Scaling in shear thickening suspensions with multidirectional flows*

Recently, we proposed a universal crossover scaling theory to describe shear thickening suspensions. This scaling formulation suggests that the suspension viscosity can be tuned by changing the particle shape, size, roughness or solvent properties which in turn changes the scaling variables. Here, we show that orthogonal perturbations to the flows, which are an effective method for tuning the thickening of suspensions without altering the properties of the suspension particles, can also be folded into this universal scaling picture.  Specifically, we show that the effect of adding in orthogonal shear perturbations (OSP) can be incorporated by simply altering the fraction of frictional contacts to include a term that decreases with the ratio of the OSP flow to primary flow shear rates. In addition, the stress dependent fraction of frictional contacts requires a small but significant modification in order to ensure data collapse. These results demonstrate the power, importance and the generality of such universal scaling formulations, and illustrate how this framework can be modified to incorporate other complex flow fields.