Torque scaling at primary and secondary bifurcations in a Taylor–Couette flow of suspensions

Abstract

The Taylor–Couette flow of non-colloidal, neutrally buoyant spherical particle suspensions in the $\phi =0\,\%-28\,\%$ concentration range and (17–250) Reynolds number ( $\mathcal {R})$ range is studied using synchronized flow visualization and torque measurements. Both methods are applied in ramp-up/down (acceleration/deceleration of the inner cylinder) experiments to detect the various flow structure states and bifurcation natures, their critical conditions and their lifetime in $\mathcal {R}$ range. Torque measurement allows us to discuss the evolution of the (pseudo) Nusselt number, $\mathcal {N}$ , and friction coefficient with $\mathcal {R}$ or alternatively the Taylor number, Ta. Flow visualization brings additional information on the unsteady dynamics of flow states. For concentrations higher than $\phi =6\,\%$ , two unsteady (spiral vortex flow, wavy vortex flow) and one steady (Taylor vortex flow) flow state are observed in both ramp-up/down experiments. Hysteretic behaviour is reported for some primary, secondary and tertiary bifurcations, which are thus found to be subcritical. A critical concentration is observed at $\phi =15\,\%$ for the range of $\mathcal {R}$ at which spiral vortex flow is encountered. Characteristic frequencies of unsteady flow state (spiral vortex flow, wavy vortex flow) for different suspension concentrations are evaluated. Finally, three hydrodynamic concentration subregimes are identified for the first time, with their distinct sets of concentration-dependent critical conditions, torque scaling exponents and friction coefficients.

Taylor–Couette flow of hard-sphere suspensions: overview of current understanding

“…As Re increased, Kang and Mirbod found that the primary transition away from CCF occurred at the same effective Re for both particle sizes, and the particles had no impact on the primary instability's critical conditions compared to pure Newtonian fluid. This behaviour conflicts with the particle-induced destabilization seen in the experimental studies discussed in the previous section [1,3,5,9]. The discrepancies between their results and the reported experimental findings were ascribed to the neglect of particle inertia and inertial migration in their simulations.…”

“…For the TVF-WTV transition, the slope change was not distinct. Additional torque measurements were conducted by Moazzen et al [9] in a rheometer-based device. This study focused on characterizing the torque behaviour in different flow states and analysing the unsteady features of NAF structures.…”

“…Based on the observed scaling exponents, Moazzen et al [9] concluded that in TVF and WTV states, the presence of particles reduces the transverse momentum transfer for φ < 0.15 and φ < 0.12, respectively, and this behaviour is reversed for higher φ. This interpretation does not agree with the enhanced radial transport in TVF with increasing particle loading for φ ≤ 0.15 reported by Ramesh et al based on their PIV measurements.…”

“…However, assessing the effect of particle-scale inertia on rheology is challenging as inertial effects grow with length scale; finite microscale inertia may be associated with large macroscopic inertia, which introduces instability and may lead to secondary flow and turbulence. Recent studies on inertial instabilities of particle-laden Taylor-Couette flow (TCF) have shown that particles play a fundamental role, and the observed dynamical behaviour cannot yet be explained by effective medium approaches [1][2][3][4][5][6][7][8][9][10].…”

Counter-rotating suspension Taylor–Couette flow: pattern transition, flow multiplicity and the spectral evolution

“…2007); see also a recent work (Moazzen et al. 2022) on torque scaling at primary and secondary bifurcations. A preliminary analysis of our torque data at indicates that the above scaling is likely to hold beyond the secondary bifurcation at .…”