Ultrasonic propagation in complex media: correlated spatial distributions and multiple dispersed phases

Lead Research Organisation: University of Manchester
Department Name: Mathematics

Abstract

Complex fluids are part of our every-day life - these are suspensions of particles, which may be solid or liquid. Foods such as milk and mayonnaise, health-care products like moisturising creams and common chemical products like paints are all examples of particle suspensions. As well as these, industrial processes often include a stage where the material is a suspension of particles, even if the final product is not in this form: drug processing is one example, where crystallisation is used to extract the drug from solution, producing crystalline particles of the pharmaceutical ingredient. Current research is fascinated by the very small: nanoparticles, and what we might be able to do with them; many of these will also be produced as a suspension in a liquid.
In some cases, the particles can clump together to form aggregates. This is certainly a problem with many nanoparticles which stick together because of electrostatic effects. It also causes difficulties for the crystallisation process just mentioned, where the aim is to produce lots of crystals of the same size. In other cases, the aggregation may be intended, and designed to create structure in the material, to give it distinct properties, such as strength or near-solid-like behaviour - some gels are like this. On an industrial scale, aggregates of asphaltene commonly form in petroleum processing, causing problems with clogging. Whatever the cause, we would like to be able to know more about the particles and the aggregation which has occurred.
When an ultrasonic wave (a sound wave at higher pitch than humans can hear) travels through a fluid which has particles or droplets suspended in it, the particles/droplets scatter the wave by sending some of it in other directions. A very similar effect produces a rainbow when sunlight is scattered by water droplets in the air. With ultrasonic waves, which are compressional waves, scattering by the particles can also convert some of the wave into other wave types, namely thermal and shear waves. These processes take energy away from the ultrasonic wave which causes a reduction in its amplitude. By measuring the attenuation (loss in amplitude) and the wave speed for an ultrasonic wave travelling through the suspensions, we can find out the concentration of particles, how big they are, or something about their properties e.g. their density. We know that the attenuation is different when the particles are close together, when they are aggregated. But we currently do not have a way to work out the properties of the particles, or their concentration or size, when there are aggregates in the suspension, nor can we say how big the aggregates are, or how closely packed the particles are in them.
What we need is a way to understand how the sound waves travel through suspensions when the particles are clumped together. At the moment we have a model (a mathematical description of what happens) for well-dispersed suspensions, but not for aggregated ones, nor for suspensions with several different types of particles. In this project we will study this problem by using mathematical models, by using computational simulations and by making experimental measurements. Each of these parts to the project will investigate how sound waves interact with the clumps of particles, or the different types of particles. What we want to achieve in the end is a way to make measurements and use the data to characterise the suspension, to tell us the particle size distribution, the aggregate size, the aggregate structure or other properties. The outcomes of the project will be models and methods that can be used to characterise particle suspensions. This will enable ultrasonics to be used with confidence as a process monitoring technique in a wide range of industrial contexts.

Publications

10 25 50
 
Description 1) We have answered the question as to what can be measured about a random medium by using backscattered waves, emitted from and received at a single source. That is, measuring waves that are directly reflected back is one of the simplest possible measurements for a complex medium. Yet it has previously not been possible, with theory alone, to answer what properties of a random medium can be predicted by measuring just reflected waves. We were able to make progress by introducing a mixture of theory and machine learning techniques. An associated paper is currently under review.
2) We deduced the effective wavenumber (characterising propagation in a medium) associated with, and reflection from, a material comprising multiple types of particles (multi-species). These expressions have been derived for the first time for densely packed particles. We demonstrated failures in the alternatives used in the literature, published a paper on the subject, and are promoting the work by giving talks and visiting other research groups.
Exploitation Route We will, as the project develops, aim to incorporate the analytical results, validated by numerical simulations and experimental work, into tools for making useful predictions in a variety of industries. Our work on using machine learning also serves as a prototype to demonstrate, to industry and a wider audience, what future devices could be designed that make use of theory and machine learning.
Sectors Aerospace, Defence and Marine,Agriculture, Food and Drink,Chemicals,Education,Pharmaceuticals and Medical Biotechnology

 
Description We have written and made publicly available software to exhibit wave scattering phenomena. The software produces videos of wave motion, which we are using to promote physics and mathematics to a wider audience.
First Year Of Impact 2017
 
Title Backscattering from randomly placed Dirichlet particles 
Description A simulated data set of backscattered waves, governed by the 2D wave equation, from randomly placed Dirichlet particles. The particles are circular with 0.2 < radius < 2.0 and 1% < volume fraction < 20%. The incident wave is of the form ei k (x - xR - t) where the particles are placed in the halfspace x>0 and the backscattering is emitted and received at (xR, 0) with xR = -10.0. The data named bunny and bunnytest is for incident waves with 0 < k < 1 (where the term e- i k t factors out). The data named train and test is for incident waves of the form e0.1(x - xR - t)^2, with 9.5 < t < 98. 
Type Of Material Database/Collection of data 
Year Produced 2018 
Provided To Others? Yes  
Impact With this data, we were able to use machine learning algorithms to determine, for the first time, what can be measured from a random particulate medium from just direct backscattered waves. 
URL https://zenodo.org/record/1126642#.WqKh5nXFKCg
 
Description Collaborative links between Manchester, Leeds and Loughborough 
Organisation Loughborough University
Department School of Electronic, Electrical and Systems Engineering
Country United Kingdom 
Sector Academic/University 
PI Contribution This is a collaborative project whereby we will input the mathematoical modelling.
Collaborator Contribution This is a collaborative project whereby Loughborough will offer the computational work and Leeds will input experimental effort.
Impact None yet
Start Year 2015
 
Description Collaborative links between Manchester, Leeds and Loughborough 
Organisation University of Leeds
Department School of Food Science and Nutrition Leeds
Country United Kingdom 
Sector Academic/University 
PI Contribution This is a collaborative project whereby we will input the mathematoical modelling.
Collaborator Contribution This is a collaborative project whereby Loughborough will offer the computational work and Leeds will input experimental effort.
Impact None yet
Start Year 2015
 
Title EffectiveWaves.jl 
Description A package to calculate the effective waves travelling in materials comprised of randomly distributed particles or inclusions. 
Type Of Technology Software 
Year Produced 2017 
Open Source License? Yes  
Impact We used this software to show counter intuitive results of multiple scattering involving multi-species particles. 
 
Title MultipleScattering-Mathematica 
Description A Mathematica package to calculate exact multiple scattering, in time and frequency, according to the 2D wave equation. 
Type Of Technology Software 
Year Produced 2017 
Open Source License? Yes  
Impact This is an educational software, which easily allows users to place circular particles, specify incident waves and create graphics that demonstrate multiple scattering. 
 
Title MultipleScattering.jl 
Description A Julia library for simulating, processing, and plotting multiple scattering of acoustic waves. 
Type Of Technology Software 
Year Produced 2018 
Open Source License? Yes  
Impact This software is a high performance software. It has allowed us to do a large number of multiple scattering simulations, which has lead to new insight about what properties of particulate materials can be predicted from backscattered waves. 
URL https://arxiv.org/abs/1801.05490
 
Description Outreach talks: Science Showdown - Manchester - 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Undergraduate students
Results and Impact Summary: Isn't science awesome? But are you convinced your field is the most awesome of them all? Do you save lives, discover truly fundamental properties of nature, master logic and reasoning, create mind-blowing technology, understand how the Universe works, or something along those lines? All the willing speakers will be asked to give a short talk of exactly p minutes (yes, 3m 14s), not exceeding 2 slides to talk about something super interesting in science. This doesn't have to be directly related to your own projects and props are always encouraged! Impact: the audience of students and general public voted on the best talks. The later discussions indicated that many greatly changed their views of the role of physics and mathematics in our society.
Year(s) Of Engagement Activity 2017
URL https://www.eventbrite.co.uk/d/united-kingdom--manchester/mcrc-science-showdown/