Michael McPhail

A number of popular cereal products are made using a manufacturing process known as extrusion. There is a stage during this process in which some of the liquid component of the cereal mixture changes phase into a gas. The subsequent evolution of gas will affect the thermodynamic and rheological properties of the mixture. The mechanisms at play include the transfer of mass, momentum, and heat, as well as the change in phase of the components and the change in volume of the product. The interactions between these mechanisms will determine the final shape and texture of the product.

The difficulty in simulating extrusion comes from the high degree of coupling between the physical processes. The evolution of every component in the system, from the size of the vapour bubbles that form to the temperature of the product, is dependent on the evolution of just about every other component. One way to approach this problem is to first write down a model for the fully-coupled system and then systematically examine the impact of weakening the coupling between the components using ideas from asymptotic analysis.

A simulation tool for extrusion can be used to aid experimentation and product development by providing a relatively cheap way of testing ideas. For example, when trying to design a product with a different shape, nozzle shapes must be built and tested in a lab. If the nozzle shape is not ideal, a new one must be built until the desired cereal shape is achieved. With the aid of simulations, the effect of different nozzle shapes on the shape of the product can be tested theoretically, informing the experimentalist of a good starting design. Such a tool may also be useful in identifying potential issues, such as the formation of slugs in the extruder.

We are using a model for extrusion in which we approximate the gas-liquid cereal mixture with a single compressible fluid. The compressible flow equations are closed by assuming an appropriate constitutive law. Conventional constitutive laws used to close the compressible flow equations assume some functional relationship between the pressure, density, and sometimes temperature. In order to account for the complexity of the evolving gas within the cereal mixture, we will close the flow equations using model derived from an understanding of the ongoing physics on the length scale of a bubble. We have investigated the dynamics of bubble evolution in a cereal mixture and constructed a model relating bubble size, and therefore the volume fraction of gas in our mixture, to the other state variables in our system. We are currently investigating the evolution of a compressible fluid undergoing extrusion by using a range of simpler constitutive laws.

*This work is part of a collaboration between Nestlé Research Orbe and the InFoMM CDT at the Mathematical Institute, University of Oxford.*

Michael McPhail is a DPhil student in Cohort two of the EPSRC InFoMM CDT at the Mathematical Institute.