Effective packing fraction for better resolution near the critical point of shear thickening suspensions.

We present a technique for obtaining an effective packing fraction for discontinuous shear thickening suspensions near a critical point. It uses a measurable quantity that diverges at the critical point-in this case the inverse of the shear rate (gamma) over dot(c)(-1) at the onset of discontinuous shear thickening-as a proxy for packing fraction phi. We obtain an effective packing fraction for cornstarch and water by fitting (gamma)over dot(c)(-1)(phi) and then invert the function to obtain phi(eff) ((gamma)over dot(c)). We further include the dependence of (gamma)over dot(c)(-1) on the rheometer gap d to obtain the function phi(eff) ((gamma)over dot(c), d). This effective packing fraction phi(eff) has better resolution near the critical point than the raw measured packing fraction phi by as much as an order of magnitude. Furthermore, phi(eff) normalized by the critical packing fraction phi(c) can be used to compare rheology data for cornstarch and water suspensions from different laboratory environments with different temperature and humidity. This technique can be straightforwardly generalized to improve resolution in any system with a diverging quantity near a critical point.