Universal correlation between jamming distance and shear-thickening strength in dense colloidal suspensions*

Tuning shear-thickening in dense suspensions is of great interest owing to its applications in soft robotics, impact armor and industrial manufacturing. Shear-thickening strength ($\beta )$, measured from slope of viscosity-stress flow curve, estimates how fast the suspension viscosity increases with applied shear rate. In this work, we show that prior knowledge of suspension jamming point ($\varphi_{\mathrm{J}})$ will solely predict the $\beta $ parameter in spherically-symmetric colloidal suspensions. In this study, we use smooth and rough poly(methyl methacrylate) colloids with diameters ranging from 0.98 -- 1.82 microns. We found that the sheared rough suspensions shear-thicken earlier and has a lower $\varphi_{\mathrm{J}}$ compared to their smooth counterparts. We incorporate experimentally obtained scalings of the contact number deficit with respect to the distance from jamming ($\Delta \varphi )$ into the mean--field description proposed by Wyarts {\&} Cates (\textit{PRL, 2014}) to predict the flow curves and compare them with experimental results. Our results suggests that there is a universal behavior in the change of $\beta $ parameter from strong (\textgreater 0.9) to weak (\textless 0.7) mode below the value of $\Delta \varphi $/$\varphi_{\mathrm{J}}=$0.1, which is supported by experiments and simulations of similar Brownian systems from the literature.