1002748_Ritchie_ENG5041P_Final_Report_14-15

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3D Acoustic Manipulation
ENG5041P
Scott Ritchie
1002748
Supervised by Anne Bernassau
Partially Funded by the
MEng in Mechanical Engineering

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Abstract
Recent developments in the field of life sciences prompt the innovation of
particle or cell tunable devices for particle separation. Acoustic manipulations
key advantage lies in the fact that, any object, insulator or conductor, magnetic or
nonmagnetic can be manipulated with minimal mechanical stress. In the course
of this investigation, a variety of acoustic techniques pertaining to node
separation values, field patterning and static phase shift implementations were
validated. Dynamic acoustic field activated cell separation (DAFACS)
techniques, developed by George Skotis, were scaled from a micron to mm level
yielding particle separation with 1.5 mm and 3.2 mm polystyrene beads whilst
supported on a horizontal glass substrate. Vertical levitation with 1.5 mm and 3.2
mm was then achieved with a source separation of 8.9 cm. Discontinuities in TTi
signal output limited the development of programmable dynamic waveforms to
implement particle separation in this orientation. An alternative Agilent signal
generator model without a prewritten LabVIEW™ driver meant only manual
inputs were possible. These manual inputs were unable to replicate the dynamic
waveform seen to separate particulates on the glass substrate. It is hoped,
development of a LabVIEW™ control suite capable of driving the Agilent model,
DAFACS can be realised mid levitation yielding improved results and expanding
the applications of this acoustic device.

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Table of Contents
Abstract......................................................................................................................................1
Acknowledgements....................................................................................................................5
Table of Figures .........................................................................................................................6
1. Project Schema.......................................................................................................................8
1.1 Objectives.........................................................................................................................8
1.2 Background ....................................................................................................................10
1.3 Project Plan ....................................................................................................................11
1.4 Pertinent Skills ...............................................................................................................14
2. Literature Review.................................................................................................................15
2.1 History of Standing Waves ............................................................................................15
2.2 Standing Wave Theory and Characteristics ...................................................................18
2.3 Particle Levitation ..........................................................................................................24
2.4 Static Wave Acoustic Manipulation...............................................................................28
2.5 Acoustic Sorting.............................................................................................................33
3. Materials ..............................................................................................................................38
3.1 Test Rig ..........................................................................................................................38
3.2 Electrical Components ...................................................................................................45
3.3 Test of Different Types of Particles ...............................................................................51
4. Method.................................................................................................................................53
4.1 Experimental Theory......................................................................................................53
4.1.1 Patterning and Static Manipulation .........................................................................53
4.1.2 Dynamic Manipulation............................................................................................55
4.2 Horizontal Setup.............................................................................................................57
4.2.1 System Characterisation and Node Separation........................................................57
4.2.2 Speaker Separation Limitations and Field Visualisation.........................................60
4.2.3 Static Wave Particle Manipulation..........................................................................62
4.2.4 Dynamic Acoustic Field Activated Particle Separation ..........................................64
4.3 Vertical Setup.................................................................................................................66
4.2.1 Acoustic Levitation and System Characterisation...................................................66
4.2.2 Static and Dynamic Wave Acoustic Manipulation..................................................68
5. Results & Discussion...........................................................................................................70
5.1 Horizontal Setup.............................................................................................................70
5.1.1 System Characterisation and Node Separation........................................................70

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5.1.2 Speaker Separation Limitations and Field Visualisation.........................................75
5.1.3 Static Wave Particle Manipulation..........................................................................77
5.1.4 Dynamic Acoustic Field Activated Particle Separation ..........................................80
5.4 Vertical Setup.................................................................................................................84
4.2.1 Acoustic Levitation and System Characterisation...................................................84
4.2.2 Static and Dynamic Wave Acoustic Manipulation..................................................86
6. Conclusion & Future Work..................................................................................................88
References................................................................................................................................90

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Acknowledgements
Firstly I would like to thank my primary supervisor, Anne Bernassau for her
patience and support, without which, this project would not have been possible.
I would also like to thank the GU68 Trust for financial support which assisted in
the purchasing of materials and equipment which were paramount to the success
of the project.
Special thanks to George Skotis for assistance and guidance in the lab during the
course of the project.
Thanks to the mechanical workshop especially Brian Robb and Ewan Russell for
their advice and guidance during rig construction. I would also like to thank Tom
Rieley for assisting on some of the experiments.
Finally I would also like to thank Lucia Johnston for her help throughout this
project.
This project is dedicated to my family who have supported me throughout my
time at University.

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Table of Figures
Figure 1 – Standing Wave Pattern ...........................................................................................19
Figure 2 – Acoustic Forces ......................................................................................................19
Figure 3 – Standing Wave Acoustic Levitation.......................................................................25
Figure 4 – Standing Wave Acoustic Levitation for Large Planar Objects ..............................26
Figure 5 – Near Field Acoustic Levitation ..............................................................................27
Figure 6 – Array Controlled Acoustic Manipulation...............................................................29
Figure 7 – Rotational Array Controlled Acoustic Manipulation .............................................29
Figure 8 – Frequency Change Particle Manipulation ..............................................................30
Figure 9 – Phase Shift Manipulation .......................................................................................32
Figure 10 – Ultrasonic Standing Wave Actuated Valve..........................................................33
Figure 11 – Binary Ultrasonic Standing Wave Actuated Valve System .................................34
Figure 12 – Particle Separation by Means of Frequency Modulation .....................................36
Figure 13 – Particle Separation through Phase Modulation ....................................................37
Figure 14 – BG13p Visaton™ Technical Drawing .................................................................38
Figure 15 – Rig Design 1.........................................................................................................39
Figure 16 – Rig Design 2.........................................................................................................40
Figure 17 – Finalised Mount Design .......................................................................................40
Figure 18 – Aluminium Frame ................................................................................................41
Figure 19 – 3D Printed Speaker Frame....................................................................................41
Figure 20 – BMS™ 4550 Technical Drawing.........................................................................42
Figure 21 – BMS™ 4550 Rig Attachment ..............................................................................43
Figure 22 – Final Rig Design...................................................................................................43
Figure 23 – Assembled Test Rig..............................................................................................43
Figure 24 – Visaton™ Frequency Response Curve.................................................................45
Figure 25 – BMS™ 4550 Frequency Response Curve............................................................46
Figure 26 – LA50b Schematic Diagram ..................................................................................47
Figure 27 – Agilent Power Supply Model E3631A.................................................................48
Figure 28 – TTi TGA12104.....................................................................................................48
Figure 29 – Agilent 33250A ....................................................................................................49
Figure 30 – Tektronix™ DPO4014 Oscilloscope....................................................................49
Figure 31 – Electrical Components Setup ...............................................................................50
Figure 32 – Theoretical Static Phase Shift vs Displacement of a 2 mm Particle.....................54
Figure 33 – LabVIEW™ Waveform Generated......................................................................55
Figure 34 – LabVIEW™ User Interface..................................................................................56
Figure 35 – Glass Screen Support............................................................................................57
Figure 36 – Experimental Setup Overview..............................................................................60
Figure 37 – Acoustic Levitation Vertical Test Setup...............................................................66
Figure 38 – Susceptible Properties Agglomerating .................................................................71
Figure 39 – Unsuitable Properties Subjected to the Standing Wave .......................................72
Figure 40 – Super Hydrophobic Coating with Water ..............................................................72
Figure 41 – Node Separation ...................................................................................................73
Figure 42 – Transverse Component of Acoustic Force on 6 Bead 1.5 mm Towers................74
Figure 43 – Speaker Separation Limitations............................................................................75

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Figure 44 – Standing Wave Visualisation Using Propylene Glycol and Liquid Nitrogen ......76
Figure 45 – 180° Phase Shift Particle Mapping.......................................................................77
Figure 46 – 90° Phase Shift Particle Mapping.........................................................................78
Figure 47 – Phase Shift vs Displacement of a 2 mm Particle Graph.......................................78
Figure 48 – Dynamic Acoustic Field Activated Particle Separation .......................................81
Figure 49 – 1.5 mm Particle Deviations ..................................................................................83
Figure 50 – 3.2 mm Particle Acoustic Levitation....................................................................84
Figure 51 – 1.5 mm Particle Acoustic Levitation....................................................................85
Figure 52 – Agilent vs TTi Waveform Displayed on the Oscilloscope...................................86
Figure 53 – Acoustic Manipulation in Levitation....................................................................87
Table 1 – Binary Ultrasonic Standing Wave Actuated Valve Outputs....................................34
Table 2 – BMS™ 4550 Mounting Information .......................................................................42
Table 3 – LA50b Power Amplifier Specification....................................................................47
Table 4 – Volume Selectivity Testing .....................................................................................51
Table 5 – Density Selectivity Testing......................................................................................52
Table 6 – System Characterisation Parameters........................................................................58
Table 7 – Field Visualisation and Source Separation Limitation Parameters .........................61
Table 8 – Static Waveform Acoustic Manipulation Parameters..............................................62
Table 9 – Dynamic Waveform Parameters..............................................................................64
Table 10 – Step Size & Ramp Period Parameters....................................................................64
Table 11 – Acoustic Levitation System Parameters ................................................................67
Table 12 – Static and Dynamic Wave Acoustic Manipulation Parameters.............................68
Table 13 – Susceptible Properties Table..................................................................................70
Table 14 – Dynamic Acoustic Field Activated Particle Separation Property Table................80
Equation 1 – Wave Addition Formula.....................................................................................21
Equation 2 – Standing Wave y Equation .................................................................................21
Equation 3 – Primary Acoustic Force on a Sphere..................................................................22
Equation 4 – Acoustic Contrast Factor....................................................................................22
Equation 5 – Viscous Drag Force ............................................................................................23
Equation 6 – Basic Wave Equation .........................................................................................23

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1. Project Schema
This section provides the outline of the investigated work. The key aims
and objectives, as well as time frames and essential technical skills have been
identified.
1.1 Objectives
 Demonstrate acoustic particle agglomeration utilising standing waves
generated by 2 speakers.
o Recorded node position and separation will be compared against theoretical
results leading to a better understanding of the acoustic device. It is hoped
tests conducted will assist in visualising the standing wave acoustic field
patterning.
 Demonstrate static acoustic manipulation by means of implementing a phase
shift.
o The phase of 1 signal source will be manually modified to look at particle
displacement under a phase shift.
 Separate and sort various particles by the introduction of a dynamic acoustic
field (DAF).
o The phase of 1 signal source will be computationally cycled from 0° to 360°
and the resulting particle translation mapped. This phase modulation will
be developed to yield a dexterous and controlled translation of particles
ranging in size from 25 𝜇𝑚 to 5 mm.

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o Employing recognised techniques developed at the University of Glasgow,
separation is achieved by exploiting the permutations in magnitude of the
acoustic force, caused by the variances in particle density and volume. The
behaviour of the particulates manipulated by this sorting technique will be
studied and an understanding will be developed.
 Exhibit particle levitation and develop phase shift manipulation techniques
using static and dynamic waveforms.
o Levitation will be explored in both the horizontal and vertical speaker
orientation. Manipulation will then be attempted using the previously
discussed phase change technique. This project ultimately aims to separate
and sort particles during levitation.

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1.2 Background
Acoustic manipulation has identified itself as a promising technology
which has advantages in a range of applications. Previously, particle
agglomeration and levitation utilising near field acoustic levitation (NFAL) and
standing waves[1] has been at the forefront of acoustic innovations however,
recent developments employing more than 1 wave source have opened the door
for dexterous particle manipulation in 3 dimensions. This technology has a
comprehensive range of applications from container-less organic substance
transport to blue chip component assembly.
Acoustic sorting has recently emerged as an increasingly exciting field
which has gained momentum and prominence in the field of life sciences. These
new biocompatible technologies are based on the fact that any object or organism,
insulator or conductor, magnetic or nonmagnetic can be manipulated with
minimal mechanical stress (hence, maintaining vitality).

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1.3 Project Plan
Refining the project into sub-objectives allowed the progress to be
structured, dynamic and progressive. Revaluating after each section provided
clarity and direction. A Gantt chart was utilised to ensure this project was kept on
track.
Sub-objectives
1. Background Research and Readings
2. Design Methodology
a. Rig Design
b. CAD and Rapid Prototyping
c. Rig Assembly and Construction
d. Electrical Components
e. Test Materials (EPS beads)
3. Acoustic Agglomeration and Field Visualisation Experiments
a. Identify Suitable Particulates
b. Characterise Test Materials
c. Introduce Visible Gas to the Standing Wave Field
4. Static Wave Acoustic Manipulation Experiment
a. Implement Manual Phase Shift
b. Implement Programmable Phase Shift (Using LabVIEW™)
c. Review Phase Change Effects
5. Dynamic Acoustic Field
a. Identify Suitable Wave Parameters Specific to a Particle Subset
b. Attempt Particle Sorting
6. Levitation
a. Implement Levitation in a Horizontal Speaker Setup
b. Implement Levitation in a Vertical Speaker Setup

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c. Develop Mid-Levitation Manipulation
7. Analyse Results
a. Discussion
8. Conclusion
9. Future Work

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Gantt Chart
Task
1. Introduction
Background Research
Supervisor Brief
Recommended Literature
Link Literature to Video Experiments
Design Parallel Speaker Enclosure
Identify Suitable Test Components `
Preliminary Report
2. Experimental Work
Construct Parallel Test Rig
Static Wave Manipulation Results
Test Dynamic Acoustic field
Attempt Dynamic Wave Particle Seperation
Construct Vertical Test Rig
Attempt Particle Levitation
Vertical Static Wave Manipulation Results
Vertical Dynamic Wave Particle Seperation
Scope for Progressive Research
Interim Report
3. Evaluation
Literature Review
Final Report Draft
Final Report
Prepare Presentation Not Scheduled
Presentation
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January
5 12 19 24
December
1 8 15 2213 20 27
November
3 10 17 24
October
6
September
8 15 22 29

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1.4 Pertinent Skills
An in-depth background knowledge of acoustics and associated
research developments is essential for this project. An understanding of
mathematical relationships concerning acoustic forces and acoustic contrast
factors is of paramount importance.
A familiarity in the operation of lab equipment such as signal
generators, oscilloscopes, power supplies and computer software packages
(such as LabVIEW™) will also be very useful.
Professional lab etiquette will be exercised during the course of this
investigation.

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2. Literature Review
This section provides a brief history of the innovations which have assisted
in developing relatively rudimentary physics theory concerning standing waves,
into acoustic devices for the levitation and manipulation of particles. The various
approaches adopted by the modern scientific community have been discussed and
a selection of schematic diagrams explaining their operation has been included.
2.1 History of Standing Waves
Acoustic standing waves were initially demonstrated in 1866 by August
Kundt[2]. He studied the behaviour of cork dust and lycopodium powder
contained in a horizontal glass tube subject to vibrations. He found stationary
points (nodes) in the acoustic wave pattern. These nodal positions were also found
to shift by changing the cork stopper position at one end of the tube. This is
comparable to changing the reflector position in modern reflected source
experiments. In 1902 Rayleigh developed this standing wave concept, with a
focus on studying the acoustic forces caused by pressure variations[3]. His
pioneering work highlighted the significant advances possible upon harnessing
acoustic forces to achieve acoustic levitation. This was introduced as an acoustic
counterpart to the forces induced by electromagnetic waves. These governing
forces were expanded in 1934 where L. V. King described acoustic radiation
forces on a sphere in an incompressible fluid[4]. Although not addressing the
effects of sphere compressibility and medium viscosity, L. V. Kings expanded
model allowed calculation of radiation forces in the correct order of magnitude
as experimental results.
Considerations surrounding the compressibility of a sphere were then taken
into account by Hasegawa in 1969[5]. By assuming; the sound field is plane
progressive; the solid sphere is isotropic and elastic; and the surrounding fluid is

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non-viscous, he was able to numerically evaluate a system with a higher degree
of accuracy than previously made possible by the L. V. King method. A very
different approach to the understanding of radiation forces was proposed by
Kawasima and Gor’kov in 1955[6] and 1962[7] respectively. Gor’kov presented
a very simple approach when determining the incident forces on a particle in an
arbitrary acoustic field. He represented the velocity potential as the sum of the
incident (𝜙𝑖𝑛) and a scattered term(𝜙𝑠𝑐). Gor’kovs perspective was indicative of
Barmatz in 1984 when he adopted this simplistic approach to extend the
understanding of localised force strength in cylindrical, plane, and spherical
standing wave fields[8].
Nyborg proposed that a more general model was required in 1967 due to a
negligible 𝛥 value when exposed to a relatively small sound source. His theory
suggested that the symmetrical sound field extended only to the immediate
vicinity of a small sphere[9]. Haar and Wyard applied Nyborgs concept along
with the Crum model[10], when they pioneered acoustic applications in life
sciences in 1978, achieving arrested blood cell flow in living tissue. In this paper
the notion of intercellular and unseen forces was also developed[11]. Their
findings also conclude the magnitude of secondary forces to be negligible in
comparison with primary radiation forces[12]. This approach pertaining to
negligible secondary radiation effects has been adopted in this investigation.
Although the Kundt tube experiment was the first to demonstrate the
elementary phenomena regarding acoustic standing waves, Karl Bücks and Hans
Müller went on to present an experimental set up for acoustic levitation in
1933[13]. They achieved the levitation of a small particle at a position slightly
below the identified node location. The principles behind such a discovery is seen
in section 2.2.
Whymark suggested possible applications of acoustic levitation within the
aerospace sector in in 1975[1]. His investigation focused on the capabilities of

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liquidising and solidifying aluminium, glass and plastic in the container-less state.
Lierke built upon these foundations in 1983 proposing an adaptation of a tube
levitator to a monoellipsoidal mirror furnace. Results demonstrated potential
applications of fluid physics in microgravity[14] where a higher degree of
accuracy and reliability can be achieved. In 1985 Trinh managed to construct a
compact acoustic levitation device which similarly allowed the study of surface
waves on freely suspended liquids as well as variations in surfaces tension when
affected by temperature and contamination. The optical diffraction characteristics
of transparent liquids were also investigated. Trinh hoped the compact nature and
simplistic design would make his device more suited for applications in the
aerospace industry[15].
Lierke led a comprehensive investigation in conjunction with the European
and US space associations published in 1996[16] which was followed by a study
into container-less processing with space applications by B. Wei in 1999[17]. He
used a single-axis ultrasonic levitator to investigate the levitation region and
stability characteristics of trapped particles.
In recent years acoustic manipulation has been implemented using a wide
range of novel and innovative techniques. These novel approaches have been
described in the following sections documenting the operation and limitations of
each design. Acoustic devices exploiting this relatively simple phenomena are
currently being refined and developed for use in many aspects of industry and life
sciences, maintaining acoustic manipulations position at the forefront of
innovation.

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2.2 Standing Wave Theory and Characteristics
The standing wave (a wave that remains in a constant position) is the
fundamental phenomenon allowing acoustic levitation and
manipulation[18],[20]. The acoustic forces affecting particles are caused by air
pressure variations in the standing wave pattern. A reflected source[21] or two
opposing transverse travelling waves with identical frequency and amplitude can
be combined to produce constructive interference. This in turn produces a
standing wave in superposition.
Interference between these two waves cause air pressure variations in the
pressure potential field. The resultant wave generated introduces points of zero
amplitude known as nodes. These points are found at increments of 𝜆/2 along the
wave pattern. Oppositely, antinodes constructively interfere at maxima to
generate points of double amplitude. Antinodes are also found at 𝜆/2
increments[22]–[24].
Providing that particles affected by the acoustic field differ in acoustic
impedance from the surrounding medium, we are able to utilise air pressure
potential wells to agglomerate particles in a stable position in the x axis.
Additionally a vertical signal source setup allows particles to equilibrate at points
of the acoustic force spectrum within the standing wave which countervail
gravitational force yielding levitation.
Figure 1 shows how the 2 incident waves interference to generate the
standing wave pattern. Nodes and antinodes are indicated by an N and A
respectively. Each of the incident waves travelling in opposite directions are
described mathematically later in this section. Node and anti-node separation
values have also been indicated.

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The red and blue lines denote the incident travelling waves interfering to
generate the black pressure wave in superposition. Primary and secondary
acoustic radiation forces are experienced by particles affected by the waveform.
The primary radiation force (PRF) is a direct result of the standing wave field and
therefore translates to the strongest acoustic forces. Secondary forces are caused
by reflections and scattering of the primary force radiating from particles
contained in the waveform. These forces are calculated to be many orders of
magnitude smaller than the primary force. For this reason secondary force
consideration has been omitted in our proposed application[25],[26].
Figure 2 shows how the acoustic forces act on the particles in the standing
wave to produce agglomeration at the nodes[27].
𝐴
𝑁
𝐴
𝑁
𝑁
𝐹𝑇𝑟
𝐹𝐴𝑥
𝐹
𝐹𝐵
𝜆/2
−𝜆/2
0
PressureNodes
𝑇1 𝑇2
Figure 2 – Acoustic Forces
Figure 1 – Standing Wave Pattern
𝑥
𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒
𝑁𝑁𝑁 𝑁 𝑁
𝐴
𝐴
𝐴
𝐴
𝐴
𝐴
𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑊𝑎𝑣𝑒 1
𝐼𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑊𝑎𝑣𝑒 2
𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑊𝑎𝑣𝑒
𝜆
𝜆/2
𝜆/2
/2

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In this diagram 𝐹𝐴𝑥 and 𝐹𝑇𝑟 refer to the axial and transverse component of
the primary acoustic force respectively. 𝐹𝐵 denotes the inter-particle secondary
force. At 𝑇2 particles can be seen settling at an equilibrium position after forces
have had an ample time period to act. The force diagram illustrates and underlines
the various forces acting on a particle affected by a standing wave. An expression
describing acoustic force on a particle is explained in equation 3.
These agglomeration characteristics have been harnessed to increase
filtration system efficiency in industry. Power plants already employ acoustic
agglomeration technologies to condense harmful fine ash (smaller than 2 micron)
into larger particulates which then continue towards the filtration system with
increased level of efficiency and operation[28],[29].
Generally solid particles in a liquid are observed translating away from the
antinode pressure maxima towards the nearest node reaching equilibrium at the
pressure well[30]. Conversely gas bubbles are seen travelling to the nearest
antinode. The compressibility and density of a particle dictates whether it travels
to the node or antinode of the standing wave. The theory pertaining to this
phenomena and its associated forces acting on particles are explained in equation
4.
Piezo-ceramic elements are predominantly used as the signal source. These
are either installed directly in conjunction with the aqueous medium or via a
coupling substance such as agar jelly which eliminates the mean flow from
dissipating transducer surface[31],[32]. Agar is selected due to its viscous
characteristics. Our proposed application involves a homogenous gaseous system
where this streaming effect poses less of a concern, therefore can be ignored.
The interference generating a standing wave can be described
mathematically as a summation of expressions denoting each incident wave. The

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pair of equations described below represent each of the incident opposing incident
waves.
Equation 1 – Wave Addition Formula
𝑦1 = 𝑦0 sin( 𝑘𝑥 − 𝜔𝑡)
𝑦2 = 𝑦0 sin( 𝑘𝑥 − 𝜔𝑡)
where 𝑦0 denotes the amplitude of the wave, 𝜔 represents the angular
frequency of the wave (measured in angular frequency) and 𝑥 and 𝑡 represent the
longitudinal position and time respectively. 𝑘 denotes the wave number
expressed in radians per meter, found by dividing 2𝜋 by the wavelength.
The resultant standing wave y expression is then found by adding these
terms.
𝑦1 = 𝑦0 sin( 𝑘𝑥 − 𝜔𝑡) + 𝑦0 sin( 𝑘𝑥 − 𝜔𝑡)
By evaluating employing trigonometric sum-to-product identity for
‘sin( 𝑢) + sin( 𝑣)’ the following term is derived.
Equation 2 – Standing Wave y Equation
𝑦 = 2𝑦0 cos(𝜔𝑡) sin(𝑘𝑥)
This relationship outlines a standing wave that oscillates in the time
domain however displays spatial dependence that is stationary in the sin(𝑘𝑥)
term. From this standing wave equation it is possible to deduce that at positions
𝑥 = 0,
𝜆
2
, 𝜆,
3𝜆
2
the amplitude will be found to zero (nodes) whereas at the x
positions 𝑥 =
𝜆
4
,
3𝜆
4
,
5𝜆
4
the amplitude is found to be at its maximum (antinodes).
The displacement between 2 incremental conjugative maxima or minima
is found to be
𝜆
2
.
Fluctuations in pressure (caused by the formation of this standing wave)
ultimately results in radiation forces experienced by particles entering the

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waveform. This is under the prevision that the diameter of said particle is
substantially smaller than half the wavelength of the standing wave[6],[70],[80].
Equation 3 – Primary Acoustic Force on a Sphere
𝐹𝑎 = − (
𝜋𝑃0
2
𝑉𝑐 𝛽 𝑤
2λ
) × 𝜙(𝛽, 𝜌) × sin(2𝑘𝑥)
Equation 4 – Acoustic Contrast Factor
𝜙(𝛽, 𝜌) =
5𝜌𝑐 − 2𝜌 𝑤
2𝜌𝑐 + 𝜌 𝑤
−
𝛽𝑐
𝛽 𝑤
where 𝑃𝑜is the power amplitude, 𝑉𝑐 is the volume of particle, λ the
wavelength and 𝛽 𝑤 and 𝛽𝑐 being the compressibility of the medium and particle
respectively. K is taken to be the wave number (2𝜋/λ) and 𝜌𝑐 and 𝜌 𝑤 are taken to
be the density of the particle and medium respectively. 𝑥 is taken to be the
distance from a pressure node.
The direction of applied forces is determined by the sign of the contrast
factor 𝜙[81]. This determines whether a particle will be at equilibrium at either
the pressure node or antinode. A positive 𝜙 factor results in manipulation towards
a node and negative 𝜙 factor to an antinode respectively. Generally it can be
assumed solid media will be translated towards a pressure node and gaseous
media to an antinode in an aqueous medium[82].
Disparity in the acoustic forces is caused by variations in mechano-
physical properties of the particles trapped in the system. Acoustic force scales
heavily with a particles volume and the medium viscosity.
Secondary acoustic forces have been deemed negligible in our applications
as they are found to be many orders of magnitude smaller than that of the primary
radiation force[12].
Opposing this axial primary force is the viscous drag[83].

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Equation 5 – Viscous Drag Force
𝐹𝑑 = −6𝜋𝜇𝑅𝑣
where R is the radius of the particle in m, v is the velocity of the particle
and μ denotes the dynamic viscosity of the liquid given in Ns/m2
.
The basic wave equation will also be useful when calculating node location
and separation[62].
Equation 6 – Basic Wave Equation
𝑣 = 𝜆 × 𝑓
where 𝑣 denotes sound velocity 𝑚/𝑠, 𝜆 the wavelength in m and 𝑓 being
the frequency of the wave in question.
In summary, 2 incident waves interfere to produce a standing wave in
superposition. The pressure variations apply an acoustic force on a particle
subjected to the acoustic field. This force either translates media to a node, or
anti-node depending on both the particle and medium properties. Relationships
describing this particle behaviour are seen in equations 3 and 4. The act of field
activation translating particles to a node or anti-node site is called agglomeration.

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2.3 Particle Levitation
Acoustic levitation has identified itself as a promising technology which
has advantages in both the micro and macro scale. This method of levitation is
expanding in its applications against established technologies which utilise
magnetic[33], optical[34], electrostatic[35], aerodynamic[36] and
superconducting magnetic forces[37][38]. This is fundamentally due to the fact
these more traditional methods of levitation are intrinsically material property
reliant. Acoustic levitations main advantage lies in the fact that any object,
insulator or conductor, magnetic or nonmagnetic can be manipulated with
minimal mechanical stress[39]. Research in the past has also concluded that the
vitality of living organisms are unaffected by the levels of acoustic radiation
present[40]. Applications of acoustic agglomeration and levitation range from
the separation of blood (yielding plasma) to cell culture fermentation
devices[11],[41],[42].
While the pressure forces principally agglomerate particles at the node
positions in the standing wave, with sufficient acoustic force, levitation can be
realised[7]. There are 2 main techniques employed to achieve this phenomena
using standing waves. These are tailored to the levitated object in question. An
alternative method will also be explored within this section, which takes
advantage of the acoustic radiation force generated directly from the signal
source.
The first method outlined utilises a sound source as well as a reflector to
generate a standing wave. Figure 3 outlines how gravitational forces are
counteracted by the acoustic forces using this technique[43]. The particle can be
seen dropping just below the pressure node due to the gravitational force (g)
affecting it. Once the level of acoustic force (𝐹𝑎) experienced in the upward
direction (due to the particles position in the waveform) equals that of the

25
gravitational force, equilibrium is achieved with subsequent levitation. 𝐹𝑑
denotes the viscous drag caused gaseous medium, opposing particles movement
through the medium.
This method also covers the use of 2 opposing speakers but principally
covers all setups that effectively immerse a particle in a standing wave field. This
technique allows levitation of particles with a radius smaller than that of the
wavelength (mm scale) of the signal generated.
Building on this elementary technique it is possible to levitate larger
objects by employing the object as the reflector itself[3],[43],[44]. This technique
widens the applications of acoustic levitation as the size of the object in question
is no longer limited by the signal wavelength. This is due to the fact an entity is
suspended over a complete standing wave as opposed to being trapped within its
pressure node.
In the figure 4, a reflected wave denoted by the red and blue field lines
interferes with one another to create a full standing wave in the interstitial space.
Any number of full standing waves can be realised in subspace between the
source and entity in question providing sufficient acoustic forces allows
levitation. A separation of 𝑛𝜆/2 translates to the entity resting on the nth node on
the standing wave.
Figure 3 – Standing Wave Acoustic Levitation
Reflected signal producing a standing
wave
𝐹𝑎
𝑔
𝐹𝑑

26
The final acoustic levitation device discussed allows the suspension of
objects extremely close to the radiation surface at distances much smaller than
source signal wavelength[45],[43]. This system primarily applies to objects with
a flat surface. Its operation is principally controlled by 2 linear magnetic actuators
with parallel surfaces oscillating opposite one another generating a positive load
bearing force. This technique is chiefly known as squeeze film or near field
acoustic levitation (NFAL). Unlike other methods previously discussed
pertaining to acoustic levitation, this technique uses the object itself as a blockade
for the free propagation of the waveform. Levitation is achieved through the
formation of a thin gas film varying with the pressure movement between the
radiation source and entity in question[46].
The schematic diagram of this system described is seen in figure 5. It
describes also system behaviour. It is possible to deduce from the diagram that
when a minor deviation from the centre of the circular radiation source occurs, a
correcting force returns the planar object back into concentric suspension. This
corrective force oscillates in magnitude with the fluctuations in the suspended
objects position. 𝐹𝑐 Denotes the corrective force caused by displacement 𝛥𝑟[47]–
[49].
Figure 4 – Standing Wave Acoustic Levitation for Large Planar Objects
Signal source
Levitated entity
𝑛𝜆
2

27
The possibility of acoustic levitation eventually simulating micro-gravity
test conditions on a substantial scale is an exciting prospect for the scientific
community. These test conditions currently achieved in zero gravity settings
during orbit (freefall) which are extremely costly. Tests in these conditions
chiefly focus on material solidification and the complex fluid phenomena
associated[50].
To summarise, acoustic levitation can be achieved by either inserting
particles or planar objects to the node points of the standing wave or by
suspending flat objects parallel to the radiation source. Standing wave levitation
is achieved by allowing the particle to drop marginally in the standing wave until
the level of acoustic force (𝐹𝑎) experienced in the upward direction equals that of
the gravitational force. NFAL is achieved from radiation emanating from the
signal source. The acoustic device described in this investigation will used the
former technique involving standing waves.
𝑅
𝑦
𝑟
0
𝐹𝑐
Δ𝑟
Signal source
Levitated object
Figure 5 – Near Field Acoustic Levitation

28
2.4 Static Wave Acoustic Manipulation
Techniques involving particle agglomeration and levitation have paved the
way for more advanced techniques exploring the possible methods of both
particle manipulation and translation. These exciting techniques have attracted
vast media coverage and have captured the imagination of the scientific
community[51][52]. Applications of acoustic manipulation range from container-
less transport of reactive or volatile substances to moving delicate components in
hardware assembly[53][17]. The key to furthering this field of acoustics is
developing and improving the level of dexterity and control associated with this
type of manipulation.
Many of the techniques for the manipulation of particles are built on the
fundamental principles discussed in section 2.2, namely standing wave acoustic
levitation.
This previously discussed approach has been adapted and developed to
extend the capability of the device to translate a particle from one location to
another. These system adaptations manipulate particles by either, trapping
particles in an array of travelling signal sources[54][1] in 2 or 3 dimensions or
altering the phase[55],[56] or frequency[21] of the signal source.
The most basic form of these controlled manipulation methods employs an
array of reflected signal sources(or opposing speakers)[58][59]. The signal seen
in figure 6 is relayed through the loudspeaker array translating the particle to the
target location.
Figure 6 shows the principles behind the operation of 1 and 2 dimensional
acoustic array manipulator devices. Similarly, a 3D system can be realised using
stacks of transducers in the 2D setup. Dexterity and control is directly
proportional to the number of transducers employed within the device[60].

29
Another array technique previously proposed orientates transducers into a
ring setup. This translates to manipulation in a rotational sense[38]. The proposed
setup below requires 3 independently driven transducers opposed by 3
reflectors[61].
The schematic shown in figure 7 depicts a ring made up of transducers and
reflectors. In this setup the signal is passed from 𝑇1 through 𝑇2 and onwards to 𝑇3.
This cycle is then repeated. During this period, the particle follows the orbit
shown in red. This system requires 2 complete signal cycles for the translation of
a particle in 1 complete orbit.
Signalsources
Reflector
Reflector
Signalsources
Figure 6 – Array Controlled Acoustic Manipulation
1 Dimension 2 Dimensions
𝑇2 𝑅2
Figure 7 – Rotational Array Controlled Acoustic Manipulation

30
Another possibility for particle manipulation is realised by changing the
source signal frequency. By increasing the frequency the wavelength is decreased
thus altering the positions of the nodes. This pertains to the previously discussed
node separation concept (𝜆/2) found in section 2.2. The equation outlined below
describes the relationship between 𝜆 and 𝑓 found in the basic wave equation[62].
𝑣 = 𝜆 × 𝑓
Figure 8 shows how the nodal positions shift when doubling a signal input
frequency[63]. It is possible to observe from the diagram that when doubling a
signal input frequency the number of nodes double. The particles behaviour
(destination node selection) is controlled by changing the frequency increments
taken to reach the target frequency[63].
Frequency modulation not only allows particle manipulation but in unison
with a frequency variable acoustic field, individual particles can be separated.
This will be explored in depth in section 2.4.
A particularly favoured approach to particle manipulation concerns the
modulation of the phase of signal wave, due to the fact this method of transporting
particles displays significant dexterity potential and associated
control[56],[64],[65]. However, unlike previous systems, this technique requires
2 independently programmable wave sources (a reflected source is not suitable).
𝑓1 2𝑓1
𝜆1
2
𝜆1
4
Figure 8 – Frequency Change Particle Manipulation

31
Although the general approach to phase shift transportation is built on the
same fundamental principle, specifications dictate the exact characteristics of the
acoustic device[60]. Applications range from delicate electrical component
construction (mm scale) to cellular transport[66],[67] (micrometre scale)
maintaining the sufficient spatial resolution in each case.
In this section the rudimentary theory behind the behaviour of the standing
wave, when introducing a phase shift will be covered. How these principles are
employed in each application will then be explored.
By introducing a gradual phase shift of 0° to 360° to speaker 1 (𝑆1) of 2
opposing signal sources we are able to translate each node 1 integer position away
from 𝑆1.
Figure 9 shows this manipulation approach first hand. It demonstrates how
the phase shift of one of the signal sources (while the blue wave emanating from
𝑆2 remains static) gradually alters the position of the node 𝑁𝑖 rooted in the
pressure waveform interference pattern between signals 𝑆1 and 𝑆2. While 1
complete phase shift cycle (0° to 360°) can only transport particles from one node
to its neighbouring node (distance 𝛥 𝑛), this can be repeated any number of times.
It is important to note that an appropriate 𝑇𝑟𝑎𝑚𝑝 period (time taken for the phase
to be increased from 0° to 360°) is required for the particles in question to track
the node movement.
In effect, a particle can be transported any desired distance between the
signals providing the signal generates a sufficient pressure amplitude for the
specified object to maintain levitation over the entirety of the waveform. An
increased resolution of control can be realised by using marginal increments with
regards to the phase shift.

32
Due to the varying magnitudes of acoustic forces derived from different
particles properties (namely density, volume and compressibility) this technology
is currently being developed as a selective manipulation tool (sorting device). The
schematic workings of this device will be discussed in the next section (2.5).
By incorporating this phase shift technique with an acoustic array it is
possible to manipulate a point of pressure minima within an acoustic landscape
in 3D[60]. This method of manipulation has shown real promise in the media and
entertainment sector[68].
Alternative implementations of this phase shift technology take the form
of octagonal[56] and heptagonal[64] sonotweezer devices. These multi element
configurations have demonstrated high levels of dextrous acoustic trapping and
manipulation comparable with the levels of control currently displayed by optical
tweezers[69].
In review of these approaches, static phase manipulation has seen to
demonstrate the most controlled, dexterous and adaptable from of acoustic
manipulation. Previous tests have shown frequency manipulation from gradually
increasing phase change effects produce consistent particle displacement and
target locations. Phase change techniques have been adopted in this investigation.
0°
90° 180° 270° 360°
Δ 𝑁
N𝑖
N𝑖+1
Figure 9 – Phase Shift Manipulation
S1
S2

33
2.5 Acoustic Sorting
Building upon research previously conducted at the University of Glasgow
by George Skotis, this investigation aims to demonstrate acoustic sorting in the
cm scale (from the introduction of a phase shift) and will be visible to the human
eye for the first time.
Acoustic manipulation is highly regarded as an efficient and effective
sorting technique due to its characteristics of being a low damage, biocompatible,
high recovery method of transporting particles. Its main advantages lies in its
large displacement capabilities (cm range) and its label free isolation in the field
of life sciences[55].
Rudimentary forms of acoustic agglomeration sorting already feature in
regenerative medicine (lipid separation[70]). Although only a binary duty cycle
operation, this agglomeration activation switching can be developed into a
valuable tool[71]. Combined with sample detection this technology could prove
invaluable in modern medicine. This most elementary method of acoustic
separation uses flow splitters in conjunction with a laminar steady flow. Although
this technology is still in its infancy more complex designs and methodologies
are being more commonplace in industry. The principal operation of such a
system is explained in figure 10.
S 𝐴
S 𝐵
Transducer
Sensor Unit
N𝑖
Figure 10 – Ultrasonic Standing Wave Actuated Valve

34
In this example device, 2 contrasting particles are transported in a laminar
flow toward the sensing unit. This sensing unit identifies the particle and controls
the actuation of the standing wave valve. When the transducer is activated the
pressure variation forces the particles into the central node (denoted by 𝑁𝑖). The
flow splitter at the end of the inlet separates the 2 streams of particulates, hence
controlled sorting is realised. Although the operation and functionality of this
devices appears basic and limited in application, with the addition of just 1 other
transducer in a similar arrangement, a binary sorting system is realised. A rough
outline of such a system is seen in figure 11[72].
When transducer 𝑇1, shown in figure 11 is activated, particulates are
diverted towards the AB route. By actuating 𝑇2 the entity is then guided into path
A. In essence when the transducer is activated particulates are guided into the
uppermost path. The subsequent results of the full spectrum of system inputs can
be seen in table 1 where 1 denotes a transducer in operation. With the addition of
more flow splitters and transducers a more complex binary system is realised.
Table 1 – Binary Ultrasonic Standing Wave Actuated Valve Outputs
𝑻 𝟏 𝑻 𝟐 Outlet
0 0 D
0 1 C
1 0 B
1 1 A
inlet
𝑇1
𝑇2
𝐴
𝐵
𝐶
𝐷
𝐴𝐵
𝐶𝐷
Figure 11 – Binary Ultrasonic Standing Wave Actuated Valve System

35
These concepts involving static field activated sorting have inspired new
approaches involving dynamic waveforms. The fundamental principle behind
these innovative new techniques is that, a selection of different particles with
varying size and or density ultimately experience variations in magnitude of
acoustic radiation force (while viscous drag remains the same). These
inconsistences in primary acoustic force translate to variations in acceleration to
the nodes. Theory relating a particles density, volume and compressibility to its
magnitude of acoustic force as well as the acoustic contrast factor effects are
covered in equations 3 and 4[73]–[75].
The first dynamic acoustic field activated separation technique described
concerns frequency modulated waveforms. This technology exploits the fact
larger, more dense particles agglomerate to node positions faster than smaller,
less dense particles. The increased acceleration is a direct result of a stronger axial
primary radiation force caused by pressure differences in the standing wave[76].
Figure 12 shows the behaviour of the particles at each stage of the dynamic
waveform. It works by first employing a signal frequency at time 𝑇1 which forms
nodes at a quarter of a channels width. A change in frequency in the waveform
then excites the particles to the centre of the channel (half wavelength) at time 𝑇2.
At this point disparities begin to emerge in the various particulates displacements
from the initial node. The system then reverts to the original excitation frequency
at 𝑇3 followed by modulation to resonance frequency at 𝑇4 (identical as system
conditions at point 𝑇2). Finally at 𝑇5 the channel is excited at a frequency which
generates nodes at both the centre and the quarter width of the channel. The
duration of each stage of the frequency waveform is paramount to the efficiency
of separation. These time duration values are found experimentally.

36
This technique presents a number of key disadvantages such as: marginal
particle displacement, inherent inflexibility (due to limitations concerning the
dimensions of suitable transducers), unstable forces on identical particles causing
disparity in displacement[77],[78].
The final method of acoustic sorting detailed in this section will focus on
dynamic acoustic field activated particle separation by means of implementing a
phase shift. This is the focal point of this investigation. Its principles, largely
similar to those raised in frequency modulation, involve separating particulates
by exploiting disparities in particle displacement (due to permutations in acoustic
force)[55][77].
Figure 13 outlines our proposed method for particle separation. This is
achieved by modulating the phase of one of the transducers with respect to the
other. This dynamic waveform is adjusted using LabVIEW™. This technique has
previously demonstrated micro-particle acoustic selectively[64][79].
The preferred approach adopted in this investigation employs a phase ramp
period as well as a time-varying phase delay. The system repeats this basic
𝑇0
𝑇2
𝑇4
𝑇1
𝑇3
𝑇5
Figure 12 – Particle Separation by Means of Frequency Modulation

37
waveform to achieve separation over large distances (several centimetres). Each
complete cycle transports the particles of interest 1 node on the standing wave.
This process can be repeated indefinitely allowing a continuous separation
process.
Figure 13 shows how the larger and or denser particles travel past the mid
antinode when the slave wave 𝜓 is increased from 0˚ at 𝑡0 to 360˚ at 𝑡1. The
smaller and or less dense particles however, do not cross this midpoint. The
greater displacement from 𝑁𝑜𝑑𝑒𝑖 seen in the large or more dense particles
compared with the small and or less dense particles is due to the increased
acoustic force derived from a particulates properties. During the 𝑇𝑟𝑒𝑠𝑡 period both
particles are allowed to relax back to their nearest node, equilibrating the system.
Repeating this process transports the large particles from node to node towards
the master wave signal source while keeping the small particles stationary.
To summarise, the tuneable, adaptable nature of dynamic acoustic field
activated separation make it the ideal selection of sorting technique employed in
this investigation. The property independent biocompatible nature of acoustic
manipulation lends itself to a whole range of industries and branches of life
sciences. It is the aim of this investigation to separate arbitrary particles using
this dynamic waveform described above.
𝑁𝑜𝑑𝑒𝑖
𝑁𝑜𝑑𝑒𝑖+1
𝑡1
dψ(˚
)
𝑡2𝑡0
180˚
360˚
𝑑𝜓(˚) 𝑇𝑟𝑎𝑚𝑝 𝑇𝑟𝑒𝑠𝑡
𝑃ℎ𝑎𝑠𝑒 𝑆ℎ𝑖𝑓𝑡
𝑃𝑜𝑠𝑖𝑡𝑜𝑛 𝑜𝑓 𝑆𝑚𝑎𝑙𝑙/𝐿𝑖𝑔ℎ𝑡 𝑃𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
𝑃𝑜𝑠𝑖𝑡𝑜𝑛 𝑜𝑓 𝐻𝑒𝑎𝑣𝑦/𝐿𝑎𝑟𝑔𝑒 𝑃𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
Figure 13 – Particle Separation through Phase Modulation

38
3. Materials
The following chapter briefly documents the design process of the
framework of the test rig as well as providing specifications of electrical
equipment used. The specification of expanded polystyrene micro-particles used
in the characterisation and testing of the system have also been included.
3.1 Test Rig
To implement acoustic techniques it is essential 2 signal sources must be fixed
securely to prevent the test rig resonating when the loudspeakers are excited. The
rig must also permit a degree of customisation in terms of separation which in
turn expands the scope of the investigation as a whole. The derived design
specifications are as follows;
 BG13p Visaton™ loudspeaker mountable
 Rigid frame mount in which speakers faces are parallel
 Customisable speaker setup which facilitates further equipment
implementation
 Cheap, easy and quick to manufacture using rapid prototyping
Figure 14 – BG13p Visaton™ Technical Drawing

39
The overall dimensions of the loudspeakers dictated the general scale of
the mount and rail system. Figure 14 shows the schematic of the BG13p
Visaton™ speakers[84]. This technical drawing provided by Visaton™ allows a
secure mount to be designed using the Solidworks™ CAD package.
The fast production and high degree of accuracy characteristics associated
with rapid prototyping made 3D printing an ideal selection as a speaker mount
manufacturing technique[85].
A number of different rigs were deliberated upon and improved until the
final mount design emerged.
Figure 15 shows the first
rig proposed. This design
however, raised concerns
regarding the complications of
3D printing, involving packing
material required for supporting
uprights as well as dimensional
limitations of the 3D printing
machine. Advice from the technical workshop was taken on board and the rig
was redesigned, incorporating a fabricated aluminium base while utilising 3D
printed individual parts for the speaker mounts.
Refinement of the original idea developed more suitable designs in terms
of rigidity and ease of assembly which also dramatically reduced the cost of the
3D printing. The improved design illustrated in figure 16 allowed the part to be
constructed using multiple sections (fixed with a lip and groove), simplifying the
RP process and reducing the need for upright packing materials.
This design also incorporates a fixing seen on the side of the mount. This
allowed the part to be fixed to the rail with ease.
Figure 15 – Rig Design 1

40
Design 2 was further refined and simplified finally yielding the final mount
design seen in figure 17.
In this final design the side rail fixing section was streamlined into an
internal set of 2 fixings on each leg support. The rig was then 3D printed using
ABS plastic. ABS plastic was identified as an ideal material satisfying the desired
specification in terms of rigidity and working conditions[86].
The final mount design combines simplicity and ease of construction while
meeting all design requirements.
While the main focus of the rig was to fulfil the primary specification, it
was also apparent the rig must provide sufficient scope for development as the
project progressed. Detachable speaker mounts running on adjustable rails
provide the potential to expand the applications of the acoustic device.
Figure 17 – Rig Design 2 Figure 16 – Finalised Mount Design

41
Figure 18 – Aluminium Frame
The schematic diagram of the derived design shown in figure 18 details the
30 mm incremental fixings on the aluminium bed.
The rail was constructed using 20x10 mm aluminium bar. This material
selection helped guarantee the speakers were perfectly parallel. The final
assembly, fixed with bolts and plastic cement can be seen in figure 19.
Assembly and initial system verification confirmed the ABS plastic frame
was fit for purpose however ongoing tests concluded the loudspeakers employed
were simply not strong enough for the applications proposed. Frequency response
curves examined in section 3.2 underlines this point.
Figure 19 – 3D Printed Speaker Frame

42
For this reason an additional mount attachment was designed. The
specifications of this component were defined by the dimensions of the new
loudspeakers model (which in previous tests conducted at the University of
Bristol proved to provide sufficient sound pressure to allow levitation of
expanded polystyrene beads[87]). This new component was designed to fix
securely to the existing frame to reduce the construction time and costs associated
with manufacturing a brand new set of speaker mounts. CAD drawings provided
by the manufacturers of the BMS 4550 replacement speakers outlined the fixing
points required[88]. These 2D technical drawings can be seen in figure 20.
Additional mounting information can be seen in table 2.
Figure 20 – BMS™ 4550 Technical Drawing
As the overall dimensions of the replacement speaker was smaller than that
of the BG13p speakers only minor design reconsiderations were required.
Table 2 – BMS™ 4550 Mounting Information
These measurements translated to the final design seen in figure 21. Figure
22 further demonstrates how this additional component is fixed to the primary
structure.
Overall Diameter 123 mm
Depth 52 mm
Fixings 2 x M6 180° 76.2 mm Diameter

43
A
The final figure below shows how the final test rig is assembled as well as
demonstrating how the BMS™ 4550 loudspeakers are attached securely to the
frame. Figure 23 also aids understanding of the orientation and general test setup
employed.
Figure 21 – BMS™ 4550 Rig Attachment
Figure 22 – Final Rig Design
Figure 23 – Assembled Test Rig

44
In summary, the components described in this section were designed in
SolidWorks™ and 3D printed using ABS plastic. This components allow the
mounting of both the Visaton™ BG13p and BMS 4550 loudspeakers. These
stands were then in turn, fixed to an aluminium bed with incremental fixings
(which expand the scope of this project).

45
3.2 Electrical Components
The investigation required 2 identical opposing independent signal sources
driven from a signal generator. This signal was then amplified from separate
power supplies to the desired level. Preliminary tests also showed that an
oscilloscope was also paramount to the success of the project as it allowed the
signal at various reference points of the system to be monitored, allowing faults
to be identified efficiently and effectively when matching the signal output at both
loudspeakers.
Hence concluding, the electrical equipment required were as follows:
 2 x Loudspeakers
 2 x Power Amplifiers
 2 x Power Supplies
 Independently Variable Multiple Signal Generator
 Oscilloscope
Loudspeaker
Initially the Visaton™ BG13p were identified as a suitable model of direct
cone radiating loudspeaker for this investigation.
Figure 24 – Visaton™ Frequency Response Curve

46
Generating a mean sound pressure level (SPL) of 92 dB, its specifications
were believed to produce a sufficient amplitude waveform to achieve levitation.
The frequency response curve of this particular model of loudspeaker can be seen
in figure 24[84].
From this graph it is possible to deduce that the SPL attainable at an
operating frequency of 20 kHz is 92 dB. Later sections will show that a
combination of insufficient SPL as well as a non-uniform field (generated by the
BG13p direct cone radiating operating mechanism) did not permit particle
levitation. For this reason an alternative loudspeaker model was researched and
sourced for experiments involving particle manipulation, sorting and levitation.
Previous experiments conducted at the University of Bristol concluded that
reflected single source standing wave levitation was possible utilising the BMS
4500 series compression driven loudspeaker[89]. Compression driven
loudspeakers are known to operate at 10 times the efficiency of cone radiated
sound sources[90] while generating a more uniform waveform. After researching
the 4500 series of BMS™ compression driven speaker the 4550 model was
selected. The frequency response curve for this particular model can be seen in
figure 25[91].
Figure 25 – BMS™ 4550 Frequency Response Curve

47
This graph shows that when driving the speakers at the frequency just
below 20 kHz, it is possible to achieve a SPL of almost 110 dB, compared to the
92dB attainable with the speakers used in the preliminary tests. The far superior
SPL is made possible with a more complex speaker design in which the internal
diaphragm dome is coupled to the exit tube by means of a phase plug. This creates
a pressure ratio thus allowing a much higher SPL to be achieved[92].
Power Amplifier
Power amplifier specification limitations were imposed only by the 40 W
max power capacity of the Visaton™ loudspeakers. The LA50b audio amplifier
was identified as an ideal selection. Relevant information pertaining to the
specification of the Prism Audio power amplifier can be found in table 3.
Table 3 – LA50b Power Amplifier Specification
The amplifier was connected along with 2 quick blow fuses as instructed
on the attached schematic diagram as seen in figure 26[93]. This process was
repeated when assembling the identical circuit of the opposing loudspeaker setup.
Output Power 50W RMS
Frequency Response 5 Hz to 50 kHz
Supply Voltage ±35 Volts
Figure 26 – LA50b Schematic Diagram

48
Power Supply
The Agilent model E3631A,
capable of supplying up to 50 𝑉𝑝𝑝, was
connected to the power amplifier[94].
This voltage supply capacity was more
than sufficient for the needs of the
investigation. The Agilent model
E3631A can be seen in figure 27.
Signal Generator
During the course of this
investigation both the TTi
TGA12104 and the Agilent
33250A signal generators were
used. This was due to erratic and
unreliable results achieved when
vertical manipulation was attempted with the TTi model. In this particular
experiment, static pops occasionally caused levitated particles trapped in the
standing wave field to drop from suspension. This was caused by discontinuities
during phase shift manipulations. A breif investigation on the characterisation of
both signal generators can be found in section 5.4 of this report.
The TTi waveform generator seen in figure 28[95], was used in
conjunction with LabVIEW™ to drive the loudspeakers with an adjustable
dynamic waveform. This waveform can be manipulated in a program designed
by George Skotis. Variables were adapted in this prewritten program for the
desired applications of this investigation.
Figure 27 – Agilent Power Supply Model
E3631A
Figure 28 – TTi TGA12104

49
The Agilent 33250A signal
generator seen in figure 29, replaced
the TTi model in the concluding
tests due the decreased
discontinuities associated with the
produced dynamic waveform when
a phase shift is implemented.
However, this meant the code
previously written for the TTi model was no longer suitable. Phase shift
manipulation was only possible using a manual input, introducing a non-
programmable dynamic waveform.
Oscilloscope
Preliminary tests
stressed the importance of
being able to monitor both
the waveforms produced by
the signal generator as well
as the amplified signals
reaching the speaker
output. Minor adjustments
were then able to be made
to correct for systematic
errors generated in each
component of the test system. The Tektronix™ DPO4014 model seen in figure
30 was employed during the course of this investigation.
In summary, figure 31 shows how the system is connected using BNC
connecters for oscilloscope connections. This diagram identifies oscilloscope
connection points and has been simplified to show only 1 loudspeaker output to
Figure 29 – Agilent 33250A
Figure 30 – Tektronix™ DPO4014 Oscilloscope

50
aid understanding. The full system is realised by mirroring this single output
setup, connecting to the input ports 3 and 4 on the oscilloscope.
1
𝐵𝑁𝐶 𝑆𝑝𝑙𝑖𝑡𝑡𝑒𝑟
21
𝑆𝑖𝑔𝑛𝑎𝑙 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟
𝑂𝑠𝑐𝑖𝑙𝑙𝑜𝑠𝑐𝑜𝑝𝑒
𝑃𝑜𝑤𝑒𝑟 𝑆𝑢𝑝𝑝𝑙𝑦
𝐴𝑚𝑝𝑙𝑖𝑓𝑖𝑒𝑟
+ −
3 4
𝐿𝑜𝑢𝑑𝑠𝑝𝑒𝑎𝑘𝑒𝑟
Figure 31 – Electrical Components Setup

51
3.3 Test of Different Types of Particles
A selection of polystyrene particles ranging in diameter were required to
test the systems volume selective capabilities. It was important that a vast array
of particles, varying in diameter, were subjected to the acoustic standing wave to
ensure thorough system characterisation. Limited previous research made
selecting the particle diameter range difficult. Yoichi Ochiai (University of
Tokyo) advised that the 1.5 mm micro-beads (identical to the ones used in the
paper, “Three-dimensional mid-air acoustic manipulation by ultrasonic phased
arrays”[52]) were most suitable. The list of particles found in table 4 were
identified as most suitable for testing volume variable sorting and system
characterisation[96]–[99].
Table 4 – Volume Selectivity Testing
It was essential that only the volume of each particle varied while the
density remained constant. This allowed the selectivity capacity of the acoustic
device to be tested independently with both density and volume.
Expancel™ was employed in preliminary experiments when visualising
the standing wave field. This was due the clarity in node definition realised. These
particles however, were unsuitable for testing with a dynamic acoustic waveform
as mounds behaved more like a whole entity as opposed to a group of particles.
Disparities in density also made volume variable tests inconclusive.
Particle Diameter Particle Type Density
4 𝑚𝑚 EPS 0.025 g/𝑐𝑚3
3.2 𝑚𝑚 EPS 0.025 g/𝑐𝑚3
2 𝑚𝑚 Micro-Bead 0.025 g/𝑐𝑚3
1.5 𝑚𝑚 Micro-Bead 0.025 g/𝑐𝑚3
100 𝜇𝑚 Expanded Expancel™ 0.025 g/𝑐𝑚3

52
A range of widely available household particles were employed to test the
systems density selectivity capacity. Density variant particles utilised can be seen
in table 5[100][101].
Table 5 – Density Selectivity Testing
Particles Diameter Density
Instant Coffee 300 microns 0.22 g/𝑐𝑚3
Ground Coffee 5 – 400 microns 0.32 g/𝑐𝑚3
Flour 1-100 microns 0.48 g/𝑐𝑚3
Baking Powder / Bicarb Soda 1-80 microns 0.64 g/𝑐𝑚3
Salt 500 microns 0.72 g/𝑐𝑚3
Powdered Sugar (caster) 350 microns 0.80 g/𝑐𝑚3
Granulated Sugar 500 microns 0.85 g/𝑐𝑚3
Baking Soda 1-100 microns 1.12 g/𝑐𝑚3
It was intended groups of particles sharing similar volumes but varying
density would be subjected to the dynamic acoustic waveform and their
respective behavior monitored.
Test particles described in this section will first be subjected to the
waveform to observe susceptibility. If no field affects are observed by certain
particles the density limitations of the system will be deduced and only particles
less than this value will be employed in in subsequent tests.

53
4. Method
Initial tests concerning system characterisation, node separation and field
patterning were conducted utilising the BG13p Visaton™ speakers. Later tests
focusing on static wave particle manipulation and dynamic acoustic field
activated particle separation were realised using an alternative BMS™ 4550
compression driven loudspeaker. The underlying theory behind techniques have
been identified initially. A core system setup was adjusted and adapted to
facilitate the experimental processes required to explore a number of different
avenues and applications of acoustic manipulation. These minor adaptations
have been documented in this section.
4.1 Experimental Theory
4.1.1 Patterning and Static Manipulation
Theoretical node separation is found using equation 4 listed in section 2.2.
A brief explanation can be seen below with 342 𝑚/𝑠 relating to the speed of
sound in air[62].
𝜆
2
Denotes the distance between nodes using the Viston™
loudspeakers at a driving frequency of 20 kHz.
𝑣
𝑓 × 2
=
𝜆
2
342
20000 × 2
= 8.55 × 10−3
𝑚
The same technique was used to find the calculated node separation when
the BMS 4550 loudspeakers were employed at a driving frequency of 17.5 kHz.
A separation of 9.8 × 10−3
𝑚 was found in this case.

54
An additional objective of this project is to validate and build
understanding of previous of examples of static manipulation using a phase shift.
This technique concerns the translation of nodes by implementing a phase in one
of the signal sources. An explanation of this technique can be found in the
concluding paragraphs of section 2.4.
Finally, with the introduction of visible gases to the system it is hoped the
high pressure nodes of the systems can be easily visualised, aiding understanding
of the acoustic standing wave field.
Particle translation was mapped against the phase shift value implemented,
to validate the existing theory that proposes the proportion of distance travelled
by each particle from 1 node to the next, theoretically matched that of the
proportion of completed phase shift from 0° to 360°. It can be deduced from this
model that a phase shift of 180° must translate to a particle displacement of half
the theoretical node separation.
During a static wave manipulation the particles are expected to have a
linear displacement with a phase shift of 0° to 360°. The graph of the particles
expected translated is seen in figure 32.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 50 100 150 200 250 300 350 400
Displacemnt(mm)
Phase Shift (Degrees)
Phase Shift vs Displacement of a 2 mm Particle
Figure 32 – Theoretical Static Phase Shift vs Displacement of a 2 mm Particle

55
4.1.2 Dynamic Manipulation
The theory that particles with a greater volume and or density experience
a higher magnitude of acoustic forces (described by equations 3 and 4) was
employed in attempts to separate 2 contrasting particles. This increased acoustic
force, translates to a faster acceleration of particle to the node location. By tuning
the implemented dynamic waveform, it is hoped to find a particle specific
waveform that allows large particles to cross the anti-node found at 180° after a
full completion of the 0° to 360° phase shift, while minimising small particle
movement to less than halfway between node locations. A full explanation of the
particle behavior will be described in the results section 5.1.4 of this report.
To test this theory a programmable dynamic acoustic waveform replaced
the manual phase shift seen in previous experiments. A program written in
LabVIEW™ (created by George Skotis) allowed the required dynamic waveform
to be generated by adjusting variables concerning the phase shift step increments,
cycle duration, number of cycles and equilibrating period. This directly affected
particles ability to track the nodes movements. Waveform adjustments were
implemented until a particle specific waveform was established.
𝑁𝑜𝑑𝑒𝑖
𝑁𝑜𝑑𝑒𝑖+1
𝑡1
dψ(˚
)
𝑡2𝑡0
180˚
360˚
𝑑𝜓(˚) 𝑇𝑟𝑎𝑚𝑝 𝑇𝑟𝑒𝑠𝑡
𝑃ℎ𝑎𝑠𝑒 𝑆ℎ𝑖𝑓𝑡
𝑆𝑡𝑒𝑝 𝐼𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡𝑠
𝑡1
Figure 33 – LabVIEW™ Waveform Generated

56
Figure 33 demonstrates the degree of control the LabVIEW™ code is
capable of implementing in the generation of the dynamic waveform.
The voltages and frequency parameters are defined by the user within the
LabVIEW™ code. The 𝑇𝑟𝑎𝑚𝑝 period is derived from a combination of the step
increment and 𝑡1 value elected by the user. The desired values are entered into
the user interface. Figure 34 demonstrates the options available to the user. The
variables controlling the master and slave wave voltage and driving frequency
have been highlighted in red. Variables governing the phase step incremental
value have been highlighted in blue while 𝑇𝑟𝑎𝑚𝑝 and 𝑇𝑟𝑒𝑠𝑡 variables are shown in
green.
A range of different waveforms varying in step size and 𝑇𝑟𝑎𝑚𝑝 were tested
systematically with all susceptible test materials and particle behaviour and
displacement was mapped then compared. Eventually validating this acoustic
separation theory by subjecting 2 different particles to the same waveform
simultaneously.
To summarise, the LabVIEW™ suite will be employed in driving the
dynamic waveform with programmable 𝑇𝑟𝑎𝑚𝑝 and 𝑇𝑟𝑒𝑠𝑡 values. An example of
the waveform produced is seen in section 2.5, figure 13. Previous research has
shown the 𝑇𝑟𝑎𝑚𝑝 period is paramount to the separation of particles.
Figure 34 – LabVIEW™ User Interface

57
4.2 Horizontal Setup
4.2.1 System Characterisation and Node Separation
It was key to the success of the project, a strong understanding concerning
the formation of the standing wave pattern and nodes separation was developed.
Initial tests proposed, aimed to assist in visualising the pressure maxima and
minima by studying the behavior of particles effected by these air pressure
variations. These tests also provided an opportunity to compare theoretical values
of node separation with experimental results.
The experimental setup consisted of 2 opposing signal sources fixed
securely to a rigid bed. The Visaton™ loudspeakers were then driven with an in
phase, frequency constant waveform. This waveform was programmed
manually on the TTi signal generator. A glass screen was fixed between the
loudspeakers to support the particles in a constant y position in the waveform.
The positioning of this glass screen seen in figure 35 ensures particles remain in
the area of the wave with the highest intensity pressure wells (produced in the
center of the tweeter cone).
Figure 35 – Glass Screen Support
𝑆𝑖𝑔𝑛𝑎𝑙 𝑀𝑖𝑑𝑝𝑜𝑖𝑛𝑡
𝐺𝑙𝑎𝑠𝑠 𝑆𝑐𝑟𝑒𝑒𝑛
𝑇𝑒𝑠𝑡 𝑃𝑎𝑟𝑡𝑖𝑐𝑙𝑒
𝑆𝑖𝑔𝑛𝑎𝑙 𝑆𝑜𝑢𝑟𝑐𝑒 𝑆𝑒𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛
8.9𝑐𝑚

58
A host of particles ranging in size from 25 𝜇𝑚 to 5 mm (seen previously in
tables 4 & 5 in section 3.3) were scattered randomly on the glass stage and the
acoustic field was activated causing some particles to agglomerate at nodes.
Water droplets suspended on a super hydrophobic surface layer were also
experimented with, using this test setup. Particles that did not react to the
activation of the acoustic field were not suitable for subsequent tests.
Tests aimed at building an understanding regarding the transverse
component of the acoustic force (described in figure 2, section 2.2) and its
associated magnitude were also conducted. This was attempted by constructing
vertical towers of six 1.5 mm particles at node locations where the transverse
component acts as the supporting force of these mini structures. The system
parameters used in this series of experiments can be seen in table 6.
Table 6 – System Characterisation Parameters
Objectives
I. Identify particles susceptible to the standing wave generated by the
acoustic device whilst validating node separation theory
A wide range of particles varying in both volume and density (found in
tables 4 and 5) were subjected to the standing wave acoustic field and
agglomeration effects were observed. Particles susceptible to the
agglomeration from acoustic forces are then identified and utilised
during subsequent tests, which employ more complex techniques.
Parameter Value
Signal Generator Model TTi
Loudspeaker Model Visaton™ BG13p
Loudspeaker Voltage 40-48 Vpp
Frequency 20 kHz
Speaker Separation 8.9 m
Theoretical Node Separation 8.55 mm

59
II. Validate node separation theory
During particle agglomeration, node separation was calculated using
Image J software and compared to theoretical values found in section
4.1.1.
III. Investigate the transverse component of the acoustic force
A brief investigation of the transverse component of acoustic force was
conducted, developing a better understanding of vertical levitation
forces in a horizontal speaker orientation.

60
4.2.2 Speaker Separation Limitations and Field Visualisation
Optimum speaker separation was explored after primary characterisation
of the system was conducted. This separation distance was vital in striking a
balance between minimising detrimental air streaming effects while allowing the
largest possible test area to develop dynamic acoustic sorting waveforms.
Theoretical evaluation predicted the formation of 10 nodes (with a node
separation of 8.55 mm) when driving the loudspeakers at 20 kHz in the primary
system with a speaker separation of 8.9 cm.
Speakers were gradually separated and particle agglomeration was
observed. The source separation limit was considered to be the point where the
standing wave no longer affected particles subjected to the field. It was important
that the stability and uniformity of the acoustic field were monitored closely.
In addition to the schematic diagrams seen in section 4.2.1 a general system
overview has been included in figure 36. This figure shows the 2 individual
circuits connected to their respective opposing loudspeakers, mounted on the
speaker stand, fixed to the aluminum bed.
Figure 36 – Experimental Setup Overview

61
In an attempt to visualise standing wave pressure maxima (nodes) and
minima (anti-nodes), liquid nitrogen and propylene glycol (ECig Vapouriser gas)
were subjected to the acoustic standing wave. It was intended, a coloured gas
substance would provide an effective visual aid, agglomerating to areas of high
pressure. System parameters for these experiments can be found in table 7.
Table 7 – Field Visualisation and Source Separation Limitation Parameters
Objectives
I. Investigate speaker separation limitations and associated air
streaming effects
Speakers were gradually separated until the standing wave no longer
affected the particles supported on the glass substrate. It is hoped a fine
balance between maximum separation distance and streaming effects
can be struck.
II. Visualisation of the standing wave field
Adopting techniques already employed at the University of Bristol and
the University of Tokyo, it is hoped the standing wave field can be
visualised using a visible gas. In these experiments node positons
produce areas of thicker smoke contrasting with anti-nodes with a
sparse smoke distribution. Dry ice and propylene glycol have been used
to demonstrate this novel technique.
Parameter Value
Loudspeaker Model Visaton™ BG13p
Loudspeaker Voltage 40-48 Vpp
Frequency 20 kHz

62
4.2.3 Static Wave Particle Manipulation
The system setup required for static waveform particle manipulation was
identical to that described previously however field activation was no longer the
cause of particle manipulation. Node translation was realised by implementing a
manual or programmable phase shift of 1 of the signal sources. The theory
concerning the underlying concept of the transport of these trapped particles is
explained in figure 9 found in section 2.4 of this report.
It was important to ensure both waveforms were perfectly in phase as
implemented previously. This functionality was controlled under the offset wave
function menu in the TTi signal generator. Rudimentary implementations of a
phase shift were conducted by manually cycling through the phase parameter on
the signal generator input. This phase shift method then progressed to a remote
programmable operation in LabVIEW™ however the majority of static
manipulation was achieved using a manual input. In each case the position of the
particles at 90° intervals were recorded.
This exploration into the capabilities of manipulation was very useful in
developing an understanding of LabVIEW™ and its utilities in relation to
programming a dynamic acoustic wave (these skills were then put into practice
in section 4.2.4).
System parameters employed during this stage of testing can be seen in
table 7.
Table 8 – Static Waveform Acoustic Manipulation Parameters
Parameter Value
Loudspeaker Model BMS 4550
Loudspeaker Voltage 40 Vpp
Frequency 17.5 kHz

63
Objective
I. Achieve static wave acoustic manipulation with a range of particles
relating phase change value to distance translated
A gradual phase shift of 0° to 360° will be implemented to a range of
trapped particles using a variety of phase increments. Particle
displacement from the original node location will be measured and
mapped along with the induced phase change increment, validating
existing acoustic theory.

64
4.2.4 Dynamic Acoustic Field Activated Particle Separation
After a fundamental understanding of static waveform manipulation
behavior was developed while experimenting with phase change techniques
involved in section 4.2.3, the focus of the investigation progressed to the more
complex task of separating and sorting contrasting particles. While techniques
discussed so far only validate existing acoustic theory, this technique hopes to
achieve dynamic acoustic field activated particle separation on a mm scale for the
first time.
Table 9 shows the general system parameters when investigating suitable
dynamic waveforms.
Table 9 – Dynamic Waveform Parameters
Table 10 shows the range parameters the dynamic waveform was cycled
through while attempting find a particle specific waveform.
Table 10 – Step Size & Ramp Period Parameters
Parameter Value
Frequency 17.5 kHz
Step Size 𝑻 𝒓𝒂𝒎𝒑 (s)
5° 14.4 7.2 3.6
10° 7.2 3.6 1.8
20° 3.6 1.8 0.9
40° 1.8 0.9 0.45
45° 1.8 0.9 0.45
60° 1.8 0.9 0.45
90° 1.8 0.9 0.45
120° 1.8 0.9 0.45

65
The operation of the LabVIEW™ program and how to achieve these
waveform parameters from system variable is described in section 4.1.2.
Past research concluded the most influential variable on particle separation
was the 𝑇𝑟𝑎𝑚𝑝 period taken to cycle from 0° to 360° however, the effects of
varying the phase step increment size have also been explored[55]. A 𝑇𝑟𝑎𝑚𝑝
period of 1 second was used in all of the dynamic waveform tests as this value
was found to be less significant in previous research conducted by George Skotis.
Objectives
I. Identify a dynamic acoustic waveform that manipulates a selection
of particles of varying properties discordantly
Employing a program developed in LabVIEW™, it is hoped a particle
specific dynamic waveform can be generated that manipulates some
particles while other remain unaffected. A table comparing particles
behavior will then be drawn up in order to identify suitable waveforms
to achieve separation.
II. Implement acoustic separation using 2 particles with discordant
translation when simultaneously subjected to a dynamic wave
Ultimately the project aims to implement acoustic separation using
comparative data collected during objective 1. The sorting capabilities
of the system will then be investigated.

66
4.3 Vertical Setup
4.2.1 Acoustic Levitation and System Characterisation
The test setup required for vertical levitation was simply constructed by
adjusting the previous rig design employed so far and rotating it 90°. The
aluminiun bed was clamped to an upright frame to ensure rigidity. This vertical
test setup is seen in figure 37.
A range of different sized polystyrene beads were carefully inserted into
the standing wave pattern using an implement designed to generate minimal
acoustic impedance. Separation distance between 2 signal sources was
experimented with until the limits of the acoustic system were deduced. The node
separation during this separation have been touched upon during this test.
Figure 37 – Acoustic Levitation Vertical Test Setup

67
The parameters employed during this set of experiments can be seen in
table 11.
Table 11 – Acoustic Levitation System Parameters
Objective
I. Implement levitation with a range of particles and discern max
speaker separation
It is hoped by characterising the acoustic levitation device with regards
to system parameters, stable levitation can be achieved with a selection
of particles. Node separation will also be calculated during this
experiment.
Parameter Value
Frequency 17.5 kHz

68
4.2.2 Static and Dynamic Wave Acoustic Manipulation
Initial tests investigating vertical levitation did not require the glass screen
(as seen in figure 37) however manipulation in this orientation was only possible
with the introduction of the glass plate in an identical position to that of horizontal
tests. Manual and computational (static manipulation) phase change techniques
employed during tests concerning manipulation in a horizontal orientation, were
repeated and particle behavior was mapped.
Test results raised concerns regarding irregularities in the signal produced
by the TTi signal generator. Discontinuities in the TTi signal caused
unpredictable particle behavior. It was apparent a brief investigation was required
to explain these inconsistences in particle behavior caused by static pops in the
speakers output.
The Agilent signal generator replaced the TTi model for the penultimate
experiments as it showed minimal output discontinuity when a phase shift was
implemented. However, a LabVIEW™ program was not available at this stage in
the project therefore a manual phase shift was required. In this case the manual
signal generated, attempted to mimic suitable waveforms found previously. Table
12 shows the system parameters used in attempting static and dynamic wave
manipulations in mid-air.
Table 12 – Static and Dynamic Wave Acoustic Manipulation Parameters
Parameter Value
Signal Generator Model TTi then Agilent
Frequency 17.5 kHz

69
Objectives
I. Demonstrate static wave particle manipulation
Using manual input on the TTi signal generator it is hoped manipulation
can be realised in the y axis. This in similar to tests conducted in section
4.2.3.
II. Investigate discontinuities in the waveform produced by the TTi
model
By comparing outputs from both the Agilent and TTi signal generators
on an oscilloscope the investigation aims to discover the cause of the
static pops dislodging particles form their nodes.
III. Implementing a dynamic acoustic wave through the manual input
on the Agilent signal generator, mimicking LabVIEW™
waveforms
The final aim of this investigation is to implement the dynamic acoustic
wave seen in section 4.2.4 in an attempt to separate discordant particles
in vertical levitation. As LabVIEW™ cannot be used with this specific
signal generator at this point in time, best efforts have been made to
match the suitable dynamic waveform identified in previous
experiments using a manual input.
In summary, a series of horizontal oriented tests, investigating system
characteristics, node separation and field patterning (conducted with the Viston™
loudspeakers) were described (including system parameters). The BMS model
then replaced the Visaton™ model when attempting static wave particle
manipulation and dynamic acoustic field activated particle separation. This
loudspeaker models then went on to facilitate similar tests in the vertical domain.
System parameters used in this round of testing have also been documented.

70
5. Results & Discussion
Initial test results investigating the limitations in the acoustic device as
well as techniques used in trying to visualise the field will be documented first
and foremost. This will be followed by a section exploring particle translation
behavior. More complex techniques involving dynamic wave implementation and
its associated sorting capabilities will then be investigated culminating in
experimental results of attempting acoustic sorting in a vertical levitation setup.
5.1 Horizontal Setup
5.1.1 System Characterisation and Node Separation
Primary tests explored the limitations of the acoustic device in terms of the
kinds of particles susceptible to the standing wave pattern. The outcome of these
tests can be seen in table 13.
Table 13 – Susceptible Properties Table
Particle Diameter Density
Cooshtie Micro beads 1.5 mm 0.025 g/𝑐𝑚3
Large Beads 3-5 mm 0.025 g/𝑐𝑚3
920 DE 80 d30 (Expandcel Medium) 55-85 microns 0.03 g/𝑐𝑚3
092 DET 100 d25 (Expandcel Big) 80-120 microns 0.025 g/𝑐𝑚3
461 DE 20 d70 (Expandcel Small) 15-25 microns 0.07 g/𝑐𝑚3
Instant Coffee 300 microns 0.22 g/𝑐𝑚3
Ground Coffee 5 – 400 microns 0.32 g/𝑐𝑚3
Flour 1-100 microns 0.48 g/𝑐𝑚3
Baking Powder / Bicarb Soda 1-80 microns 0.64 g/𝑐𝑚3
Salt 500 microns 0.72 g/𝑐𝑚3
Powdered Sugar (caster) 350 microns 0.80 g/𝑐𝑚3
Granulated Sugar 500 microns 0.85 g/𝑐𝑚3
Baking Soda 1-100 microns 1.12 g/𝑐𝑚3
Table entries highlighted in red show particles that displayed no
susceptibility to the acoustic field. The entry shown in yellow was seen to display

71
minimal agglomeration whereas the entries shown in green are seen to fully
translate to node locations. It was therefore deduced that the system is able to
manipulate particles under 0.07 g/𝑐𝑚3
in density. As each particle varied in
volume marginally and perceived agglomeration is subjective, it was difficult to
document with great certainty when the particles were no longer affected by the
standing wave.
Expandcel Large 3-5 mm EPS
Expandcel MediumExpandcel Small
1.5 mm Micro-beads 2 mm Micro-beads
Figure 38 – Susceptible Properties Agglomerating

72
Figure 38 shows a selection of particles and their translation behaviour
when subjected to the standing wave. The particles, identified in each case, were
observed to agglomerate at pressure nodes.
Figure 39 shows a range of particles that were found to be too dense for
the acoustic device used in this investigation.
It was proposed a super hydrophobic layer supporting water droplets
would negate the friction force preventing agglomeration. The results of this test
is seen in figure 40.
Garlic Baking Powder
Bicarbonate of Soda Flour
Figure 39 – Unsuitable Properties Subjected to the Standing Wave
Figure 40 – Super Hydrophobic Coating with Water

73
In this test the standing wave did not produce sufficient acoustic force to
manipulate the water droplets suspended on the substrate. It is believed a better
quality super hydrophobic coating could potentially lead to improved results.
A series of tests also aimed at validating existing theory regarding node
separation and location were also conducted. Image processing techniques were
used to evaluate node separation in experimental results. These were then
compared against the 8.55 mm value for a 20 kHz driving frequency calculated
in section 4.1.1. Figure 40 shows 1.5 mm micro-bead particles agglomerating to
nodes in the standing wave field. A measurement of the node separation was taken
between each particle and an average was calculated. A scale has been included
using the glass substrate dimension as a reference point. 𝑁𝑖 denotes each node in
question. The average distance was found to be 8.6 mm which is agreeable to the
8.55 mm found theoretically.
The transverse component of the acoustic force is investigated by
constructing miniature 6 bead towers, seen in figure 41. These towers are
supported in the y direction by this force.
Figure 41 – Node Separation
8.47 𝑚𝑚8.70 𝑚𝑚 8.47 𝑚𝑚8.73 𝑚𝑚
𝑁1 𝑁6𝑁2 𝑁3 𝑁4 𝑁5
1 𝑐𝑚
8.86 𝑚𝑚

74
Although tests were able to validate the existing theory pertaining to the
transverse component of acoustic force, the magnitude was not of a sufficient
level to permit particle levitation in a horizontal orientation.
Figure 42 – Transverse Component of Acoustic Force on 6 Bead 1.5 mm Towers

75
5.1.2 Speaker Separation Limitations and Field Visualisation
Separation limitations of the speakers were also evaluated. This was done
by gradually increasing the distance between speakers, until the standing wave
no longer affected the particles on the glass substrate. Fixings on the aluminiun
test bed allowed for increments of 3 cm.
Operating at full speaker capacity it is possible to see from figure 43 that
the maximum permitted speaker separation using 1.5 mm micro-beads is 23.3 cm.
The diagram on the right shows particles showing minimum agglomeration 26.3
cm fixing.
Although this maximum separation of 23.3 cm would generate more nodes
than the original 8.9 cm separation (useful when attempting manipulation and
separation), air streaming was introduced. This was attributed to the voltage
levels required for the produced wave to generate adequate forces for particle
agglomeration over the entirety of the waveform. This phenomena was
detrimental to particle manipulation near sound sources, as a mean flow of air
forced the particles away from the loudspeakers source. It was for this reason the
majority of subsequent horizontal tests were completed using a separation value
of 8.9 cm with a peak to peak voltage of about 40 volts. This provided the balance
of adequate acoustic force and minimising streaming effects required.
23.3 𝑐𝑚 26.3 𝑐𝑚
Figure 43 – Speaker Separation Limitations

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