Engineer takes first step to developing rigorous numerical model to predict the shape and size of drops and flows occurring within micro-fluidic devices

When we apply cream to our skin, take a liquid medicine or eat a delicious food, we probably don’t consider what it takes to make products of the right consistency at the point of manufacture. Particularly when the products are made up of liquid components that don’t mix, such as oil and water, and their consistency depends on the size of the drops of one liquid dispersed in the other.

Engineers like Birmingham’s Mark Simmons, Professor of Fluid Mechanics, are continually working to improve these sorts of industrial processes so they are more efficient and therefore cheaper, as well as more environmentally friendly. Mark and his colleagues have taken a significant step towards greater efficacy by harnessing the power of computation and combining it with new numerical methods. They hope their approach will enable the necessary size of liquid drops, with the appropriate flow, to be determined without experimentation.

The research on this is set out in the paper ‘Simulation of immiscible liquid-liquid flows in complex microchannel geometries using a front-tracking scheme.’ Funded by the EPSRC MEMPHIS (Multi-scale Exploration of MultiPhase Physics In FlowS) programme, the paper was published in the journal Microfluidics and Nanofluidics in late 2018 and recently won the College’s Paper of the Month Award.

‘This paper is the first attempt to develop a rigorous numerical model able to predict the shape and size of drops and flows occurring within micro-fluidic devices,’ explains Mark, who carried out the research with colleagues from Imperial College, London.

‘If you think about a lot of products you use on your body, such as drugs or skin creams, they are normally multiphase (made up of oil, water and solids), and these phases don’t mix. So what you want with, for example, a drug delivery system, is to make a small drop that might contain the active ingredient in an emulsion. But its size and composition are critical, to ensure accurate dosage. So what our research is looking at is a way of being able to produce the size of drops we need without doing experiments for new formulations.  That’s why models are needed.’

Development of the model is challenging due to the scale of the problem where you need to model accurately the interfaces – that is, the surface and shape of the drops as they are formed. 

‘For the first time we have used a front-tracking method that enables us to solve this problem without any of the traditional stability issues,’ says Mark, who is Head of the School of Chemical Engineering. ‘The ultimate aim is to simulate the formation of drops with different compositions, and to solve the problem when the fluid properties are changing, for example when you are forming encapsulates for drug delivery’.

The breakthrough has been made possible because of computational power and development of new numerical methods, he explains.

‘For the first time, this particular method has been applied to this type of problem. And also we have done some experiments to ensure the results are right. The ultimate goal is the simulation, with the computer, without doing experiments. In other words, we can go straight from the computer to the industrial process. It’s a realistic goal, but this is the first step. Industrially, the ultimate advantage is the reduction of time to market: you wouldn’t have to spend ages doing trials before going to market.’