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

复杂的流体是我们日常生活的一部分——这些是颗粒的悬浮液，可能是固体也可能是液体。像牛奶和蛋黄酱这样的食品，像保湿霜这样的保健产品和像油漆这样的普通化学产品都是颗粒悬浮物的例子。除此之外，工业过程通常包括一个阶段，其中材料是颗粒的悬浮液，即使最终产品不是这种形式：药物加工是一个例子，其中结晶用于从溶液中提取药物，产生药物成分的结晶颗粒。目前的研究被非常小的纳米粒子所吸引：纳米粒子，以及我们能用它们做什么；其中许多也将以液体悬浮液的形式生产。在某些情况下，颗粒可以聚集在一起形成聚集体。这当然是许多纳米粒子因为静电效应而粘在一起的一个问题。这也给刚刚提到的结晶过程带来了困难，结晶过程的目的是生产许多相同大小的晶体。在其他情况下，这种聚集可能是有意的，并被设计成在材料中创造结构，赋予它独特的特性，比如强度或接近固体的行为——一些凝胶就是这样的。在工业规模上，沥青质聚集体通常在石油加工过程中形成，造成堵塞问题。无论原因是什么，我们都希望能够更多地了解已经发生的粒子和聚集。当超声波（一种比人能听到的高音高的声波）穿过悬浮在其中的颗粒或液滴时，颗粒/液滴通过向其他方向发送一些声波而使声波散射。当阳光被空气中的水滴散射时，也会产生非常相似的彩虹。超声波是纵波，通过粒子的散射也可以将一些波转化为其他波类型，即热波和横波。这些过程从超声波中吸收能量，从而使其振幅减小。通过测量超声波通过悬浮液的衰减（振幅损失）和波速，我们可以发现颗粒的浓度，它们有多大，或者它们的一些特性，例如密度。我们知道当粒子靠近时，当它们聚集在一起时，衰减是不同的。但是，当悬浮液中有聚集体时，我们目前还没有办法计算出粒子的性质，或者它们的浓度或大小，也不能说聚集体有多大，或者粒子在其中的排列有多紧密。我们需要的是一种方法来理解当粒子聚集在一起时，声波是如何通过悬浮液传播的。目前我们有一个模型（对发生的事情的数学描述）用于分散良好的悬浮液，但没有用于聚集的悬浮液，也没有用于几种不同类型的颗粒的悬浮液。在这个项目中，我们将通过使用数学模型、计算模拟和实验测量来研究这个问题。该项目的每一个部分都将研究声波如何与颗粒团或不同类型的颗粒相互作用。我们最终想要实现的是一种测量和使用数据来描述悬浮液的方法，告诉我们粒度分布、骨料尺寸、骨料结构或其他属性。该项目的成果将是模型和方法，可用于表征颗粒悬浮物。这将使超声波能够在广泛的工业环境中作为一种过程监控技术而充满信心地使用。

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.