Making cereal: extrusion of a viscous compressible fluid.

Extrusion of viscous bubbly mixtures is an important stage in the manufacture of a range of products including: plastic foams, pet food and breakfast cereals. The complicated dynamics associated with multiphase flows, and the presence of a free boundary make numerical simulations of these processes difficult. By taking an average over the phases, the mixture can be treated as a single-phase compressible fluid coupled to a model describing the microscale dynamics. Using ideas from lubrication theory, we are able to derive a reduced model for the free expansion of a compressible fluid analogous to the Trouton model for an incompressible fluid. The result is a much simpler set of equations, which retains all of the necessary physics. In the limit of small surface tension and small Reynolds number, this model reduces to a single ordinary differential equation whose solution we can write analytically.