Rheological measurements and transition to turbulence for moderate Reynolds number inertial suspensions

Abstract

Particulate flows at moderate particle Reynolds numbers are important in critical engineering and geological applications. This experimental study explores neutrally buoyant suspensions in an outer-rotating coaxial rheometer for solid fractions, $\phi$, from 0.1 to 0.5, and particle Reynolds number, $Re$, from 0.5 to 800, covering laminar, transitional and turbulent regimes; $Re$ is defined in terms of the square of the particle diameter and the shear rate. For $0.1 < \phi < 0.4$ and $0.5 < Re <10$, the direct torque measurements normalised by the laminar flow torque, $M/M_{lam}$, are independent of $Re$, but depend on $\phi$. For the same range of $\phi$ and for $10< Re<100$, the normalised torques depend on both $\phi$ and $Re$, and show an increasing dependence on $Re$. As $Re$ increases, the flow transitions to turbulence. Small particles delay the turbulent transition for $\phi \leqslant 0.3$, while large particles augment the transition. A modified Reynolds number, $Re^\prime$, that depends linearly on the particle diameter and the maximum velocity, $U_{o}$, is introduced for both laminar and turbulent flows and shows a better correlation of the results as compared with $Re$. For $\phi = 50\,\%$, the normalised torque minus the torque at zero rotational speed is nearly independent of $Re^\prime$. Rheological models based on $Re^\prime$ and the Krieger–Dougherty relative viscosity are proposed in the laminar regime for $10< Re^\prime <500$; in the turbulent regime, a correlation is proposed in terms of $Re^\prime$ and $\phi$ for $1000< Re^\prime < 6000$.