Giant deviation of a relaxation time from generalized Newtonian theory in discontinuous shear thickening suspensions

We investigated the transient relaxation of a discontinuous shear thickening (DST) suspension of cornstarch in water. We performed two types of relaxation experiments starting from a steady shear in a parallel-plate rheometer, followed either by stopping the top plate rotation and measuring the transient torque relaxation or by removing the torque on the plate and measuring the transient rotation of the tool. We found that at low effective weight fraction ϕ_eff<58.8 ±0.4 % , the suspensions exhibited a relaxation behavior consistent with a generalized Newtonian fluid in which the relaxation is determined by the steady-state relationship between shear stress and shear rate. However, for larger weight fraction 58.8 %<ϕ_eff<61.0 % , near the liquid-solid transition ϕ_c=61.0 ±0.7 % , we found relaxation behaviors qualitatively and quantitatively different from the generalized Newtonian model. The regime where the relaxation was inconsistent with the generalized Newtonian model was the same where we found positive normal stress during relaxation, and in some cases we found an oscillatory response, suggestive of a solidlike structure consisting of a system-spanning contact network of particles. This regime also corresponds to the same packing fraction range where we consistently found discontinuous shear thickening in rate-controlled, steady-state measurements. The relaxation time in this range scales with the inverse of the critical shear rate at the onset of shear thickening, which may correspond to a contact relaxation time for nearby particles in the structure to flow away from each other. In this range, the relaxation time was the same in both stress- and rate-controlled relaxation experiments, indicating the relaxation time is more intrinsic than an effective viscosity in this range and is needed in addition to the steady-state viscosity function to describe transient flows. The discrepancy between the measured relaxation times and the generalized Newtonian prediction was found to be as large as four orders of magnitude, and extrapolations diverge in the limit as ϕ_eff→ϕ_c as the generalized Newtonian prediction approaches 0. This quantitative discrepancy indicates the relaxation is not controlled by the dissipative terms in the constitutive relation. At the highest weight fractions, the relaxation time scales were measured to be on the order of ∼1 s. The fact that this time scale is resolvable by the naked eye may be important to understanding some of the dynamic phenomenon commonly observed in cornstarch and water suspensions. We also showed that using the critical shear rate γ_˙c at the onset of shear thickening to characterize the effective weight fraction ϕ_eff can more precisely characterize material properties near the critical point ϕ_c, allowing us to resolve this transition so close to ϕ_c. This conversion to ϕ_eff can also be used to compare experiments done in other laboratories or under different temperature and humidity conditions on a consistent ϕ_eff scale at our reference temperature and humidity environment.