Mixing sauces

The materials around us usually exist as mixtures of constituents, each constituent with possibly a different elasto-viscoplastic property. How can we describe the material property of such a mixture is the core question of this paper. We propose a nonlinear blending model that can capture intriguing flowing behaviors that can differ from that of the individual constituents (Fig. 1). We used a laboratory device, rheometer, to measure the flowing properties of various fluid-like foods, and found that an elastic Herschel-Bulkley model has nice agreements with the measured data even for the mixtures of these foods. We then constructed a blending model such that it qualitatively agrees with the measurements and is closed in the parameter space of the elastic Herschel-Bulkley model. We provide validations through comparisons between the measured and estimated properties using our model, and comparisons between simulated examples and captured footages. We show the utility of our model for producing interesting behaviors of various mixtures.