When a plane ultrasonic wave (a sound wave at higher frequency 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. Since these sorts of materials (suspensions of particles) have many uses e.g. foods, healthcare products, agrochemicals, drug delivery systems, a way of measuring their properties is a crucial element of a production process and of great importance in a number of industries. In order to understand the measurements we make, we need to use a model, a set of equations and calculations which tell us how the properties of the particles and fluid affect the loss of amplitude and speed of the wave. The model we use has two parts: a multiple scattering theory, and a model for the scattering from a single particle. For some time, the model we used has been limited because it made some approximations about the two other wave types (the thermal and shear waves) which are produced at the particles; it assumed that those waves die away in a very short distance, and do not have any effect on the particles nearby. Although they do die away in a very short distance, they can affect the neighbouring particles when the suspension is very concentrated (i.e. there are a lot of particles in a small space). The thermal and shear waves themselves can be scattered by particles nearby and may be partly converted back into a compressional wave (an ultrasonic wave). This means we did not lose as much of the energy from the compressional wave as we thought. The process of wave conversion and re-conversion is referred to as multi-mode scattering and for many years, its effect has been ignored because we did not have a suitable model to calculate it. Last year, a group of researchers at Le Havre (France), published a new version of the multiple scattering theory, which does include this multi-mode scattering, over 40 years after the original multiple scattering model was published. This is a useful development, but at the moment the model exists as a set of rather abstract mathematical equations which include many terms which we do not yet know how to calculate. What we propose to do is to transform this model into a form which enables online ultrasonic monitoring in a pipe. We will work out which parts of those equations make the most difference to the measured ultrasonic speed and attenuation (energy loss) in typical suspensions. We will develop some new models for scattering by a single particle so that we can work out how much energy is converted between wave modes. These models will take the form of sets of equations which will be solved by computer (numerical models), and also some forms which can be written directly in mathematical notation (analytical models). To demonstrate that the models developed in the project are valid, experimental measurements will be made of the attenuation and wave speed in suspensions at relatively high concentrations 10-30% by volume, and for a range of particle sizes. The outcomes of the project will be a model in a form which can be used in online ultrasonic instrumentation. This will enable ultrasonics to be used with confidence as a process monitoring technique in a wide range of industrial contexts.