Viscosity measurements of glycerol reveal the misalignment in parallel-plate rheometers

We consider the viscosity measurement of pure glycerol in a parallel-plate rheometer over time. Due to the hygroscopic nature of glycerol, it spontaneously absorbs water vapor from the atmosphere through the outer edge of the rheometer, leading to a transient decrease in the measured viscosity. A combination of diffusion and advection drive the transport of the dissolved water through the rheometer, resulting in regions of less-viscous fluid. The measured viscosity then represents an integration of the shear stresses on the plate device. We find that the rate of decrease of the measured viscosity is a complex function of the gap thickness and angular velocity, as well as the vapor flux at the outer edge. The decrease in viscosity is a nonlinear function of the angular velocity. For small angular velocities the dynamics are diffusive, and the water only slowly proceeds inward from the outer edge of the glycerol, resulting in high concentrations in the outermost region. Because this low viscosity fluid is confined to a relatively small region, the decrease in measured viscosity is slow for this case. For cases with modest angular velocities, the recirculating advection acts to pull some of the water inwards from the outer boundary, steepening the gradient of concentration at the outer edge and increasing the flux of water vapor into the system, leading to a faster decrease in viscosity up to a point. For very fast angular velocities, much of the water is pulled all the way to the center of the rheometer, where the effect on the measured viscosity is relatively less (since the majority of the torque develops at the outer edge). Nevertheless, we see a deviation from these behaviors for very small gap heights (which should be purely diffusive), in which the measured viscosity drops much faster than expected. We propose that this is due to plate misalignment of the rheometer, and we use computational fluid dynamics simulations to support this hypothesis.