Shear-induced migration of rigid spheres in a Couette flow

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.