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
$1000< Re^\prime < 6000$
.
