A combined approach towards the understanding of mass transfer in two-phase flow: The integration of numerical modelling with MRI

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Many industrial processes require effective contact between two different liquids, or between a liquid and a gas. These processes include treatment of waste water and fermentation of alcoholic drinks. When these systems are stirred, the result is not a uniform mixture, but a very large number of small bubbles or droplets dispersed through the liquid. The droplets involved are not all the same, and have different sizes, velocities and chemical compositions. This makes it very difficult to accurately measure the important properties of the system. It is also very difficult to predict mathematically how such a system will behave.The proposed investigation has two main aims. The first is to make accurate experimental measurements of droplets within a liquid. The second is to use these measurements to develop mathematical models that can describe the system.Experimental Techniques:Droplets dispersed in a liquid undergo many different processes. Currents within the fluid can cause the droplets to follow convoluted paths. In the course of this flow through the liquid, they can join together to form large droplets, break up to form smaller ones, and their chemical composition can change through diffusion. Experimental measurement of all these processes is not an easy task: even simply visually tracing the path of a single droplet can be impossible if the liquids involved are not transparent.Magnetic Resonance Imaging (MRI) is a technique that involves tagging individual molecules by altering how they behave in a magnetic field. These molecules can then be accurately located in time and space, allowing us to determine the size, velocity and composition of moving droplets. MRI has never before been applied to a system such as this.Mathematical Modelling:The behaviour of large numbers of interacting droplets is described mathematically by using Population Balance Equations (PBEs). These equations can require vast computational power to solve, especially in complicated systems where the behaviour is dependent on many variables: size, shape, concentration profiles etc. Monte Carlo methods are a particular mathematical technique that allow us to solve these equations quickly and efficiently and predict (given the right model parameters) how the droplet-liquid system will behave.Combing Experiments and Models:The crucial aim of our research is to combine our experimental measurements and mathematical analysis. This will enable us to decide which factors have an important, noticeable effect on the system, and which can be ignored. Thus, prediction of the behaviour of complicated systems will be simplified and industrial processes will become more effective and efficient