Effects of inertia and turbulence on rheological measurements of neutrally buoyant suspensions

Abstract

For low-Reynolds number shear-flows of neutrally-buoyant suspensions, the shear stress is often modeled using an effective viscosity that depends only on the solid fraction. As the Reynolds number (Re) is increased and inertia becomes important, the effective viscosity also depends on the Reynolds number itself. The current experiments measure the torque for flows of neutrallybuoyant particles in a coaxial-cylinder rheometer for solid fractions, φ, from 10% to 50% and Reynolds numbers based on particle diameter from 2 to 1,000. For experiments for Reynolds of O(10) and solid fractions less than 30%, the effective viscosity increases with Reynolds number, in good agreement with recent numerical simulations found in the literature. At higher solid fractions over the same range of Re, the results show a decrease in torque with shear rate. For Reynolds numbers greater than 100 and lower solids concentrations, the effective viscosity continues to increase with Reynolds number. However, based on comparisons with pure fluid measurements the increase in the measured effective viscosity results from the transition to turbulence. The particles augment the turbulence by increasing the magnitude of the measured torques and causing the flow to transition at lower Reynolds numbers. For the highest solid fractions, the measurements show a significant increase in the magnitude of the torques, but the effective viscosity is independent of Reynolds number.

Momentum balance and stresses in a suspension of spherical particles in a plane Couette flow

“…However, here we did not find any particle induced transitional behaviour as our large-scale Reynolds numbers are small. The range of large-scale Reynolds numbers we consider here are well below the critical Reynolds numbers for the transition to turbulence found by Linares et al 33 in coaxial…”

“…25 , for a larger range of particle Reynolds numbers. For a suspension of particles in a coaxial Couette flow and over a wide wide range of 3 < Re p < 100, Linares et al 33 measured a monotonic increase of the effective viscosity with particle Reynolds number, but only for φ ≤ 0.3. For higher volume fractions, the effective viscosity revealed either a non-monotonic behaviour or a decreasing trend with increasing Re p .…”

“…While volume-averaged suspension balance models 7,11 and most numerical simulations of suspensions 13,[30][31][32] are focused on the Stokes flow, more recent particle-resolved numerical simulations have explored the inertial effects on stresses in suspensions and the dynamics of the particles. The inertia of particles have been shown to increase the effective viscosity of the suspension 25,[27][28][29]33 . Picano et al 25 attributed the shear-thickening behaviour of suspensions at higher Reynolds numbers to the creation of shadow regions in the suspension at high fluid inertia that contributes to higher effective volume fractions.…”

“…However, in their study particle and wall shear stresses were not significantly affected by the increase in Re p . Based on laboratory measurements in a coaxial-cylinder rheometer, Linares et al 33 discussed that at sufficiently large Reynolds numbers a transition to turbulence leads to an increase in the effective viscosity. Even before this transition, they observed an increase in the effective viscosity with increasing Reynolds number for volume fractions φ ≤ 0.3.…”

Modulation of the regeneration cycle by neutrally buoyant finite-size particles

“…Recent experiments from Majji et al (2016) have shown that particles do not have a significant impact on the transition path in Taylor-Couette flow, if the particle concentration is low and the particle size is relatively small compared to the Couette gap. With larger particles (8 times smaller than the Couette gap), Linares-Guerrero et al (2017) have shown that particles do not change the transition threshold of a cylindrical turbulent Couette flow at 10% volumetric concentration. Consistent with this finding, flow statistics performed on moderately concentrated turbulent plane Couette flow (slightly above the transition threshold), have revealed that there is no significant difference between single-and two-phase flows at equivalent effective Reynolds number (Wang et al 2017).…”