sound (cs) can be found.
cs = Z2
ρs (2.14)
From the system of equations (2.4-2.6), an equation for the attenuation co- efficient (αs) can also be derived.
αs= −1 2dsln
−A3 A2
1 R12R23
(2.15)
2.2.4 Time of flight (TOF) method
The second method used to determine the acoustic properties of the samples was the time of flight (TOF) method. To determine the speed of sound (cs), the time delay (τ) between the first and second echoes was used.
Figure 2.4: Visual representation of time delay (τ). Calculated by taking the mean of τ1 and τ2 which are the time delays between the two postive peaks and two negative peaks respectively.
The distance travelled by the second echo differs due to the second echo having additionally travelled a distance of 2dssince it travelled back and forth within the sample (Figure 2.3). Therefore, by obtaining the time delay, the speed of sound of the sample can be determined by using equation 2.16.
cs= 2ds
τ (2.16)
The acoustic impedance (Z2) of the sample can then be calculated using equation 2.17, where ρsis the density of the sample.
Z2 = csρs (2.17)
The attenuation of the sample (αs) can then be determined using the ampli- tude ratio between the Fourier transformed first and second echoes. This dif- fers to the FAR method which requires the amplitudes of the first three echoes.
αs = 1
2dsln A1
A2
(−(R212)+1)R23
R12
!
(2.18)
2.2.5 Reflection Coefficient
When the acoustic impedance of the samples was obtained, the reflection co- efficient (R) between the samples and the fluid within the microfluidic channel could be calculated.
R = Zs− Zw
Zs+ Zw (2.19)
Where Zs is the acoustic impedance of the sample and Zw is the acoustic impedance of water since that was the fluid used in this project.
2.2.6 Verification
Verification of manufacturing process
To verify that the manufacturing method of the samples was consistent, three samples of the same composition were manufactured and their acoustic prop- erties were characterised and compared. Three samples of OSTE with a glass- bead volume fraction of 8% were manufactured for this. The volume fraction chosen for this verification was arbitrary since it is only the manufacturing method that was being verified.
Verification of sample characterisation
To validate the pulse-echo experimental set-up and the analysis code used in MATLAB, a test was done on a sample made of the material PMMA. The values obtained experimentally were compared to values from literature.
2.3 Microfluidic channel
2.3.1 Manufacturing process
The sample that had the most suitable properties for acoustofluidic applica- tions, determined from the characterisation of the samples (Section 3.2), was chosen for use in the manufacture of the microfluidic channel. It was the OSTE/Glass-beads sample with a 40% volume fraction of glass-beads that was deemed to have the most suitable acoustic properties and was therefore chosen.
A 3D model of a mould for use in the manufacture of the channel was designed using CAD software (Appendix D). The design of the channel was made with the material properties in mind so that the channel would be as effective as possible. However, due to unfortunate circumstances, the micro- milling machine needed to mill the mould was not accessible. Since it was not possible to make a new channel mould, an existing channel mould was used instead (Figure 2.5).
Figure 2.5: Mould used for the microfluidic channel where the channel width is 265 µm.
The OSTE/Glass-beads mixture for the channel was produced in the same way as in section 2.1.1. The mould was then filled with the mixture using a syringe. The UV cure was only done on one side for 2 minutes before be- ing demoulded. The channel was then placed on a microscope glass slide and pressed against it to eliminate any air between the two surfaces. This assembly was then heat cured as in section (2.1.1), enabling the channel to bond to the glass.
Since particle trapping only in the middle of the channel was desired, the width of the channel had to be equal to half the wavelength of the ultrasound (see section A.2.1). The channel width was 265 µm which requires a trans- ducer with a resonance frequency of 2.83 MHz to meet the half wavelength condition. The transducer available with the most suitable resonance fre- quency was 2.5 MHz. The transducer was glued on with temporary adhesive and wires were soldered to the electrodes (Figure 2.6).
Figure 2.6: The microfluidic channel (1) bonded to a microscope glass slide (2) with an attached 2.5 MHz transducer (3).
2.3.2 Channel evaluation
To evaluate the channel, a test was first conducted to assess whether generating a standing wave to trap particles inside the microfluidic channel was possible.
The channel was placed under a Zeiss Axiovert 40 CFL microscope with 5x objective to be able to view and capture the events in the channel. A mixture of blood phantom beads with 5 µm radius and water was added to the channel by placing a drop of the mixture at the inlet of the channel. The mixture was then given time to flow through the channel by capillary forces.
To find the experimental frequency at which the ultrasonic standing wave would be generated, the transducer was tuned to the theoretical frequency value of 2.83 MHz and then frequencies below and above that value were tested until trapping was observed. Once trapping was observed, the asso- ciated experimental frequency was identified as 2.5 MHz and several videos were captured of the bead trapping using the blood phantom beads. Further- more, trapping was also tested using Thermo Fisher fluorescent beads with a radius of 10 µm and with Calcin red-orange stained human cancer cells from the K-562 cell line.
To analyse the particle trapping in the channel, a Particle Image Velocime- try (PIV) analysis was conducted on the video footage of the blood phantom
into the application PIVlab [11]. Using the frame rate of 10 fps for time cal- ibration and a known distance in the footage (the channel width) for spatial calibration, the application captured and quantified movement between two frames. It compared frame 1 with frame 2, then 2-3, 3-4 and so on. The re- gion of interest within the frame (the channel) was broken into small areas containing 64 pixels for the comparison and the application output velocity vectors representing the movement detected in each area (Figure 2.7).
Figure 2.7: Example of a PIVlab comparison between two frames from the blood phantom bead trapping video. The z-direction is across the channel width and the x-direction goes along the length of the channel. The arrows represent the velocity vectors with those that are red signifying vectors that have been post-processed.
Since only the particle velocity towards the channel centre was of interest, the particle velocity in the z-direction (vp(z)) was extracted. Thereafter, the mean vp(z)was calculated along the x-axis for each z-position (Appendix C.3 for MATLAB code). A sinusoidal curve fit was then applied to the data.
The particle velocity within a microfluidic channel is a sinusoidal curve and can be theoretically represented by equation 2.20 [12].
vp(z) = 2πΦka2sin(2kz)Eac
3πη (2.20)
Where Eacis the energy density, η is the viscosity of water, a is the particle radius, k = 2πλ is the wavenumber and Φ is the contrast factor (Equation A.12).
As a result of obtaining the particle velocity (vp(z)), the energy density (Eac) could be obtained using equation 2.20. However, experimentally the pe- riod of the velocity curve did not have the theoretical period of 2kz. Instead, equation 2.20 was modified so that the period of the curve fit was used.
Furthermore, using the energy density obtained, the pressure could be de- termined using equation 2.21 [12].
P = qEac4ρwc2w (2.21)
3.1 Verification
3.1.1 Sample manufacturing verification
The density and acoustic property values obtained from the manufacturing ver- ification are shown in figures 3.1 - 3.3. Exact values and standard deviation of the three OSTE/Glass-beads can be found in appendix B.1.
Figure 3.1: Density of the three samples of OSTE/Glass-beads 8%.
17
Figure 3.2: The calculated mean and standard deviation of the attenuation for the 5 repetitions of the BPE for the three samples of OSTE/Glass-beads 8%.
Figure 3.3: The calculated mean and standard deviation of the acous- tic impedance for the 5 repetitions for the BPE of the three samples of OSTE/Glass-beads 8%.
Table 3.1 shows the results from the verification experiment of the FAR and TOF methods using PMMA. The FAR method obtained results closest to the values found in literature.
Table 3.1: Acoustic properties of PMMA obtained experimentally using both the FAR and TOF methods with the standard deviation determined from 5 repititions. Additionally, values from literature [13] are included.
α[Npm] c[ms] Z[MPa sm ]
Literature 60.8 2750 3.28
TOF 53.1±3.58 2700±3.97 3.18±0.00472 FAR 57.4±1.76 2790±38.9 3.28±0.0458
3.2 Sample characterisation
From the data obtained, the acoustic impedance and density can be seen to increase with an increase in glass-bead volume fraction for the OSTE/Glass- beads samples, except for the acoustic impedance of the OSTE/Glass-beads 16% with the FAR method. An inverse trend can be seen for the OSTE/Glass- bubbles samples (Figures 3.4 and 3.5).
Figure 3.4: Density of all samples.
Figure 3.5: The calculated mean and standard deviation of the acoustic impedance for the 5 repetitions of the BPE.
in bubble/bead volume fraction (Figure 3.6). However, there were some out- liers such as the OSTE/Glass-beads 16% (FAR) and OSTE/Glass bubbles 30%
(TOF).
Figure 3.6: The calculated mean and standard deviation of the attenuation for the 5 repetitions of the BPE.
For the OSTE/Glass-beads hybrid material, the sample with a 40% volume fraction of glass-beads had a reflection coefficient closest to 1 and was there- fore chosen for the manufacture of a microfluidic channel (Figure 3.7). For the OSTE/Glass-bubbles hybrid material, none of the samples had a reflection coefficient close to -1 as hoped (Figure 3.7).
Figure 3.7: Reflection coefficient obtained using the mean acoustic impedance of the samples (Zs) and the acoustic impedance of water (Zw).
In table 3.2 the acoustic properties of pure OSTE and the chosen hybrid sample, OSTE/Glass-beads 40%, can be compared to other materials used in acoustophoresis applications. The acoustic impedance and reflection coef- ficient have been significantly increased compared to pure OSTE and other polymers investigated for use in acoustophoresis applications such as PMMA and polystyrene. However, it has not been increased to the point of the tradi- tionally used materials such as glass, steel, or silicon.
as well as OSTE/Glass-beads 40% and pure OSTE used in this project. The reflection coefficient is calculated between water and the respective material.
Material α[Npm] Z[MPasm ] Rp
OSTE/Glass-beads 40% FAR 202 @1.6MHz 7.28 0.662
TOF 147 @1.6 MHz 5.30 0.563
Pure OSTE 0% FAR 96.5 @1.6 MHz 3.10 0.353
TOF 106 @1.6 MHz 3.30 0.381
PMMA 60.8 @ 5MHz [13] 3.28 [13] 0.378
Polystyrene - 1.79 [1] 0.0948
Steel - 45.7 [1] 0.937
Silicon - 19.8 [1] 0.861
Pyrex (Glass) - 12.6 [1] 0.790
Silica glass - 14.5 [14] 0.815
3.3 Channel evaluation
3.3.1 Particle trapping
From the bead trapping test, it was shown that a standing wave was able to be generated inside the channel and particle trapping occured (Figure 3.8). The bead trapping was obtained at a frequency of 2.5 MHz with a peak to peak voltage of 14 Vpp.
(a) (b) (c)
Figure 3.8: Results from the particle trapping test using three different par- ticles. Image (a) shows trapping of the blood phantom beads. Image (b) shows particle trapping using the Thermo Fisher fluorescent beads and im- age (c) shows trapping of Calcin red-orange stained human cancer cells from the K-562 cell line. The channel width in all images is 265 µm.
Even though bead trapping within the channel was obtained, it was not generated throughout the entire channel. In the middle of the channel length- wise, the beads were not focused in the centre of the channel, instead, the beads were more randomly distributed (Figure 3.9).
(a) (b)
Figure 3.9: Images showing the particle trapping throughout the entire chan- nel. Both images show the trapping was not as strong in the middle lenght wise of the channel. The image (a) shows trapping of blood phantom beads where the black rectangle in the top right corner is the transducer. At the bottom and top of the image, parts of the inlet and outlet holes are seen. The image (b) shows trapping of Thermo Fisher fluorescent beads.
3.3.2 PIV-analysis
The particle velocity (vp(z)) results from the PIV-analysis on the two videos where trapping was obtained using blood phantom beads are shown in Figures 3.10 and 3.11.
Figure 3.10: Graph showing velocity in the z-direction (vp(z)) of the first video, averaged along the x-direction for the length of the channel with a si- nusoidal curve fit.
Figure 3.11: Graph showing velocity in the z-direction (vp(z)) of the second video, averaged along the x-direction for the length of the channel with a si- nusoidal curve fit.
The energy density (Eac) and pressure (P ) calculated from the PIV-analysis results and equations (2.20 and 2.21) are shown in table 3.3.
Table 3.3: Results obtained through the PIV analysis of the two videos taken of the trapping of blood phantom beads.
Eac[mJ3] P [kPa]
Video 1 1.15 101
Video 2 1.03 96.0
Discussion
4.1 Characterisation methods
The verification of the two methods showed that the FAR-method generated more accurate results than the TOF-method. However, when used on the hy- brid samples, the FAR-method generated a relatively large standard deviation for all acoustic properties. In contrast, the TOF-method generated results with a much smaller standard deviation for the acoustic properties, excluding atten- uation.
Since the FAR-method and the attenuation calculation of the TOF-method all depend on amplitude ratios, the large standard deviation is likely due to the variations in the echo amplitudes between repititions. From figure B.3 it can be seen that there is significant variation of amplitude and shape between repi- titions for echoes 2 and 3 of the OSTE/Glass-beads 40% sample. The same significant variation cannot be seen in the pure OSTE sample which, in gen- eral, has a smaller standard deviation compared to the other samples (Figure B.4).
One possible reason for the amplitude variations could be due to scattering caused by the glass-beads/bubbles. If there is a slight variation in bead/bubble packing, the wave will be scattered differently for each repitition. This would lead to the amplitudes of the second and third echoes being affected differently depending on the exact position of sonification. This theory is supported by the fact that the standard deviation between repititions is significantly lower for the samples without glass-beads/bubbles such as PMMA and pure OSTE.
28
high attenuation of the hybrid samples (Figure 3.6). The high attenuation low- ers the amplitudes of the second and third echoes. This could particularly affect the third echo as the amplitude could become so small that it becomes difficult to distinguish from the noise due to a low signal-to-noise ratio. This could particularly cause problems in the FAR method since it is dependent on the third echo.
Therefore, the FAR method does not appear suitable for non-homogenous materials that introduce significant scattering or with materials with high at- tenuation. The TOF method, on the other hand, appears to be more appropriate for non-homogeneous materials such as the OSTE-hybrids since it appears to be better suited in terms of consistency and reproducibility.
4.2 Manufacturing verification
The manufacturing verification results showed slight variations in material properties in the three samples of OSTE/Glass-beads 8%. One source of po- tential error that could account for this variation is the mass measurements.
The weighing had to be performed in a fume hood and due to the varying air pressure in this environment, the mass fluctuated. Overall, though, the variation between samples was relatively small, suggesting the manufacturing process was consistent.
4.3 The OSTE-hybrid materials
4.3.1 OSTE/Glass-beads
Through the addition of glass-beads, the acoustic impedance and reflection coefficient of OSTE/Glass-beads 40% were significantly increased by ∼60%
and ∼50% respectively compared to pure OSTE (Table 3.2, TOF method).
The increase in these properties means less energy from the standing wave is transmitted through the channel walls, resulting in more efficient particle trap- ping.
Moreover, the acoustic impedance and reflection coefficient of OSTE/Glass- beads 40% is significantly higher than other polymers used for acoustophore- sis applications. However, these properties are still significantly lower than for commonly used materials such as glass and silicon (Table 3.2).
An increase in acoustic impedance due to the addition of glass-beads was also shown in a previous master thesis conducted by Yassin [9]. In Yassin’s project she manufactured samples with glass-beads volume fractions up to 32% and the acoustic impedance was seen to increase with an increase in vol- ume fraction of glass-beads. Therefore, it was investigated in this project if the volume fraction of glass-beads could be further increased to additionally increase the acoustic impedance. The glass-beads volume fraction limit was found to be at 40%, where values higher than this were found to make the mix- ture too viscous which meant it was not fluidic enough to be poured into the syringe and injected into the mould.
A commercial OSTE polymer was used in this project that was not avail- able for use at the time of Yassin’s research [9], and thus volume fractions investigated by Yassin were also covered in this project.
The OSTE/Glass-beads 40% material had increased attenuation, ∼ 40%
greater than pure OSTE (Table 3.2, TOF method). Since the absorption com- ponent of attenuation converts energy to heat, this could result in heating prob- lems. However, since the increase in attenuation is most likely due to scattering and not absorption, the increased attenuation is not likely to lead to an increase in heat. Furthermore, due to the increased scattering of the ultrasound, the heat created could disperse more evenly, avoiding heat concentrations within the material. Nonetheless, the possibility of increases in heating due to the high attenuation should be examined in future work.
The OSTE/Glass-beads material with a glass-beads volume fraction of 16% did not show an increase in acoustic impedance and attenuation com- pared to the 8% sample when using the FAR method. Since this was only seen when using the FAR method and not the TOF method, this is most likely due to the potential error sources in the FAR method discussed previously (Sec- tion 4.1). However, it could also be due to the possibility of air bubbles being present in the sample that were not completely removed during the degassing step (Section 2.1.1).
The OSTE/Glass-bubbles was a new hybrid material that had not yet been in- vestigated in previous projects. It was hoped that the addition of glass-bubbles would decrease the acoustic impedance so much that the reflection coefficient would be close to -1 which would create a strong standing wave. However, the addition of glass-bubbles did not lower the acoustic impedance enough, in- stead bringing the reflection coefficient closer to zero which creates a small rel- fection and therefore a weak stadning wave. Therefore, a OSTE/Glass-bubbles hybrid material is not a suitable for acoustophoresis.
The glass-bubble volume fraction limit was found to be 30%. Above this, the hybrid material became too brittle after the first cure to be able to remove it from the glass slide without cracking.
However, for future work it could be investigated whether adding glass- bubbles to a polymer material with a lower acoustic impedance than OSTE, such as polystyrene, could achieve the desired result.
4.4 Microfluidic channel
A channel using the most suitable OSTE/Glass-beads hybrid material was manufactured to evaulate whether it could obtain particle trapping. A channel made of this material had not previously been tested and it was proposed as future work in Yassin’s master thesis [9].
Images 3.8 and 3.9 prove that trapping of particles can be obtained using a microfluidic channel made from OSTE/Glass-beads 40%. However, trapping was not obtained throughout the entire channel length (Figure 3.9). This could be due to small variations in the channel width, possibly caused during man- ufacturing of the channel or channel mould.
The resonance frequency at which trapping occurred differed from the the- oretically calculated frequency. This is something that has been found in other experiments on polymer-based microfluidic channels [6]. This is most likely because the polymer materials do not create an ideal rigid wall. This could re- sult in the channel width condition (Equation A.13) no longer being accurate.
According to Bruus [12], common values for energy density of microflu- idic resonators using below 10 Vpp are 10-100 Jm−3. These values were ob- tained using optimal acoustic materials such as silicon or glass [12]. This is higher than the ∼1Jm−3 generated using the microfluidic channel in this project when supplied with 14 Vpp. However, considering the resonator de- sign was not optimised for the OSTE/Glass-beads material, the energy density could most likely be improved.
Therfore, for future work, investigation into optimising the design of a mi- crofluidic channel using the OSTE/Glass-beads 40% material should be con- ducted. With an optimal design of the channel, the energy density could hope- fully be increased and closer compare to the ideal materials on the market.
In terms of the first objective of the project, the sample manufacturing and characterisation showed that for the OSTE/Glass-bubbles samples there was an inverse relationship between glass-bubbles volume fraction and acoustic impedance as expected. However, the decrease in acoustic impedance was not significant enough to bring the reflection coefficient close to -1 and was there- fore not deemed suitable for acoustophoresis.
Furthermore, for the OSTE/Glass-beads samples, there was an increase in acoustic impedance with an increase in glass-beads. The sample with the highest acoustic impedance and therefore, a reflection coefficient closest to 1, was the sample with a 40% glass-beads volume fraction. This hybrid material was deemed to have the most suitable acoustic properties for acoustophoresis and was therefore chosen for the manufacture of the microfluidic channel.
For the second objective of the project, it was shown that not only manu- facturing a microfluidic channel using the hybrid material OSTE/Glass-beads 40% was possible but that particle trapping could be obtained. Consequently, this makes it a promising material to be used in acoustophoresis applications.
33
[1] Lenshof A, Evander M, Laurell T, Nilsson J. Acoustofluidics 5: Building microfluidic acoustic resonators. LAB CHIP. 2012 Jan;12(4):684–95.
[2] Yang C, Li Z, Li P, Shao W, Bai P, Cui Y. Acoustic particle sorting by integrated micromachined ultrasound transducers on polymer-based microchips. In: 2017 IEEE International Ultrasonics Symposium (IUS).
IEEE; 2017. .
[3] Christakou AE, Ohlin M, Vanherberghen B, Khorshidi MA, Kadri N, Frisk T, et al. Live cell imaging in a micro-array of acoustic traps facili- tates quantification of natural killer cell heterogeneity. Integr Biol. 2013 Feb;5(4):712–19.
[4] Hoskins PR, Martin K, Thrush A, editors. Diagnostic Ultrasound:
Physics and Equipment. 2nd ed. New York: Cambridge University Press;
2010.
[5] Christakou AE, Ohlin M, Önfelt B, Wiklund M. Ultrasonic three- dimensional on-chip cell culture for dynamic studies of tumor immune surveillance by natural killer cells. LAB CHIP. 2015 Jun;15(15):3222–
3231.
[6] Mueller A, Lever A, Nguyen TV, Comolli J, Fiering J. Continuous acous- tic separation in a thermoplastic microchannel. J Micromech Microeng.
2013 Oct;23(12):125006–16.
[7] Gonzalez I, Tijero M, Martin A, Acosta V, Berganzo J, Castillejo A, et al.
Optimizing Polymer Lab-on-Chip Platforms for Ultrasonic Manipula- tion: Influence of the Substrate. Micromachines. 2015 May;6(5):574–
91.
34
cytes by Acoustic Separation in Plastic Microchannels. SLAS Technol.
2018 Jan;23(4):352–63.
[9] Yassin Z. Characterization of OSTE-based polymers for acoustofluidic applications [Master’s thesis]. KTH, Applied Physics. Stockholm; 2017.
[10] Inc M. Matlab R2019a; 2019. Natick, MA, USA.
[11] Thielicke W, Stamhuis EJ. PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB. Journal of Open Research Software. 2014 oct;2.31.
[12] Bruus H. Acoustofluidics 7: The acoustic radiation force on small parti- cles. LAB CHIP. 2012 Feb;12(6):1014–1021.
[13] Carlson JE, van Deventer J, Scolan A, Carlander C. Frequency and tem- perature dependence of acoustic properties of polymers used in pulse- echo systems. In: IEEE Symposium on Ultrasonics. IEEE; 2003. . [14] Krautkrämer J, Krautkrämer H. Ultrasonic Testing of Materials. 4th ed.
New York: Springer-Verlag Berlin Heidelberg; 1990.
[15] Cheeke JDN. Fundamentals and applications of ultrasonic waves. 2nd ed. Boca Raton: CRC Press/Taylor & Francis Group; 2012.
[16] Jönsson H, Holm C, Nilsson A, Petersson F, Johnsson P, Laurell T.
Particle Separation Using Ultrasound Can Radically Reduce Embolic Load to Brain After Cardiac Surgery. Ann Cardiothorac Surg. 2004 nov;78(5):1572–1577.
[17] Olofsson K, Hammarström B, Wiklund M. Acoustic separation of living and dead cells using high density medium. LAB CHIP. 2020 May;.
[18] Augustsson P, Barnkob R, Wereley ST, Bruus H, Laurell T. Auto- mated and temperature-controlled micro-PIV measurements enabling long-term-stable microchannel acoustophoresis characterization. LAB CHIP. 2011 Oct;11(24):4152–64.
[19] Ohlin M, Christakou AE, Frisk T, Önfelt B, Wiklund M. Influence of acoustic streaming on ultrasonic particle manipulation in a 100-well ring- transducer microplate. J Micromech Microeng. 2013 Jan;23(3):035008–
19.
[20] Carlborg CF, Haraldsson T, Öberg K, Malkoch M, van der Wijngaart W.
Beyond PDMS: off-stoichiometry thiol-ene (OSTE) based soft lithog- raphy for rapid prototyping of microfluidic devices. LAB CHIP. 2011 Jul;11(18):3136–47.
[21] Saharil F, Gylfason KB, Liu Y, Haraldsson T, Bettotti P, Kumar N, et al.
Dry transfer bonding of porous silicon membranes to OSTE(+) polymer microfluidic devices. In: 2012 IEEE 25th International Conference on Micro Electro Mechanical Systems (MEMS). IEEE; 2012. .
[22] Saharil F, Forsberg F, Liu Y, Bettotti P, Kumar N, Niklaus F, et al. Dry adhesive bonding of nanoporous inorganic membranes to microfluidic devices using the OSTE(+) dual-cure polymer. J Micromech Microeng.
2013 Jan;23(2):025021–29.
[23] Lynnworth LC. Ultrasonic Measurements for Process Control: Theory, Techniques, Applications. San Diego: Elsevier Science & Technology;
1989.
[24] Papadakis EP. Buffer-Rod System for Ultrasonic Attenuation Measure- ments. J Acoust Soc Am. 1968 Nov;44(5):1437–41.
[25] Jen CK, Piche L, Bussiere JF. Long isotropic buffer rods. J Acoust Soc Am. 1990 Jul;88(1):23–25.
[26] Selfridge AR. Approximate Material Properties in Isotropic Materials.
IEEE Trans Sonics Ultrason. 1985 May;32(3):381–94.
[27] Redwood M. Mechanical waveguides. The propagation of acoustic and ultrasonic waves in fluids and solids with boundaries. Oxford: Pergamon Press; 1960.
[28] Foudzi FBM. Development of Polygonal Buffer Rods for Ultrasonic Pulse-Echo Measurements with High Signal-to-Noise Ratio [Doctoral Dissertation]. Graduate School of Nagaoka University of Technology, Nagaoka University of Technology; 2016.
[29] Wynand. Read .CSV File Created with Tektronix TDS2000;
2020. MATLAB Central File Exchange. Available
from: https://www.mathworks.com/matlabcentral/fileexchange/
44606-read-csv-file-created-with-tektronix-tds2000.
A.1 Ultrasound
A.1.1 Ultrasound basics
Ultrasound is defined as sound with a frequency higher than 20 kHz [15]. One of the ways ultrasound can propagate through a medium is as a longitudinal wave. A longitudinal wave will make the particles of a medium move back and forth in the direction of the wave propagation. It will create areas of compres- sion and rarefaction in the medium which means there will be areas of high and low pressure respectively (Figure A.1). Since the particles just move back and forth, eventually returning to their original position, it is only the energy that is propagating [4].
A soundwave will have a certain frequency, wavelength and speed of sound [4]. The frequency (f), is defined as the number of wave peaks that pass a certain point per second and the wavelength (λ[m]) defined as the distance between two peaks [4]. Speed of sound for a longitudinal wave (c [ms]) is a material property that depends on the density (ρ [mkg3]) and bulk modulus (B [mN2]) of the material through which it is traveling [4].
c =
sB
ρ (A.1)
Speed of sound, wavelength, and frequency are related through equation A.2.
37
λ = c
f (A.2)
Since speed of sound is a material property and frequency is usually de- cided by the source of the sound, it is the wavelength that will vary [4].
Figure A.1: Top figure showing the pressure wave of the sound wave where the wavelength (λ) is indicated. The bottom is a representation of the particle displacement due to the traveling sound wave.
Propagating soundwaves will be reflected at interfaces of different materi- als that have different acoustic impedance [4]. Acoustic impendence (Z [Pasm ]) is also a material property and can be written as a function of speed of sound and density (Equation A.3).
Z = ρc (A.3)
There are three boundary conditions for wave reflection. There is a pres- sure continuity condition which states that the incident pressure (Pi) and re- flected pressure (Pr) in the first medium must equal the transmitted pressure
continuity condition (Equation A.5). The third condition states that there is an energy conservation condition where the incident wave intensity (Ii) has to equal the sum of the reflected (Ir) and transmitted (It) wave intensity (Equa- tion A.6) [4].
Pi+ Pr = Pt (A.4)
vi+ vr = vt (A.5)
Ii = Ir+ It (A.6)
If a soundwave encounters a smooth interface that is large relative to its wavelength and there is a difference in acoustic impedance between the two mediums, the wave will be reflected in one direction [4]. The reflected wave will be reflected at an angle equal to the incident wave angle (Figure A.2).
That means that if the soundwave travels perpendicular to the interface, it will travel back along the same path when it gets reflected [4].
Figure A.2: Reflection against a large smooth interface
To what extent the wave gets reflected at an interface of different acoustic impedance is determined by the reflection coefficient (R) [4]. The pressure
reflection coefficient (Rp) can be defined as the ratio between the pressure of the reflected wave and the pressure of the incident wave. This ratio can be determined through the difference in acoustic impedance (Equation A.7).
Rp = Pr
Pi = Z2− Z1
Z2+ Z1 (A.7)
From the pressure reflection coefficient one can acquire the intensity re- flection coefficient, Ri[15]:
Ri = Ir
Ii = |Rp|2 =
Z2 − Z1
Z2+ Z1
2
(A.8)
From the reflection coefficient equations, it follows that if there is a large difference in acoustic impedance, a large portion of the wave’s intensity and pressure will be reflected at the interface. However, unless the wave is com- pletely reflected, part of the wave will be transmitted through the interface [15]. To what extent the wave will be transmitted is determined through the coefficients for transmission intensity (Ti) and transmission pressure (Tp).
Ti= 1 − Ri (A.9)
Tp = 1 + Rp (A.10)
From the intensity transmission coefficient, it follows that if there is a large difference in acoustic impedance between two mediums, very little energy will be transmitted through.
Scattering is another type of reflection that occurs when a soundwave en- counters small objects, equal to a wavelength or smaller, with different acous- tic impedance. The soundwave will be reflected into several waves at different
wave, the wave will get reflected in all directions homogenously [4].
Scattering is a contributing factor to the attenuation that a propagating soundwave can experience. Attenuation of a soundwave means its intensity decreases exponentially as it travels. Besides scattering, there are many other factors contributing to attenuation with one important factor being absorption.
When ultrasound gets absorbed in a medium, the energy converts to heat [4].
Attenuation of soundwaves changes depending on the frequency of the wave and the temperature of the medium it is travelling through [15]. The relation- ship between frequency and attenuation is linear and an increase in frequency will lead to approximately the same factor increase in attenuation [4].
A.1.2 Standing waves
When two sound waves of the same frequency and amplitude but with pre- cisely opposite propagation direction interfere with each other, they can create a standing wave [14]. A standing wave compared to a normal soundwave has no net propagation of energy [15].
There will be certain points in the standing waves called nodes where the two waves cancel each other out due to destructive interference [14]. In an ideal case, the minimum amplitude at a node would be zero. However, in real cases it will not be exactly zero [15]. Furthermore, there will be points where the two waves maximally interfere constructively and add together, called antin- odes [14].
The nodes and antinodes of motion and pressure will be the opposite of each other. Where there is an antinode of maximum pressure, there will be a node of minimum motion [14]. In a standing wave the nodes and antinodes are spaced a quarter of a wavelength apart [14].
A standing wave can be created through complete reflection of a wave at an interface [15]. From the reflection coefficients we know that complete re- flection occurs in two different cases: either Z2 >> Z1 or when Z1 >> Z2 which represent a rigid boundary and a free boundary respectively [15]. A rigid boundary case corresponds to a reflection coefficient of 1 whereas a free boundary case corresponds to a reflection coefficient of -1 (Equation A.7).
Depending on the case, the position of the nodes and antinodes will change [15]. In the free boundary case, there will be a pressure node at the interface whereas in the rigid boundary case there will be an antinode (Figure A.4 and A.3) [15].
Figure A.3: A soundwave is reflected at a rigid boundary Z2 >> Z1 and creates a standing wave. The figure shows the pressure characteristics of the wave.
Figure A.4: A soundwave is reflected at a free boundary Z1 >> Z2and creates a standing wave. The figure shows the pressure characteristics of the wave.
Ultrasound is utilised in many different fields such as engineering, medicine and seismology [15]. One of these fields is acoustophoresis where ultrasound is utilised in the form of standing waves to manipulate the position of cells or other particles [1]. It is used in applications such as creating acoustic traps [3, 5] or particle separation [2, 6, 7, 8].
The way particles are manipulated in microfluidic channels by ultrasound can be explained through the equation for acoustic radiation force for a one- dimensional standing wave (A.11). The acoustic radiation force is the force that acts on particles within a microfluidic channel [12].
Frad = 4πΦka3Eacsin(2kz) (A.11)
Where Eacis the energy density, a is the particle radius where a << λ, z is particle position and k = 2πλ = 2πfc is the wavenumber. Furthermore, Φ is the contrast factor that can be determined using equation A.12 [12].
Φ = 1 3
5ρp− 2ρf 2ρp+ ρf −Kp
Kf
!
(A.12)
Where ρp and ρf are the densities of the particle and fluid respectively.
Furthermore, Kp and Kf are the compression coefficients of the particle and fluid respectively [12].
From equation A.11, it follows that an increase in frequency, energy den- sity or particle size leads to an increase in radiation force. Furthermore, from the acoustic contrast factor Φ, it follows that depending on the particle’s den- sity and compressibility coefficient, Φ will either be negative or positive. If Φ is positive, the particles will be pushed towards the pressure node of the stand- ing wave. In contrast, if Φ is negative, the particles will be pushed towards the antinode [12]. This is utilised in particle separation in acoustophoresis where particles with differing density or compression coefficient can be separated
into the pressure nodes and antinodes of the standing wave [16, 17].
A.2.1 Design
Most microfluidic channels used in acoustophoresis are half wavelength res- onators which means the width of the channel is equal to half the ultrasonic wavelength. This enables particles to be trapped in a single node in the middle of the channel (Figure A.5). However, the channel width (w) can be any mul- tiple n of half a wavelength and still create a standing wave (Equation A.13).
The standing waves will, however, differ in the number of nodes and antinodes [1].
w = nλ
2 (A.13)
Figure A.5: A representation of particles trapped in a half wavelength mi- crofluidic channel. The orange circles represent particles.
The half wavelength condition of the channel width is one of the contribut- ing factors to most acoustophoresis applications being in the micrometre do- main. Since a relatively high frequency around 1-10 MHz is needed to produce an acoustic radiation force strong enough to manipulate particles, the wave- length of the wave becomes small. Since the wavelength is small, the width of the channel must also be small.
Besides the channel width condition, there are other important design fac- tors to consider to be able to manipulate cells in an acoustic resonator [1]. It
make sure they achieve the acoustic forces neccessary [1]. Depending on the type of resonator, the design and material requirements will differ [1].
According to Lenshof et a.l [1], there are three types of acoustic resonators:
layered resonators, transversal resonators and surface acoustic wave (SAW) resonators. Designing a layered resonator is very complex as exact dimen- sions of the different layers are extremely important to enable the creation of standing waves. However, the material choice is flexible [1].
In a transversal resonator on the other hand, it is the choice of materials that is crucial for creating standing waves [1]. This is due to standing waves being created through reflection at the walls of the transversal resonators [1]. From equations A.3, A.7 and A.9, one can see that for the wave to be significantly reflected there needs to be a large difference in acoustic impedance between the medium in the channel and the resonator wall.
Furthermore, if there is only a small difference in acoustic impedance, the resonator will not be very energy efficient because most of the wave will trans- mit through the wall (Equation A.9). Therefore, materials such as glass and silicon are often used in transversal resonators because they provide a large difference in acoustic impedance. Glass, for example, is a suitable material for transversal resonators because it has a high acoustic impedance relative to the fluids used inside the channels [1].
Polymers, on the other hand, do not have desirable acoustic properties.
Therefore, they are not considered suitable materials for transversal resonators.
For instance, due to the low acoustic impedance of polymers, the reflection co- efficient of the polymer-fluid interface is small. As a result, polymer transver- sal resonators are not very energy efficient [1].
In addition, polymers have a high attenuation coefficient. As mentioned in section A.1.2, this can lead to heating problems since the absorption part of attenuation converts wave energy to heat in the material. However, despite the undesirable acoustic properties of polymers, they have the benefits of being cheap and are easy to use for mass production [1]. Consequently, this would also make polymers well suited for disposable microfluidic applications.
A.2.2 Polymers used in acoustophoresis
Due to the fact that polymers are inexpensive, suitable for disposable applica- tions and are easily mass produced, there have been many studies exploring the utilisation of polymers in building acoustic resonators. For instance, Yang et al. [2] used a polymer-based microchip in an acoustophoresis cell sepa- ration application. In their study, they used two opposing transducers where the sound waves from the two transducers were superimposed and created a standing wave. Their use of two transducers meant that they didn’t need to use materials with acoustic properties suitable for creating standing waves through reflection at the channel walls [2].
Mueller et al. [6] conducted a study where they used the polymer, poly- styrene (PS), to build an acoustophoresis microchannel for separation of blood cells. In this study, a layered resonator was used where the resonance was achieved by choosing suitable dimensions of the resonator layers. Their mi- crofluidic separator was shown to work efficiently, however, they found that due to the polymer not being an ideal reflecting surface for acoustic waves, the actual frequencies giving the optimum result were lower than those predicted [6].
Furthermore, Mueller et al. noted that for this kind of resonator, where dimensions are very important, polymers can be a challenge to use because certain stages in the manufacturing process of microchannels can cause the dimensions to change. In addition, for this method Mueller et al. needed an extensive heat removal apparatus and process [6]. This is likely due to heating in the polymer due to its high attenuation coefficient.
One reason that heat removal can be needed in acoustophersis applica- tions is that acoustic properties such as density and speed of sound change with temperature. As a result of the acoustic properties changing, the reso- nant frequency will change which will in turn, affect the acoustic energy [18].
This is something that can then lower the efficiency of the system as noted by Ohlin et al. [19].
A separate study was conducted by Lissandrello et al. [8] where they used acoustophoresis to separate lymphocytes from other blood cells using microchannels made of PS. One of the reasons they chose a polymer material was their desire to have parts of the separation apparatus be disposable. They
