1. FINAL YEAR PROJECT
Design, Development and Testing of a Device for Acoustic
Trapping of Live Cells and Micrometre-Scale Particles
Author: Frederick A. O. White
Project Code: NPSM1012
Date Submitted: April 27, 2015
Supervisors: Dr Adrian Barnes &
Dr Monica Berry
Assessor: Dr Terence McMaster
Number of Words: 7405

2. i
Declaration
This report is solely my own work and was written and compiled using LATEX. Some sections of the introduction and theory are
modified from my own literature review on acoustic trapping. The device design was inspired by the work of Scholz et al. but
my lab partner and I introduced significant modifications for this work. During construction, my lab partner and I operated the
laser cutter and 3D printers to produce device bodies and cases. The final construction of the device was also a joint effort. All
experimental work and results were produced jointly. I wrote the code used to analyse particle distributions while the ellipse
eccentricity fitting was completed by my lab partner. All results were cross checked between us. All plots, analysis and
interpretation of the data presented in this report are my work. My lab partner and I were not qualified to handle live cell
cultures directly; therefore Dr Berry assisted with work involving live cells. Throughout the project, day-to-day practical help
and advice was provided by Tom Kennedy.

3. ii
Contents
Declaration i
Abstract iii
I. Introduction and Background 1
II. Theory 1
A. Acoustic Trapping 1
B. Piezoelectric Transducers and Acoustic Power 1
C. Cell Viability 2
III. Experimental 2
A. Design and Setup 2
B. Polymer Bead and Fixed Cell Studies 4
C. Image Analysis 5
D. Temperature Variation 6
E. Live Cell Experiments 6
IV. Results 6
A. Observations of Alignment of Fixed Cells and Polymer Beads 6
B. Computational Image Analysis 8
C. Temperature Variation 9
D. Cell Viability 9
V. Discussion 10
A. Device Design 10
B. Directional Distribution Analysis 10
C. Alignment of Polymer Beads and Fixed Cells 10
D. Cell Viability 11
E. Future Work 11
VI. Conclusions 11
VII. Acknowledgements 12
VIII. Appendices 12
A. Cell Culturing Technique 12
1. Live Cell Culturing 12
2. Cell Fixation 12
B. Angular Distribution Calculator 12
1. Theta Calculator Code 12
C. Certificate of Ownership 13
References 14

4. iii
Abstract
A simple non-resonant, centimetre-scale acoustic trap was designed and constructed. The device used Lead Zirconate Titanate
transducers to produce a standing wave acoustic field at 6.7 MHz. It successfully aligned human cells and 8 µm polystyrene
beads in aqueous suspensions at separations of 115 µm. The quality and rate of alignment was studied via analysis of
directional distribution of particle positions. The device also demonstrated the ability to maintain viability of greater than 50%
compared to controls for Araki-Sasaki and IOBA cells when aligned for up to two hours.

5. 1
I. INTRODUCTION AND BACKGROUND
Acoustic trapping was first observed in 1868 by Kundt. In
his work, cork dust aligned with a standing wave in a resonant
air-filled cylinder[1]. Since its discovery the technique has
been used in the manipulation of inert particles, filtering and
cell–cell interaction studies[2–5].
Acoustic manipulation provides a non-contact, non-
invasive method for trapping particles and cells without re-
moving them from culture[6]. Trapping is achieved using the
pressure gradient produced in a non-uniform acoustic field.
The technique produces forces on the order of pN to nN when
working with µm-scale particles. This makes it ideal for han-
dling cells[2, 7, 8]. It is also cheap and simple to integrate with
other equipment for observations and cell culturing[9]. The
only requirement to acoustically trap a particle is a density and
compressibility contrast to the suspending medium[10, 11].
This makes the approach applicable to a broad range of parti-
cles and cells without any modification to the technique used.
Significant work with a variety of cells has been carried out in
the last decade and there are several demonstrations that cell
viability can be maintained during manipulation in a variety
of devices[12–15]. Recent work with non-adherent cells has
demonstrated the usefulness of acoustic trapping to manipu-
late cells that do not naturally cluster during culturing[4].
Acoustic manipulation is one of several techniques that ex-
ist for non-contact particle handling. For the manipulation
of live cells it has several advantages over the alternatives.
Magnetic trapping and electrophoresis use non-uniform mag-
netic and electric fields respectively. Magnetic trapping re-
quires either naturally magnetic cells or doped cells, limit-
ing its applicability. Electrophoresis risks cell damage due
to Joule heating of the fluid medium and has a limited range
as the electrodes must be closely spaced[16]. Optical tweez-
ers utilise the radiation force due to a focused laser beam
to manipulate particles with nanometre precision. However,
the laser can rapidly induce heat-related cell-death and the
equipment required is difficult to integrate with cell culture
containers[3, 9].
The aim of this project was to construct a centimetre-scale
device capable of aligning living cells using ultrasound while
maintaining their viability, allowing optical observations and
simple sterilisation between uses. The device also had to be
as cheap and simple to manufacture as reasonably possible.
Overall robustness and simplicity were two primary goals of
the design. Having constructed a device, the aim was to study
its effect on living cells. However, due to loss of access to
cell-containment facilities, the bulk of work in this paper was
undertaken with inert polystyrene microbeads and fixed cells,
to analyse the rate and quality of trapping and alignment pro-
vided by the device.
II. THEORY
A. Acoustic Trapping
In an acoustic trap, particles are manipulated using the pri-
mary radiation force (PRF). This arises when an ultrasonic
standing wave scatters off a particle or cell with an acoustic
contrast to the fluid medium.
The first theoretical description of the PRF for incom-
pressible spheres was produced in 1934 by King[17]. This
was extended to compressible particles in 1955 by Yosioka
and Kawasima[18] and finally generalised for viscid fluids in
1962 by Gor’kov, whose derivation is most commonly used
today[19]. Bruus provides a full derivation which results in a
description of the primary radiation force, acting on a spher-
ical object, Frad
, as the negative gradient of an acoustic po-
tential, Urad
[20]:
Frad
= − Urad
(1a)
Urad
=
4π
3
a3
f1
1
2
κ0 p2
1 − f2
3
4
ρ0 v2
1 (1b)
The quantities f1 and f2 are dimensionless scattering coeffi-
cients defined by the compressibility and density of the parti-
cle compared to that of the surrounding fluid:
f1(¯κ) = 1 − ¯κ with ¯κ =
κp
κ0
(2a)
f2(¯ρ) =
2(¯ρ − 1)
2¯ρ + 1
with ¯ρ =
ρp
ρ0
(2b)
In Eq. 1b, p2
1 and v2
1 are the time-averaged incoming pres-
sure and velocity fields squared, κ0 and ρ0 are the compress-
ibility and density of the fluid and subscripts p in Eq. 2 denote
the same quantities for the spherical particle with radius a.
The form of the coefficients f1 and f2 means that most cells
will move to the minima in the potential since their density
tends to be higher and their compressibility lower than the sur-
rounding medium[6]. These minima are coincident with the
positions of the pressure nodes of the acoustic field and so are
separated by a distance of half an acoustic wavelength. In one-
dimensional trapping, these pressure nodes form in lines par-
allel to the driving transducer. With multiple transducers, or
the use of reflectors, more complex nodal patterns can be pro-
duced by interference of multiple standing waves. This gives
the ability to trap particles in multiple dimensions. Once the
first cells are entrapped, secondary forces gather nearby cells
into a cluster centred on the nodal point or line.
B. Piezoelectric Transducers and Acoustic Power
A piezoelectric crystal produces electric charge when
placed under mechanical stress[21]. In the inverse piezo-
electric effect, an applied voltage across a crystal causes it

6. 2
to expand or contract. Applying an alternating voltage sig-
nal across a piezoelectric material will cause it to expand and
contract at the same frequency as the applied signal with an
amplitude proportional to the applied electric field. This os-
cillation in the size of the crystal can be used to produce a
propagating longitudinal wave. If one face of a piezoelectric
crystal is placed firmly against a material, the wave can be
made to propagate through the material in order to produce an
ultrasonic acoustic field.
In order to achieve efficient trapping, it is desirable to con-
vert as much electrical power as possible to acoustic power,
via the transducer, producing the strongest acoustic field with
minimum heating. Conversion is governed by the impedance
and phase of the transducer. Maximum power is converted
when the transducer acts as a pure resistor. This occurs when
the phase difference, φ, between current and voltage is equal
to zero. The resistance can be calculated from the impedance
using:
R = Z|cos(φ)| (3)
where R is the resistance and Z the impedance. In a range of
frequencies near resonance, the impedance has a characteristic
dip followed by a peak as the transducer passes through res-
onance and anti-resonance. Using a resonant frequency max-
imises the transfer of electrical power to acoustic power. The
impedance and phase can both be measured in order to find
the ideal frequency at which to drive the transducers. Having
calculated the resistance of the transducer using Eq. 3, the
power input to the transducers can be estimated using:
P =
V 2
rms
R
(4)
where P is the power, Vrms the root-mean-square of the alter-
nating voltage and R the resistance.
It is desirable to use pairs of transducers with closely
matched resonant frequencies, ideally with as little as 10 kHz
difference, to ensure that both have similar responses when
loaded[2].
When choosing materials from which to construct an acous-
tic device, the acoustic impedance of materials is an important
consideration. Acoustic impedance is a measure of a mate-
rial’s resistance to longitudinal waves propagating through it.
If acoustic impedance is not matched between materials, en-
ergy is reflected. This causes losses in the system and in turn
requires more power to be supplied to the transducers in order
to produce the same trapping force. The reflection coefficient,
R, for a wave propagating from material 1 (with characteris-
tic acoustic impedance Z1) to material 2 (with characteristic
acoustic impedance Z2) is given by[22]:
R =
Z1 − Z2
Z1 + Z2
(5)
Since all the input energy is either reflected or transmitted, the
fraction of energy transmitted can be calculated as T = 1−R.
C. Cell Viability
In order to maintain cell viability, the effects of ultrasound
on living tissue must be considered. There is a large body of
evidence that low-intensity ultrasound has no significant im-
pact on bulk human tissue[23, 24]. The effects of ultrasound
are generally considered as either thermal or non-thermal.
Thermal effects arise due to heating of the cell medium push-
ing the temperature outside the narrow ideal range[24]. Hu-
man cells have best viability at 37 ± 1◦
C, corresponding
to body temperature. Bulk tissue can tolerate a temperature
range of 33–39◦
C and in vitro cells can tolerate an even wider
range than this[24]. In the range 1–10MHz, absorption of
acoustic energy by water is low, so acoustic heating should
be minimal. For small volumes of liquid, as used here, direct
heating by the transducers can become significant. For heat-
ing to rapidly affect cell viability the temperature of the cell
medium would have to exceed 40◦
C[24].
Non-thermal effects include streaming, cavitation and
stress due to the PRF. Eckart streaming is the dominant pro-
cess in systems with scales greater than λ/2. It is caused by
energy absorption by the fluid leading to bulk motion[25].
The amplitude of streaming scales with the depth of fluid,
so can be limited by reducing the depth[26]. If the stream-
ing is too large, particles can be pulled out of the acoustic
trap[12, 27]. At the frequencies and depth of fluid used in this
work, streaming should not affect trapping[26]. Cavitation is
also a consideration as the formation of bubbles inside cells
can cause them to rupture. Fortunately, cavitation is limited
with acoustic frequencies greater than 1 MHz. In addition
to this, bubbles formed in a water based medium are lower
density than the medium, while cells are higher density. Bub-
bles are attracted to the pressure antinodes of the acoustic field
while cells travel to the pressure nodes, physically separating
the cells and damaging bubbles[24].
III. EXPERIMENTAL
A. Design and Setup
In order to achieve acoustic trapping, an ultrasonic stand-
ing wave field must be produced. While the ultrasonic wave
is almost always provided by piezoelectric ceramic transduc-
ers, the arrangement of these transducers and the structure of
the device can take several forms[10]. The most common
approach is multi-layer resonant systems. Each layer must
be precisely the right thickness, requiring precision engineer-
ing. Resonant systems also limit the potential for manipula-
tion as the trapping positions are defined by their geometry.
Two other alternatives, which have been proved experimen-
tally, are the use of focused ultrasound beams[28] or linear
arrays of transducers parallel to a reflector[29]. The approach
used in this work is to use two opposing transducers. The
standing wave for trapping is set up by interference of the two
counter-propagating travelling waves produced. This method
gives a standing wave which is independent of the resonant
frequency of the chamber through which it propagates, reduc-

7. 3
FIG. 1: The original device showing the circular mount holding the
transducers. This is then inserted into a petri-dish containing the cell
culture.
ing the effects of high particle densities[8]. It also produces
a system which is robust to partial misalignment of the trans-
ducers. Any misalignment merely introduces a phase shift
between the two travelling waves, moving the nodes of the
standing wave rather than interrupting it. This reduces the
need for high precision manufacturing. Deliberate introduc-
tion of a phase difference between the two input waves, can
be used to arbitrarily position the nodes[30].
The basis of the design was a previous device developed
in the UoB Biosciences group, which used two pairs of op-
posed piezoelectric transducers glued into a 3D printed frame,
shown in Fig. 1. This frame was then submerged in the
cell culture medium. The transducers used in the original de-
vice and in all subsequent work were Noliac group NCE51,
2 × 15 × 0.975 mm Lead Zirconate Titanate (PZT) piezo-
electric elements[31]. The device successfully aligned cells
but did not maintain viability. Placing the transducers in
the fluid medium had the advantage of maximising acoustic
power transfer to the fluid, since there were no additional ma-
terial boundaries to cause reflections. However, It was diffi-
cult to maintain sterility with the design due to the porosity
of the printed plastic. In addition, all heat output from the
transducers was deposited directly into the fluid, potentially
risking cell viability. Construction of the power supplies was
also complicated by the need to feed them under the petri-dish
cover.
Due to the difficulties with the original device, it was de-
cided that separating the transducers and fluid medium would
make sterilisation easier. However, the opposing transducer
approach to trapping was retained due to its simplicity and
resilience when handling large particle concentrations. One
pair of transducers was used, allowing only one-dimensional
trapping but minimising the complexity of the design. The de-
vice developed and used in this work is based on the work of
Scholz et al.[8].
As shown in Figs. 2 and 3, the device was designed around
a standard optical microscope slide, to ensure that it would
be compatible with standard microscopes. The design used
three chambers – a central one to contain the sample fluid and
two smaller chambers to hold the transducers providing the
acoustic field. The body of the device was laser cut in 3 mm
PolyMethylMethacrylate (PMMA) acrylic, avoiding the use
of porous plastic in the fluid chamber. Acrylic was chosen as
it is cheap enough that the body of the device could be dispos-
able and can be laser cut easily, in a matter of minutes, making
FIG. 2: Top and side cut-through schematics of the new device. A –
PMMA, B – air gap, C – fluid chamber, D – PZT transducer crystal,
E – microscope slide. When in operation a second transducer was
placed opposite the first, on the far side of the fluid chamber.
FIG. 3: Completed two transducer device in the 3D printed case.
for rapid construction. Glass was considered as an option but
required water-cutting, which would have added significantly
to construction time as this can only be carried out by work-
shop technicians. Laser cutting required digital models of the
device to be made in order to produce two-dimensional out-
lines for cutting. The body was then glued to the slide using
commercially available silicone sealant.
The transmission of acoustic energy into the fluid cham-
ber is vital for trapping. The acoustic impedance of PMMA
is 3.4 MPasm−1
s[32] while that of the PZT crystals is 35.1
MPasm−1
[33]. This means that ∼ 70% of the applied acous-
tic energy is reflected at the PZT–PMMA boundary. How-
ever, water has an impedance of just 1.5 MPasm−1
[33] lead-
ing to the reflection of only ∼ 15% of the remaining energy
at the PMMA–water boundary. Overall this gives a transmis-
sion of ∼ 25% of the input energy assuming minimal absorp-
tion. Glass has an impedance of 14.1 MPas−s
, leading to an
FIG. 4: Autocad model of the device case prepared for 3D printing.

8. 4
FIG. 5: Completed four transducer device with two transducers and
aluminium reflector mounted.
overall transmission to a water-based sample of ∼ 28%. This
marginal improvement in transmitted energy did not warrant
the increased difficulty involved in the use of glass.
A 3D printed case, shown in Fig. 4, was designed and man-
ufactured to hold the device and the transducers’ electrical
connectors. Transducers were held in place on opposite sides
of the fluid chamber using 3D printed x-shapes, allowing the
transducers to be separated from the body of the device while
still attached to the power supplies. Having removed the trans-
ducers, the acrylic and glass body of the device could be sub-
merged in ethanol for sterilisation without risk to the transduc-
ers or power cables. Alternatively, the whole body of the de-
vice could be replaced, retaining only the transducers and the
case. It was found that a coupling medium was required be-
tween the transducers and the PMMA body to fill any air gap
and transmit acoustic power effectively to the fluid chamber.
Medical ultrasound gel was used here as it is a close acous-
tic impedance match to water-based media so should transmit
acoustic energy efficiently. A thin layer of this gel was applied
to the front face of the transducers, before they were mounted,
every time the device was used. This device was used for all
experimental work using cells in this paper.
A second device, shown in Fig. 5, was constructed with ad-
ditional spaces for a second pair of transducers. This was con-
structed on three microscope slides, and an enlarged case was
also manufactured. However, by this stage in the project, only
two transducers were available, so a 2 mm thick aluminium
reflector was introduced at 45◦
to two orthogonal transducers,
in order to produce a two-dimensional grid pattern of nodes in
the half of the fluid chamber with the transducers.
For efficient conversion of electrical power to acoustic
power, the transducers had to be driven at their resonant fre-
quencies. Since both were driven from a single signal gener-
ator, it was necessary to identify pairs with closely matched
resonances to achieve the highest acoustic field strength. The
resonant frequency of the transducers was identified by mea-
suring their impedance and phase using a Wayne Kerr 6500B
Impedance Analyser[34]. The resonance of each transducer
was identified in air. The two transducers were then mounted
in the device, with water acting as the fluid medium, and tested
again to find the combined minimum impedance. This fre-
quency was then used to drive the transducers for trapping.
Fig. 6 shows a sample graph of impedance and phase mea-
surements. The plotted resistance was calculated using Eq.
3. For work with cells of ∼ 10 µm in diameter, the short-
est wavelength of sound possible was used to produce maxi-
mum acoustic forces as predicted by Eq. 1. The highest res-
onant frequency varied between transducers in the range 6.7–
6.9MHz, corresponding to wavelengths of 215–220 µm in a
water-based medium. It was noted that when the transducers
were operated while mounted in the device, rather than in air,
the peaks in the phase corresponding to resonance broadened
but did not change in frequency. This broadening reduced
the requirement for extreme close matching of resonant fre-
quencies between transducers, as it increased the range of fre-
quencies at which energy conversion would be improved over
non-resonant conditions. The driving voltage for trapping was
provided by a Tektronix AFG2021 arbitrary function genera-
tor producing a sinusoidal alternating current with a voltage
range of 0 − 10V and an output impedance of 50 Ω[35]. The
impedance was approximately 15 Ω for all transducers at res-
onance. This presents a considerable mismatch to the output
impedance of the function generator. However, extracting the
maximum power was not the goal of this design, so improve-
ments on impedance matching were not carried out.
B. Polymer Bead and Fixed Cell Studies
Initial tests to study the performance of the device were
carried out with Sigma-Aldrich 8 µm polystyrene microbeads
suspended in Phosphate buffered saline (PBS). A suspension
with a concentration of ∼ 107
beads ml−1
was produced by
mixing 1 × 10−4
g of beads with 10ml PBS. 0.5% v/v Tri-
ton TX-100 surfactant was added to prevent clumping. This
suspension was then diluted at 1% v/v in PBS for experimen-
tal work. Beads were aligned using both the one-dimensional
and two-dimensional devices.
Live cell cultures and fixed cells were provided by Dr
Berry; the process for their production is recorded in Ap-
pendix A. Araki-Sasaki (AS) human corneal epithelial and
IOBA human conjunctival epithelial cells were used in this
project. Visibility of lines formed under application of the
acoustic field was found to be best when 1.5% v/v fixed cell
concentrate was added to PBS. This produced suspensions of
∼ 5 × 105
cells ml−1
. The central sample chamber of the
device has a volume of 650µl, but since the transducers are
2mm high only 450 µl of this is exposed to ultrasound, there-
fore 400 µl of the fluid under inspection were used.
Alignment was studied over 90 s exposures to an acous-
tic field at driving voltages of 4, 6 and 8 Vpp using both
polystyrene microbeads and fixed AS cells. The effect of volt-
age on quality of alignment was also studied by recording the
movement of fixed AS cells over 90 s exposure to fields at
voltages between 4 and 10 Vpp in 0.5 V increments. For each
test, 400 µl of suspension were placed in the central cham-
ber of the device while the field was inactive. The field was
then activated and snapshots were taken at 0.5 s intervals us-
ing an Olympus SZX16 microscope[36] coupled to a Lumen-

9. 5
FIG. 6: Plots of the measured impedance and phase for one transducer. The upper red line is resistance and the black impedance. There are
several peaks in the lower frequency range corresponding to various resonances of the piezoelectric crystal; the rightmost peak is the highest
frequency resonance and the one used for trapping.
era InfityX-21C[37] camera and a KL1500 LCD co-axial light
source[38].
The two-dimensional trap using an aluminium reflector was
briefly tested using the polystyrene beads. The transducers
were driven at 6.7 MHz and 8 Vpp for 90 s before imaging, as
with the one-dimensional device.
C. Image Analysis
The quality of alignment was investigated via analysis of
the directional distribution of particles. The angle, θ, from
the horizontal of the line between pairs of particles was cal-
culated for all particles within a given radius from a “home”
particle. This process was repeated with each particle in an
image acting as the “home” particle in turn. For each image,
the values of θ were then plotted as histograms with 5◦
bins.
For a random distribution, there should be no preferred val-
ues of θ, as there is no preferred relative position of particles.
Where alignment is present, there will be two preferred val-
ues of θ – in opposite directions along the lines of particles.
This is because where lines form, higher densities of parti-
cles exist in the line than away from it. By analysing circular
areas with a radius just less than the expected separation of
lines, the histograms produced should start as circular distri-
butions at t = 0, when cells are randomly distributed. They
should tend towards straight lines along the axis of alignment
as time progresses. In the case of partial alignment, elliptical
distributions were expected to form. Therefore ellipses were
fitted to these histograms and the eccentricity calculated as
(1 − (b/a)2) where a and b are the semi-major and semi-
minor axis lengths. The value of the eccentricity of the fitted
ellipse for each frame gives a single value ranging from 0 for
non-aligned particles to 1 for perfectly aligned particles.
For each video, frames 1, 10, 20, 40, 90, 120 and 180 were
FIG. 7: Schematic of the parallax problem. The blue grid represents
the pixels, the green point represents the “home” pixel and red
points represent pixel centres as recorded by (x,y) coordinates.
Overlaid are 36 radial bins with the apparent pixel count for each
around the edge. The pattern of counts repeats every 90◦
.
processed using the ImageJ analysis package and the approach
described by Costa and Yang to enhance contrast and remove
background noise[39]. Images were converted to binary with
a threshold of 5%. Cell counts and (x,y) coordinate data were
extracted in ImageJ using the inbuilt analyse particles option.
The coordinates of the cells were then processed using the
code presented in Appendix B. The code took the (x,y) coor-
dinates of each particle in turn and calculated the distances
∆x and ∆y to every other particle in the data set. From
these, the radial distance was calculated. For all particles in-
side a 45 pixel radius from the “home” particle, the angle θ
from the horizontal was calculated as tan−1
(∆y
∆x ) using the
inbuilt atan2 function available in C. This pixel distance cor-

10. 6
responded to a half-wavelength of the acoustic wave applied
to the particles and correspondingly the line separation in our
images. The values of θ were then written to a new file for
producing histograms.
One challenge in this technique was that ImageJ produced
(x,y) coordinate data from pixel counts leading to discrete val-
ues. This in turn produced discrete values of θ which in-
troduced a parallax effect when producing histograms. This
occurred because, despite the fact that all bins occupied the
same total area, each bin was sensitive to cells in a different
number of pixels. This is demonstrated in Fig. 7. To cor-
rect for this effect, the program was run with a “full-field”
where every (x,y) coordinate contained a “cell”. The resul-
tant values of θ were then placed in 5◦
bins. The histogram
counts produced by this “full-field” are in effect a response
function for the binning process when applied to discrete (x,y)
values. Subsequent results were scaled by the average count
of this response function for all bins divided by the count in a
given bin to remove the parallax effect. Ellipse fitting was car-
ried out using an open source Python conversion of a Matlab
script[40]. This code used a linear least squares method based
on the method of Gander et al. to produce values for the semi-
major and semi-minor axes of an ellipse fitted to a given data
set[41]. The code and process were tested using two pseudo-
random distributions. The first was a uniform distribution of
3000 points and the second a set of 3000 points distributed
randomly along straight lines separated by 50 pixels with a
gradient of 0.1. Both were distributed over the same pixel
range as experimental images.
D. Temperature Variation
The temperature variation of a cell sample was investigated
to ensure that direct heating of the cell culture would not
present a risk to viability during live cell tests. The tem-
perature was recorded during a 90 minute exposure to an 8
Vpp acoustic field. This was the highest voltage and there-
fore the highest power supplied to the transducers during live
cell work, so represents an upper limit on the rate of heating.
A 400µl sample of fixed IOBA cells in PBS at a concentra-
tion of ∼ 5 × 105
cells ml−1
was placed in the fluid chamber
in place of a live cell sample. The room temperature, cul-
ture temperature and temperature of both transducers at three
points across their length were recorded at 10 minute inter-
vals over a 90 minute exposure. Ideally the temperature in
the acoustic field would have been measured via Rhodamine
B fluorescence to avoid interrupting the acoustic field. How-
ever, a real-time fluorescence microscope was unavailable so
an RS206–3750 Digital Thermometer was used instead[42].
This did not present significant issues as it was not necessary
to measure temperature while maintaining trapping.
E. Live Cell Experiments
The viability of IOBA and AS cells after exposure of up
to two hours to the acoustic field of the device was studied.
Prior to live cell studies, the device was submerged in 50%
ethanol for 10 minutes to sterilise it. It was then rinsed ex-
haustively with PBS before the sample chamber was filld with
cell medium. Sterilisation was repeated between every test.
The process for exposures was to place a 400 µl sample of
PBS in the sample chamber, activate the signal generator and
then add the appropriate cell sample. This allowed more ac-
curate timing of exposures. In order to culture the cells for
viability studies, it was necessary to remove them from the
device. This was achieved by placing a fibronectin-soaked
13 mm cover-slip in the device before adding cells. The fi-
bronectin improved binding of cells to the cover-slip when
they settled. The cover-slip could then be removed, with the
cells, for overnight culturing. After the allotted exposure, the
acoustic field was switched off and the cells left to settle onto
the fibronectin plate for 30 minutes. The test sample was then
placed in a 24 well plate with 400 µl of fresh medium. A
second, unexposed 400 µl sample of cells was placed on a
fibronectin-soaked cover-slip to act as a control. All samples
were then incubated at 37◦
C, 4.5% CO2 and 90% humidity
overnight. The cultures were incubated for a further hour with
Calcein AM dye before inspection with a Spectra Max M2
spectrometer. The relative fluorescence of the test and control
cultures gives a measure of the number of living cells in each
sample. Since the samples initially contained the same num-
ber of cells, the relative fluorescence gives a measure of the
relative viability of the cells exposed to the acoustic field. The
presence of viable cells was visually double-checked using
Trypan Blue dye, which only permeates the ruptured mem-
branes of dead cells.
Viability was measured for exposures of 2 minutes and 60
minutes at 4, 6 and 8 Vpp for IOBA cells and 2, 15, 30, 60 and
120 minutes at 8 Vpp for the AS cells. Finally AS cells were
tested after a 60 minute exposure using a pulsed signal alter-
nating 100 ms on and 100 ms off at 8 Vpp. Cell viability was
quantified using relative fluorescence counts between control
cultures and cultures after exposure to ultrasonic fields. The
fluorescence count of the test cultures was then converted to a
percentage of the control count.
IV. RESULTS
A. Observations of Alignment of Fixed Cells and Polymer
Beads
The initial goal of aligning cells using the acoustic force
was successful. Despite the significant acoustic impedance
mismatch between the transducers and the PMMA body of
the device, alignment of both 8 µm polystyrene beads and 12
µm fixed AS cells was reliably achieved in under a minute.
The output voltage of the signal generator and the resistance
of the transducer were used to estimate the power supplied to
each transducer using Eq. 4. The power supplied at 10 Vpp
was calculated to be 0.83 W, while at 4 Vpp the power was
0.13 W, per transducer. These values are only an estimate of
the true quantities as the impedance mismatch between the
source and load is not taken into account. As visible in Fig.

11. 7
FIG. 8: Microscope image of AS cells aligned after 90s exposure to
a 10Vpp acoustic field.
FIG. 9: Microscope image of AS cells aligned after 90 s exposure to
a 4 Vpp acoustic field.
8, fixed AS cells suspended in PBS were clearly aligned after
90s with the transducers excited at 10 Vpp. The separation
of lines was ∼ 110 µm, corresponding to λ/2 of the acoustic
wave, as expected theoretically. The visual quality of align-
ment did not significantly reduce as the voltage was lowered,
as shown by Fig. 9. Polystyrene microbeads aligned more
rapidly than AS cells, with alignment apparent from as little
as 10s exposure. Despite this, visual quality of alignment was
not significantly different after 90s at any voltage. The high-
est voltage applied to the beads was 8 Vpp, which produced
distinct lines, as shown in Fig. 10. The minimum voltage at
FIG. 10: Microscope image of 8 µm polystyrene beads aligned after
90 s exposure to an 8 Vpp acoustic field.
FIG. 11: Polymer beads trapped using the device equipped with an
aluminium reflector and orthogonal transducers.
FIG. 12: Histogram using 5◦
bins of θ counts for a pseudo-random
uniform test distribution. The radial axis is counts and the angular
axis θ bin centre.
which reliable alignment was achieved was found to be 4 Vpp.
The second device, using an aluminium reflector, was
tested using the same polymer bead suspension as the one-
dimensional trap. Only preliminary tests were carried out with
this device. The reflector partially worked, producing partial
alignment to a grid and broken lines of particles as seen in Fig.
11.
FIG. 13: Histogram using 5◦
bins of θ counts for a pseudo-random
test distribution with lines separated by 50 pixels. The radial axis is
counts and the angular axis θ bin centre.

12. 8
FIG. 14: Images at 0, 20 and 90 s from video footage of AS cell alignment under a 9.5 Vpp applied field. The images have been processed to
remove background noise and converted to binary images; this is the format from which cell counts were taken.
FIG. 15: Histograms using 5◦
bins of θ counts corresponding, from left to right, to the images in Fig. 14. The eccentricity of fitted ellipses
was, from left to right: 0.33, 0.37 and 0.82. The radial axis is counts and the angular axis θ bin centre.
B. Computational Image Analysis
The process for analysing directional distribution was con-
firmed by running a pseudo-random and linear test distribu-
tion through it. All histograms are normalised to a total count
of 1000. The pseudo-random distribution produced an almost
circular distribution in θ, shown in Fig. 12, with a fitted eccen-
tricity of 0.18. The straight-line test distribution produced Fig.
13. The lines of the test distribution had a gradient of 0.1, cor-
responding to an angle of 5.74◦
from the horizontal. Almost
all values of θ lay in the 5–10◦
degree bin. However, a small
number fell in the 0–5◦
bin. This demonstrated the ability of
the method to detect structure not visible to the naked eye –
the “straight” lines of the test distribution were pixelated and
so contained groups of pixels on the same row. This produced
a fitted eccentricity of 0.99.
Having confirmed the ability of θ histograms to discern
structure in an image, the process was applied to videos of
polymer bead alignment and AS cell alignment under various
field strengths. Figs. 14 and 15 show the resultant histograms
compared to the images they result from. The final distribu-
tion in Fig. 15 is not, as originally expected, a true ellipse but
is instead a highly eccentric ellipse overlaid on a small circu-
lar distribution. This is due to cells floating on the surface of
the medium which did not align but were still detected by the
particle analysis. This introduced a random background dis-
tribution to the data. While there were sufficiently few floating
particles that the alignment was not obscured, if this technique
FIG. 16: Eccentricities of fitted ellipses for histograms of θ
distributions of AS cells under 8, 6 and 4 Vpp applied fields.
was used for further work, removal of particles away from the
plane of alignment would be ideal.
While alignment of fixed AS cells was successful, the back-
ground random distribution did produce relatively small val-
ues for the eccentricity of fitted ellipses. For fields of 8, 6
and 4 Vpp, as used for the cell viability study, the eccentricity
never exceeded 0.6, as shown in Fig.16. For fields at 9.5 and
8.5Vpp the eccentricity peaked at 0.87 and 0.82 respectively
whereas for fields at 7.5 and 4.5 Vpp it did not exceed 0.6, as
shown in Fig. 17. As Fig. 16 and Fig. 17 show, the eccen-
tricity generally increases after 10 s. Lines are added to these

13. 9
FIG. 17: Eccentricities of fitted ellipses for histograms of θ
distributions of AS cells under 9.5, 8.5, 7.5 and 4.5 Vpp applied
fields.
FIG. 18: Eccentricity of ellipse fits to histograms of θ for polymer
bead alignment under 8, 6 and 4 Vpp applied acoustic fields.
plots for clarity. It is thought that for t < 10 s particle motion
is dominated by the initial motions, whereas for t > 10 s the
applied acoustic field dominates.
Polymer bead alignment was more rapid and reliable than
that for the fixed AS cells. Fig. 18 shows that the eccentricity
for the polymer bead tests rose rapidly under 6 and 8 Vpp to
a peak of ∼0.95, corresponding to strong alignment with al-
most no random background distribution. Under a 4 Vpp field
alignment progressed more slowly and was never as strong as
that under the more powerful fields. This matches the results
of the AS cell observations in Fig. 17 that the stronger acous-
tic force produced by the higher applied voltages led to more
effective alignment of particles.
C. Temperature Variation
The average temperature of a 400 µl PBS sample increased
by 1.6◦
C within 10 minutes of an 8 Vpp field being ap-
plied, as shown in Fig. 19. The average temperature of
the transducers also rose sharply in the first 10 minutes, by
2.8◦
C. Subsequently the temperature of the sample rose by
0.010 ± 0.002◦
C min−1
and the temperature of the trans-
ducers by 0.018 ± 0.002◦
C min−1
during the remaining 80
FIG. 19: Average temperature of both transducers and a 400 µl PBS
sample over a 90 minute exposure to a 10 Vpp acoustic field.
Triangles are the fluid temperature, the square points are the average
transducer temperature.
minutes. Temperature measurements were taken at 3 points
along the length of each transducer. Errors were then calcu-
lated as the standard deviation of the values. The error on the
temperature of the fluid was taken to be twice the precision of
the digital thermometer, 0.1◦
C.
D. Cell Viability
TABLE I: Relative cell viability of IOBA cells after exposure to
acoustic fields.
Voltage/V Time/min Relative viability/%
8 2 89.9
6 2 149.7
4 2 136.4
8 60 62.8
6 60 51.0
4 60 136.8
TABLE II: Relative cell viability of AS cells after exposure to
acoustic fields.
Voltage/V Time/min Relative viability/%
8 15 111.7
8 30 172.2
8 60 86.7
8 120 87.7
8 (Pulsed) 60 94.8
The study of cell viability was limited by available lab time.
However, it was possible to test both IOBA and AS cells with
the device. For all exposures of up to two hours between 4 and
8 Vpp it was found that cell viability was greater than 50% in
both IOBA and AS cell lines. Full results are presented in Ta-
ble I and Table II. For exposures at 4 Vpp the relative viability
was greater than 100%, indicating better cell reproduction in

14. 10
the exposed culture than in the control. The pulsed signal pro-
duced marginally better viability than the continuous exposure
for 60 minutes in AS cells.
V. DISCUSSION
A. Device Design
The device designed and constructed in this work success-
fully achieved its primary goals of enabling acoustic trapping
of both inert particles and cells while allowing optical obser-
vations. Using opposing transducers to produce the standing
wave field for trapping produced a non-resonant device which
could handle high concentrations of particles, in the range of
106
ml−1
. The non-resonant design also removed the need
for any high-precision manufacturing or tuning of the device,
unlike resonant systems. This made the device robust to re-
peated dismantling and general handling during experimental
work as partial misalignment of the transducers merely relo-
cated the position of nodes rather than destroying the trap-
ping effect. It was also simple to manufacture and operate.
Once the design was finalised, it was possible to produce a
new body for the device within 15 minutes, although up to
24 hours was required to cure the silicone sealant. No cus-
tomised electronics were required and an off-the-shelf MHz
range function generator was used. Furthermore all of the ma-
terials required for construction are cheap and readily avail-
able. The use of acrylic and microscope slides would allow
simple and rapid manufacture of custom sized devices for fur-
ther research, making this device versatile. For live cell work,
the device was simple to sterilise using ethanol.
B. Directional Distribution Analysis
The method for analysing the directional distribution of par-
ticles from video images of the alignment process, developed
for this paper, proved successful. It was independent of the
particle shape, requiring only (x,y) coordinate data for each
particle. This process gave a systematic measurement of the
alignment of particles within the device. The value of eccen-
tricities in the theoretical limit of an infinite, perfectly random
distribution is 0, from an absolutely circular histogram, and
that in the case of a set of lines is 1, corresponding to a his-
togram with equal counts 180◦
apart. However, experimental
results fall far short of an infinite sample, with only a few
thousand cells visible in any frame. The results produced by a
pseudo-random test distribution with 3000 points reflect this,
producing an eccentricity of 0.18. This gives a reasonable
lower bound for the eccentricity of an experimental unaligned
distribution. The upper bound, provided by the straight-line
artificial distribution was 0.99. The result was not 1 due to the
pixelation of the lines introducing horizontal sections. This
test had no background noise at all, so it is unsurprising that
experimental data did not reach eccentricity values this high.
The experimental range of values was 0.13–0.95, with the ex-
treme values recorded at 0 s and 90 s exposure respectively.
C. Alignment of Polymer Beads and Fixed Cells
Alignment was observed in both polystyrene micro-beads
and fixed AS cells for power inputs of 0.13 W to 0.83 W.
During all alignment tests, a layer of unaligned particles was
visible above the plane of alignment throughout exposure to
an acoustic field. This implies that the depth at which acous-
tic forces were produced was limited to a layer close to the
base of the device. This suggests that some component of the
force may have been produced by a surface wave propagating
through the glass slide forming the base of the device, rather
than the plane wave propagating through the fluid medium.
To fully investigate this effect, it would be necessary to either
analyse alignment footage taken at multiple focal depths or
to produce computational models of the device and compare
theoretical and experimental rates of alignment.
Micro-bead alignment was faster and more consistent than
that of the fixed cells, reaching a maximum eccentricity in
just 20s. The alignment of micro-beads progressed at an al-
most identical rate at both 8 and 6 Vpp, reaching a maximum
eccentricity of = 0.95 in both cases; this corresponds to ap-
proximately 10 times as many particles being found along the
axis of alignment as perpendicular to it. At 4 Vpp the align-
ment progressed more slowly, reaching a maximum after 45
s. However, the quality of the alignment never matched that
at higher voltages, peaking at = 0.8 and not increasing over
the subsequent 45s, as seen in Fig. 17. This corresponds to
approximately 4 times as many particles being found along
the axis of alignment as perpendicular to it. These results sug-
gest that other forces acting on the beads, such as streaming,
did not reduce in magnitude as quickly as the PRF, limiting
alignment. The effect of streaming could be studied by re-
ducing the depth of the chamber, using cover slips, as Eckart
streaming scales with depth.
The fixed cell alignment did not reach a maximum value
within the 90s exposure time. The lower values of the fixed
cell results are in part due to the layer of unaligned parti-
cles. Due to the darker colour of the cells relative to the
beads, the randomly aligned cells out of the plane of align-
ment were more visible in images and therefore more likely
to be picked up in the cell counting process. However, since
the unaligned cells were approximately uniformly distributed,
their presence should reduce the peak value of eccentricity
but should not change the trend of variation over time of the
value. Lower voltages tend to produce less effective align-
ment overall, however in the fixed cell tests in Fig. 15 the ec-
centricity was highest for the 4 Vpp field. This is surprising as
the acoustic force is approximately proportional to the square
of the voltage, so is significantly weaker at lower voltages.
However, for the 0.5 V increments higher voltages did pro-
duce higher eccentricities, as expected. For all exposures with
fixed cells, the alignment did improve. However, it was not
as pronounced nor as smooth as that of the polystyrene beads,
reaching a peak value of just 0.85. The generally poorer align-
ment produced using fixed cells suggests that the PRF acting
on the cells was lower than that on the beads. The fixed cells
were larger in diameter than the polystyrene beads, at an av-
erage of 12 µm compared to 8 µm. This increased radius

15. 11
should increase the force produced by a given acoustic field,
which scales with volume for particles of the same material.
Both particles are similarly close in density to the water-based
medium they were suspended in, giving similar values for the
density-dependent constant in the acoustic potential. Any re-
duction in force on the cells is therefore likely due to a lower
compressibility contrast between the cells and the water, due
to their structure, than the beads and the water, reducing the
magnitude of the acoustic potential in Eq. 1b. Further study
would be required to confirm this, with the force applied mea-
sured externally, either via particle image velocimetry or the
use of optical tweezers.
Only rudimentary two-dimensional alignment was
achieved. Fig. 11 demonstrates that simple modifications to
the device used here could be used to produce more complex
patterning of molecules.
D. Cell Viability
Cell viability was successfully maintained while alignment
took place. The limited quantity of data available on cell via-
bility in the device limits the definition of trends. Ideally, sev-
eral cultures would have been produced for every voltage, and
over a broader range of exposure times, in order to produce
firmer bounds on the impact of acoustic exposure. However,
higher voltages generally reduced viability in the tests carried
out here, suggesting that the higher forces and energy densi-
ties produced reduced cell viability. Longer exposures at the
same voltage did not seem to have as much effect on viabil-
ity as increasing the voltage. The pulsed signal delivered only
half the energy to the cell culture of the continuous signal and
produced a marginally better viability, as shown in Table II.
This suggests that pulsed signals could be used to maintain
viability during longer exposures. For all these results more
data is required to make statistically significant conclusions.
For cell studies the device was operated at room tempera-
ture of approximately 21◦
C. Even with the temperature in-
crease induced by the active transducers this left the medium
temperature at only ∼ 24◦
C, considerably below the ideal
culture temperature of 37.5◦
C. Lower than ideal temperatures
are only expected to lead to slow cell death due to reduced
metabolic function. If cultures were produced in the device,
with it running in an incubator, the temperature rise induced
would push the culture to ∼ 40◦
C or higher, which would
likely produce rapid cell death as with the previous genera-
tion device. It is thought that the stabilisation of the fluid tem-
perature at a lower temperature than the transducers may be
in part due to evaporation of the fluid. In long term cultures
this would present a problem. One option would be to mod-
ify the device so that the central chamber was covered during
operation to minimise evaporation.
E. Future Work
There is great potential for further development of the de-
vice and processes used in this project. Future work could
include development of the ability to manipulate trap posi-
tions, further live cell studies or computational analysis of the
device functionality. The introduction of a second signal gen-
erator or an electronic phase shifter would allow manipula-
tion of the acoustic trap positions in one dimension. Prelimi-
nary work on two-dimensional trapping has been successfully
demonstrated. A multi-dimensional trap combined with con-
trol over trap positioning could allow patterning of trap sites.
This ability could be used to arrange cells for controlled cul-
turing or organise inert particles to produce scaffolds for cell
growth.
With respect to live cell work, additional studies are nec-
essary to confirm the ability of the device developed here to
maintain viability during longer term exposure to the acous-
tic field. Ideally, these tests would include culturing cells
in the device while an acoustic field was active and expo-
sures greater than 24 hours. The success of these tests would
demonstrate that the device has potential for structured tis-
sue culturing. If temperature variation in the culture chamber
proved to be a problem for cell viability a Peltier cell attached
to the base of the device could be used to provide in-device
temperature control.
For an accurate knowledge of the forces acting on parti-
cles trapped in the device finite element modelling and the
creation of 1D transmission-line models would be necessary.
These could be used to produce more accurate estimates for
the sound energy density in the cell medium and guide modi-
fications to the design. Modelling would also make it possible
to calculate the pressure amplitude of the acoustic field pro-
duced in the device, making it possible to directly calculate the
expected force. This could then be compared to experimen-
tally measured values. In addition it would allow for better
comparison of cell-viability results with previous literature.
VI. CONCLUSIONS
A simple non-resonant device for one-dimensional acous-
tic trapping of µm particles and cells has been designed and
constructed. Using this device, polymer beads, fixed human
corneal epithelial cells and live corneal epithelial and conjunc-
tival cells have been aligned. Preliminary evidence suggests
that cell viability greater than 50% compared to control cul-
tures can be maintained during trapping for up to two hours
with power inputs of up to 0.83 W. Significant further work is
desirable to confirm these results.
It has also been shown that 8 µm polystyrene spheres and
fixed AS cells can be aligned at separations of λ/2 of the ap-
plied acoustic field, as expected from theoretical descriptions
of the PRF. Additionally, a computational process was devel-
oped for analysing structure in images of acoustically manip-
ulated particles. It was used here to show that polystyrene
beads reached maximum alignment after 20 s in a field of 8
Vpp while the alignment of fixed cells continued to improve
over the full 90 s exposure at the same voltage.
Overall the device achieved its initial goals. However, there
is significant potential for future development in a variety of
directions.

16. 12
VII. ACKNOWLEDGEMENTS
I would like to thank both Dr Barnes and Dr Berry for their
support and supervision and Mr Tom Kennedy for his invalu-
able practical advice during the construction of the device. Fi-
nally, I would like to thank my lab partner, Clara Hughes, for
her hard work and patience throughout the project.
VIII. APPENDICES
A. Cell Culturing Technique
The cells used in this project were Araki-Sasaki human
corneal epithelial and IOBA human conjunctival epithelial
cells.
Throughout experiments the medium used was RPMI 1640
with L-glutamine and a pH indicator supplemented with 10%
(v/v) foetal bovine serum and antibiotics from Invitrogen, Life
Sciences warmed to 37◦
C.
1. Live Cell Culturing
To culture the cells they were removed from cryostorage
in liquid N2 and rapidly warmed to 37◦
C. Dimethylsulfox-
ide (DMSO) cryopreservative was used during storage; this
is rapidly toxic above 4◦
C. To avoid cell damage, excess
medium at 37◦
C was added to dilute the DMSO. The suspen-
sion was then centrifuged at 100g for 5 minutes at room tem-
perature before the removal of the supernatant. 1ml of fresh
medium was then added. Cells were differentially counted
and the average diameter measured by an automated Life Sci-
ences Countess cell counter. Trypan Blue dye was used to
identify dead cells.
2. Cell Fixation
Fixed cells were produced by incubating live cells with 4%
glutaraldehyde at 4◦
C overnight. They were subsequently ex-
haustively rinsed with 0.1M PBS before storage in 1ml PBS.
B. Angular Distribution Calculator
The following code was written in C and compiled using
GNU GCC compiler in Codeblocks.
1. Theta Calculator Code
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define M PI 3.14159265358979323846
double x y array [12000][2]; // Array to contain x and y data
double theta calc ( int ex, double x, double y, int k){
/∗ex is the current ”home” cell row number, x and y are the current x and y’s, k is row number of the current particle under consideration ∗/
long double delt x , delt y , r , theta 2 ; // doubles for the value of delta x, delta y and r for each cell
if (k!=ex){// excludes the ”home particle ” from caculations
delt x = x y array [k][0]−x;
delt y = x y array [k][1]−y; // calculate delta x and delta y
r = sqrt (( delt x ∗delt x )+( delt y ∗delt y )); // calculate radius from the initial value of x and y.
if (r<45){ // enter the true value (in pixels ) of lambda/2
theta 2 = atan2( delt y , delt x ); // calculates arctan of y/x
}
else{
theta 2 = 380; // if a cell is outside the sample radius , set value to extreme
}
return theta 2 ;
}
else{
return 380;
}
}
int fileopen (void){// function to read a tab delimited text file into a two−column array of values , x and y
int i ;
double a,b;
FILE ∗myfile;

17. 13
myfile = fopen(”xy180.txt”, ”r”); // open file
if (myfile!=NULL){ // tests for file opening
printf (”File found and openedn”);
// for (i=0;i<1000;i++){
for (i=0; ! feof (myfile); i++){
fscanf (myfile ,”%lf%lf”,&a,&b); // read the values in
x y array [i ][0]=a;
x y array [i ][1]=b;
}
fclose (myfile);
}
else{
printf (”File opening failed , file not foundn”);
i=0; // returns 0 to readout .
}
return i ;
}
int main(){
int d; // Counts number of x−y coords put in
int i , j ;
double x,y, theta ;
theta = 0;
d=0; // set d to zero for error checking
FILE ∗ Decay file ;
Decay file = fopen(”Theta. txt”,”a”); // file for readout appending each new result to the existing file
if ( Decay file != NULL){
d=fileopen () ; // call the function to open the file
printf (”The number of data sets read in is %in”,d); // count the number of coordinate pairs read in to act as iterator
if (d!=0){
printf (”nmy array[0][0] is %lf. If this is not 0, the read in has workednn”,x y array [0][0]) ; // checks array read−in has
worked
}
else{ // error check
printf (”The file did not contain any scanable item or was not found, calculation not possible .nPlease try again.n”);
}
for (i=0;i<d;i++){
x = x y array [i ][0];
y = x y array [i ][1]; // set variables with a given value of x and y
// Then calculate theta and write to file
for(j=0;j<d;j++){
theta = theta calc (i , x, y, j);
if ( theta <8){ //ignore the values outside r , set to extreme in function ” theta calc ”
fprintf ( Decay file ,”%2.15fn”, theta );
}
}
}
}
fclose ( Decay file );
return 0;
}
C. Certificate of Ownership
Project Report presented as part of, and in accordance with, the requirements for the Final Degree of MSci at the University
of Bristol, Faculty of Science.
I hereby assert that I own exclusive copyright in the item named below. I give permission to the University of Bristol Library to
add this item to its stock and to make it available for consultation in the library, and for inter-library lending for use in another
library. It may be copied in full or in part for any bona fide library or research worked, on the understanding that users are made
aware of their obligations under copyright legislation, i.e. that no quotation and no information derived from it may be published
without the author’s prior consent.
Signed: Frederick White
Full name: Frederick Alan Orlando White
Date: April 27, 2015

18. 14
Author Frederick A. O. White
Title Design, Development and Testing of a Device for Acoustic Trapping of Live Cells and Micrometre-Scale Particles
Date of Submission April 27, 2015
This project is the property of the University of Bristol Library and may only be used with due regard to the rights of the
author. Bibliographical references may be noted, but no part may be copied for use or quotation in any published work without
the prior permission of the author. In addition, due acknowledgement for any use must be made.
[1] A. Kundt. Acoustic experiments. Phil. Mag., 4:41–48, 1868.
[2] P. G. Bassindale, D. B. Phillips, A. C. Barnes, and B. W.
Drinkwater. Measurements of the force fields within an acous-
tic standing wave using holographic optical tweezers. Applied
Physics Letters, 104(16):–, 2014.
[3] M. Evander et al. Noninvasive acoustic cell trapping in a mi-
crofluidic perfusion system for online bioassays. Analytical
Chemistry, 79(7):2984–2991, 2007. PMID: 17313183.
[4] J. Nilsson, M. Evander, B. Hammarstr¨om, and T. Laurell. Re-
view of cell and particle trapping in microfluidic systems. Ana-
lytica Chimica Acta, 649(2):141–157, 2009.
[5] W. T. Coakley. Ultrasonic separations in analytical biotechnol-
ogy. Trends in Biotechnology, 15(12):506–511, 1997.
[6] M. Evander and J. Nilsson. Acoustofluidics 20: Applications in
acoustic trapping. Lab Chip, 12:4667–4676, 2012.
[7] A. Grinenko et al. Efficient counter-propagating wave acoustic
micro-particle manipulation. Applied Physics Letters, 101(23),
2012.
[8] M. S. Scholz, B. W. Drinkwater, and R. S. Trask. Ultrasonic
assembly of short fibre reinforced composites. In Ultrason-
ics Symposium (IUS), 2014 IEEE International, pages 369–372,
Sept 2014.
[9] Y. Qiu et al. Acoustic devices for particle and cell manipulation
and sensing. Sensors, 14:14806–14838, 2014.
[10] T. Laurell, F. Petersson, and A. Nilsson. Chip integrated strate-
gies for acoustic separation and manipulation of cells and par-
ticles. Chem. Soc. Rev., 36:492–506, 2007.
[11] D. Bazou et al. Gene expression analysis of mouse embryonic
stem cells following levitation in an ultrasound standing wave
trap. Ultrasound in Medicine & Biology, 37(2):321 – 330, 2011.
[12] D. Bazou, A. K Larisa, and W. T. Coakley. Physical enviroment
of 2-d animal cell aggregates formed in a short pathlength ultra-
sound standing wave trap. Ultrasound in Medicine & Biology,
31(3):423–430, 2005.
[13] A. Haake et al. Manipulation of cells using an ultrasonic pres-
sure field. Ultrasound in medicine & biology, 31(6):857–864,
2005.
[14] J. Hulstr¨om et al. Proliferation and viability of adherent cells
manipulated by standing-wave ultrasound in a microfluidic
chip. Ultrasound in Med. and Biol., 33(1):145–151, 2007.
[15] D. Bazou, W. T. Coakley, A. J. Hayes, and S.K. Jackson. Long-
term viability and proliferation of alginate-encapsulated 3-d
hepg2 aggregates formed in an ultrasoun trap. Toxicology in
Vitro, 22(5):1321–31, 2008.
[16] C. Duschl et al. Versatile chip-based tool for the controlled
manipulation of microparticles in biology using high frequency
electromagnetic fields. In H. Andersson and A. Berg, editors,
Lab-on-Chips for Cellomics, pages 83–122. Springer Nether-
lands, 2004.
[17] L. V. King. On the acoustic radiation pressure on spheres. Pro-
ceedings of the Royal Society of London. Series A - Mathemat-
ical and Physical Sciences, 147(861):212–240, 1934.
[18] K. Yosioka and Y. Kawasima. Acoustic radiation pressure on
a compressible sphere. Acta Acustica united with Acustica,
5(3):167–173, 1955.
[19] L.P. Gor’kov. On the Forces Acting on a Small Particle in an
Acoustical Field in an Ideal Fluid. Soviet Physics Doklady,
6:773, March 1962.
[20] H. Bruus. Acoustofluidics 7: The acoustic radiation force on
small particles. Lab Chip, 12:1014–1021, 2012.
[21] F. J. Holler, D. A. Skoog, and S. R. Crouch. Principles of In-
strumental Analysis (6th ed.). Cengage Learning, 2007.
[22] S. W. Rienstra and A. Hirschberg. An introduction to acoustics.
Eindhoven University of Technology, 18:19, 2003.
[23] M. W. Miller et al. Hyperthermic teratogenicity, thermal dose
and diagnostic ultrasound during pregnancy: implications of
new standards on tissue heating. International Journal of Hy-
perthermia, 18(5):361–384, 2002.
[24] M. Wiklund. Acoustofluidics 12: Biocompatibility and cell vi-
ability in microfluidic acoustic resonators. Lab Chip, 12:2018–
2028, 2012.
[25] Martin Wiklund, Roy Green, and Mathias Ohlin. Acoustoflu-
idics 14: Applications of acoustic streaming in microfluidic de-
vices. Lab Chip, 12:2438–2451, 2012.
[26] A. L. Bernassau et al. Controlling acoustic streaming in an
ultrasonic heptagonal tweezers with application to cell manipu-
lation. Ultrasonics, 54(1):268–274, 2014.
[27] J. F. Spengler et al. Observation of yeast cell movement and ag-
gregation in a small-scale mhz-ultrasonic standing wave field.
Bioseperation, 9:329–341, 2001.
[28] J. Wu. Acoustical tweezers. The Journal of the Acoustical So-
ciety of America, 89(5), 1991.
[29] C. Demore et al. Transducer arrays for ultrasonic particle ma-
nipulation. In Ultrasonics Symposium (IUS), 2010 IEEE, pages
412–415, Oct 2010.
[30] C. R. P. Courtney, C.-K. Ong, B. W. Drinkwater, P. D. Wilcox,
C. Demore, S. Cochran, P. Glynne-Jones, and M. Hill. Ma-
nipulation of microparticles using phase-controllable ultrasonic
standing waves. The Journal of the Acoustical Society of Amer-
ica, 128(4), 2010.
[31] Noliac. NCE51, accessed 31/03/2015. http://www.
noliac.com/products/materials/nce51/.
[32] J.E. Carlson, J. van Deventer, A. Scolan, and C. Carlander. Fre-
quency and temperature dependence of acoustic properties of
polymers used in pulse-echo systems. In Ultrasonics, 2003
IEEE Symposium on, volume 1, pages 885–888 Vol.1, Oct
2003.
[33] A. Grinenko, P. D. Wilcox, C. R. P. Courtney, and B. W.

19. 15
Drinkwater. Proof of principle study of ultrasonic particle ma-
nipulation by a circular array device. Proceedings of the Royal
Society of London A: Mathematical, Physical and Engineering
Sciences, 468(2147):3571–3586, 2012.
[34] Wayne Kerr Electronics. Precision Impedance Analyz-
ers Technical Data Sheet - Issue B, accessed 29/03/2015.
http://www.waynekerrtest.com/global/html/
products/impedanceanalysis/6500.htm.
[35] Tektronix. Arbitrary Function Generator Datasheet, accessed
31/03/2015.
[36] Olympus. Szx16/szx10 research stereomicroscope system,
accessed 24/04/2015. http://www.olympusamerica.
com/files/seg_bio/SZX16SZX10%20brochure.
pdf.
[37] Lumenera Corp. Infinityx-21 datasheet, accessed
24/04/2015. http://www.lumenera.com/
resources/documents/datasheets/microscopy/
INFINITY-x-21%20-%20datasheet%20-%
20v07082009.pdf.
[38] Schott Fibre Optics. Kl1500lcd, accessed 24/04/2015.
http://www.meyerinst.com/html/leica/
schott/1500-2500/UserManual_KL1500LCD.pdf.
[39] C. M. Costa and S. Yang. Counting pollen grains using readily
available, free image processing and analysis software. Annals
of Botany, 104(5):1005–1010, 2009.
[40] R. Brown. fitellipse.m, accessed 16/04/2015. www.
mathworks.com/examples/matlab/3836
-fitellipse-least-squares-ellipse-fitting
-demonstration.
[41] W. Gander, G. H. Golub, and R. Strebel. Least-squares fitting
of circles and ellipses. BIT Numerical Mathematics, 34(4):558–
578, 1994.
[42] RS Components. Digital Thermometer Operators Man-
ual, accessed 31/03/2015. http://docs-europe.
electrocomponents.com/webdocs/0034/
0900766b800340ae.pdf.