Non-linear rheology of melted cheddar cheese

The rheology of melted cheese is a fundamental parameter in the preparation of cheese for consumer foods, but remains poorly understood. We show that the linear and non-linear viscoelasticity of melted cheddar cheese can be captured by a fractional linear viscoelastic model and a strain-softening damping function, respectively. However, we show that a time-strain separable constitutive equation of the K-BKZ type using these two components fails to capture the dramatic strain stiffening observed in the steady shear response of melted cheddar cheese. We show that this stiffening effect arises due to the rapid thermally-induced phase separation, dehydration, and solidification of melted cheddar cheese, and that incorporating an appropriate mutation function in the K-BKZ equation to account for this effect results in the complete description of the non-linear shear rheology of melted cheddar cheese. We thus elucidate the origins of the solid-like behavior of melted cheese commonly seen under non-linear deformations, and provide broad insight into the modeling of the non-linear rheology of soft matter systems that exhibit temporal mutations in mechanical properties.