Updated: May 2, 2019

Mixing Sauces: A Viscosity Blending Model for Shear Thinning Fluids  

Kentaro Nagasawa1,*, Takayuki Suzuki1, Ryohei Seto2, Masato Okada1, Yonghao Yue1,3,*,
1The University of Tokyo     2Kyoto University     3Aoyama Gakuin University
*Authors contributed equally.    

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. 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.


Physical simulation, viscoplasticity, nonlinear blending, material point method, shear thinning fluids


We thank anonymous reviewers, Yuki Yoshida, and Hirotaka Sakamoto for insightful suggestions and discussions, and Louisa Andersen for her help in producing the video. This work was supported in part by JSPS Grant-in-Aid for Young Scientists (A) 17H04682, and JSPS Grant-in-Aid for Scientific Research on Innovative Areas 18H05001.

ACM Transactions on Graphics (Proc. of SIGGRAPH 2019), 38(4), 95:1-17, 2019

Paper: PDF(35.4MB)
Video: youtube video , High res MP4(235.4MB)


        author = {Nagasawa, Kentaro and Suzuki, Takayuki and Seto, Ryohei and 
                  Okada, Masato and Yue, Yonghao},
        title = {Mixing Sauces: A Viscosity Blending Model for Shear Thinning Fluids},
        journal = {ACM Trans. Graph.},
        volume = {38},
        number = {4},
        month = jul,
        year = {2019},
        pages = {95:1--17},
        articleno = {95},
        numpages = {17},