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We present a technique for obtaining an effective packing fraction fordiscontinuous shear thickening suspensions near a critical point. It uses ameasurable quantity that diverges at the critical point -- in this case theinverse of the shear rate $\dot\gamma_c^{-1}$ at the onset of discontinuousshear thickening -- as a proxy for packing fraction $\phi$. We obtain aneffective packing fraction for cornstarch and water by fitting$\dot\gamma_c^{-1}(\phi)$, then invert the function to obtain$\phi_{eff}(\dot\gamma_c)$. We further include the dependence of$\dot\gamma_c^{-1}$ on the rheometer gap $d$ to obtain the function$\phi_{eff}(\dot\gamma_c,d)$. This effective packing fraction $\phi_{eff}$ hasbetter resolution near the critical point than the raw measured packingfraction $\phi$ by as much as an order of magnitude. Furthermore, $\phi_{eff}$normalized by the critical packing fraction $\phi_c$ can be used to comparerheology data for cornstarch and water suspensions from different labenvironments with different temperature and humidity. This technique can bestraightforwardly generalized to improve resolution in any system with adiverging quantity near a critical point.

An effective packing fraction for better resolution near the critical point of shear thickening suspensions