  We investigate in detail the problem of confined pressure-driven laminar flow
of neutrally buoyant non-Brownian suspensions using a frictional rheology based
on the recent proposal of Boyer et al., 2011. The friction coefficient and
solid volume fraction are taken as functions of the dimensionless viscous
number I defined as the ratio between the fluid shear stress and the particle
normal stress. We clarify the contributions of the contact and hydrodynamic
interactions on the evolution of the friction coefficient between the dilute
and dense regimes reducing the phenomenological constitutive description to
three physical parameters. We also propose an extension of this constitutive
law from the flowing regime to the fully jammed state. We obtain an analytical
solution of the fully-developed flow in channel and pipe for the frictional
suspension rheology. The result can be transposed to dry granular flow upon
appropriate redefinition of the dimensionless number I. The predictions are in
excellent agreement with available experimental results, when using the values
of the constitutive parameters obtained independently from stress-controlled
rheological measurements. In particular, the frictional rheology correctly
predicts the transition from Poiseuille to plug flow and the associated
particles migration with the increase of the entrance solid volume fraction. We
numerically solve for the axial development of the flow from the inlet of the
channel/pipe toward the fully-developed state. The available experimental data
are in good agreement with our predictions. The solution of the axial
development of the flow provides a quantitative estimation of the entrance
length effect in pipe for suspensions. A analytical expression for development
length is shown to encapsulate the numerical solution in the entire range of
flow conditions from dilute to dense.
