Numerical predictions of the viscosity of non Brownian suspensions in the semidilute regime

The viscosity of a non-Brownian suspension in simple shear cannot be theoretically predicted in the limit of the semidilute approximation, since it depends on the initial configuration. Batchelor and Green [J. Fluid Mech. 56, 401-427 (1972)] proved that the suspension viscosity can be expressed in power series of the solid volume fraction and the second order coefficient, b, resulted undetermined. On the contrary, experimentally Pasquino [J. Rheol. 52, 1369-1384 (2008)] obtained a single steady state and estimated the value of b. We here numerically show that laminar mixing is able to induce a unique steady state also in the semidilute regime, since it is effective to break the closed orbits that may occur in these suspensions. To this end, we investigated the effect of the initial conditions on the steady state starting from seven different configurations ranging from the fully uniform and ordered one to the agglomerated one, passing through different random distributions. We, finally, numerically predict, via Stokesian dynamics, the coefficient b for the viscosity of a monolayer of rigid spherical particles suspended in a Newtonian fluid, undergoing simple shear flow obtaining b = 6.5 in a good agreement with both the data of Pasquino and the theoretical predictions obtained under the hypothesis of absence of closed orbits [Wilson and Davis J. Fluid. Mech. 421, 339-367 (2000)]. It is also shown that the Cox-Merz rule is fulfilled by the suspensions that we have numerically studied, i.e., up to a volume fraction of about 0.17. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3630943]