Industrial Mathematics Group

Mathematics for cereal manufacture

When processed in an extruder, how does a mixture of raw ingredients expand in order to take the shape and texture you find in your cereal bowl? If instead we wanted a more exotic shape (e.g. π,), what shape would we need to make the end of the cereal extruder? Intuition, experience and experimentation are currently the best tools available to engineers who wish to trial new ideas. In the figure we see Nestlé's Alphabet cereal. Developing innovative new shapes and optimizing cereal texture in this way requires significant investment of time and in equipment, alongside a lot of trial and error. The physical mechanisms that control the expansion of a cereal mixture during extrusion are well known. We are interested in how one mechanism (e.g. the vaporisation of moisture into gas bubbles) may impact the others (e.g. the rheology of the cereal as moisture is depleted), and how these complex interactions affect the final product. We aim to use our model of this process to generate the capacity to perform predictive simulations of cereal extrusion, in collaboration with Nestlé. We are also interested in the "inverse problem" of calculating how to set up an extruder if the final properties we want our cereal to possess are prescribed. A tool like this would reduce the number of physical trials that must be carried out in the development stage, and hopefully lead to greater efficiency in the production phase. In the Billion-dollar breakfast cereal industry, mathematical models of cereal extrusion will help producers better satisfy the wants of customers (i.e. by producing "π-bites").

Below we show a simulation of the extrusion of a Mickey Mouse shaped cereal.