Bubble modelling (Paul Prentice)

Cavitation bubbles are challenging to investigate experimentally. As such, the scientific literature is rather  dominated  by  simulations  of  bubble  dynamics,  via   a  number  of  models,  with  various adaptations to account for a wide range of conditions (including ultrasonic driving, hydrodynamic environments and stabilising shells – in the case of contrast agent microbubble).

The  most established  model  is  based  on  the Rayleigh-Plesset (R-P) equation. This  is  a  non-linear ordinary differential equation relating bubble dynamics to liquid properties and pressure terms.

Students  taking  this  project  will  solve  the  R-P  equation  (in  Matlab,  or  equivalent).  Options  for investigation include parametric analysis (of the influence of viscosity, for example), non-linear bubble response,  or  comparison  to  experimental  observations   (undertaken  in  the  Cavitation   Research Laboratory).

Learning outcomes:

•    Bubble theory & simulations

•    Parametric analysis

•    Non-linear bubble dynamics

•    Coding experience

•    Cavitation and applications

Further reading:

The Acoustic Bubble, T. G. Leighton (Academic London, 1994) Lauterborn & Kurz, Physics of bubble oscillations, Rep. Prog. Phys., 73 106501, 2010

Measuring non-linear pressure waveforms (Paul Prentice)

Measurement  of  a   linear  ultrasonic  signal  is  relatively  trivial.   Detection  is  undertaken  with  an appropriate hydrophone, at the relevant position relative to the source. Application of a calibration coefficient – at a single value of frequency – to the voltage output from the hydrophone, retrieves the pressure measurements.

A non-linear waveform, however, will have content across multiple frequency values. Assessment of the  non-linear  content  is  good  scientific  practice  and  critical  for  many  applications,  with  tissue absorption being highly frequency dependent, for example.

This  project  will  explore  concepts  and  techniques  for  handling  non-linear  pressure  waveforms. Experimental measurements will be provided, along with complex calibration data (supplied by the National  Physical  Laboratory) for the detecting  hydrophone. Students are expected to assess the frequency content within the  measurements  and  investigate  how  the  calibration  data  should  be applied.

Learning outcomes:

•    An understanding non-linear ultrasound

•    Assessing frequency content

•    Hydrophone calibration and uncertainties

•    Hydrophone deconvolution

•    Appropriate reporting of nonlinear measurements

Relevant papers:

[1]  L. Yusuf,  M.  Symes &  P.  Prentice  2021. Characterising the cavitation activity generated  by an ultrasonic horn at varying tip-vibration amplitudes. Ultrasonics Sonochemistry, 70 105273.

[2] J. H. Song, A. Moldovan & P. Prentice 2019. Non-linear acoustic emissions from therapeutically driven contrast agent microbubbles. Ultrasound in Medicine & Biology 45(8), pp 2188-2204.

Simulating effective frequency response (Andrew Feeney)

Relevant Research Paper: Dixon, S., Kang, L., Ginestier, M., Wells, C., Rowlands, G. and Feeney, A., 2017. The electro-mechanical behaviour of flexural ultrasonic transducers. Applied Physics Letters, 110(22), p.223502.

Ultrasonic sensors are embedded in a wide range of industrial measurement systems, for non- destructive evaluation, flow measurement for gases and liquids, and proximity sensing for robotic or automotive applications. Ultrasonic sensors for industrial applications are often capacitive or piezoelectric micromachined ultrasonic transducers (cMUT and pMUT respectively). However, more recently there has been a drive to optimise the performance of the flexural ultrasonic transducer (FUT), a configuration which does not require acoustic impedance matching to its environment.

Typically, such flexural-based ultrasonic transducers rely on the bending of a compliant plate, whose vibration modes are generated through an excitation voltage to a piezoelectric material attached to this  plate. They do  not  operate on the conventional through-thickness or radial  mode  principles, instead being analogous to an edge-clamped plate, where the vibration response of this plate can be assumed to dominate, thus governing the dynamics of the transducer. To this end, Leissa’stheory of vibrating plates has direct relevance, where fundamental and higher order modes can be predicted with confidence.

In this project, your challenge is to define suitable design and fabrication parameters for a 40 kHz flexural ultrasonic transducer for proximity measurement in ambient air. Secondly, in away you see fit on MATLAB or otherwise, you will find away to simulate the effective frequency response of the transducer for an arbitrary excitation, using the governing relationships associated with edge-clamped plates, where a clear distinction between resonant and off-resonance responses is demonstrated.

Learning outcomes:

•    An introduction to measurement / sensing with ultrasonic transducers

•    Design and fabrication considerations for industrial ultrasonic sensors

•    Appropriate use of finite element methods

•    Extension of Leissa’s theory to ultrasonic sensors using MATLAB or equivalent

•    Understand implications for deployment in different industrial environments