The transition from frictional to lubricated flow of a dense suspension of
non-Brownian particles is studied. The pertinent parameter characterizing this
transition is the Leighton number Le=σηsγ˙,
which represents the ratio of lubrication to frictional forces. The Leighton
number Le defines a critical shear rate below which no steady flow without
localization exists. In the frictional regime the shear flow is localized. The
lubricated regime is not simply viscous: the ratio of shear to normal stresses
remains constant, as in the frictional regime; moreover the velocity profile
has a single universal form in both frictional and lubricated regimes. Finally,
a discrepancy between local and global measurements of viscosity is identified,
which suggests inhomogeneity of the material under flow.Comment: Accepted for publication by Physical Review Letters (december 2004