The rheology of a capsule suspension in two-dimensional confined Poiseuille flow is studied numerically using an immersed-boundary lattice Boltzmann method. The effects of capsule volume fraction ϕ and bending stiffness Eb on the rheology of the suspension are investigated first. The apparent viscosity does not monotonically increase with ϕ: the variation curve can be divided into four flow regimes. In each regime, there is a distinct equilibrium spatial configuration. The overall lateral position of the capsules is directly connected with the apparent viscosity. Then, we propose to investigate the effect of inertia on the capsule configuration in dilute cases and the capsule transport in concentrated cases. For dilute cases, phase diagrams of flow regimes on the (ϕ, Eb) plane are plotted. It is found that, as the Reynolds number (Re) increases, the range of values for regime I, with a single-line configuration, reduces, while the range for regime II (transition configuration) increases. It is highly correlated with the equilibrium lateral position of a single capsule. For even larger Re, the range for regime IV (random configuration) increases rapidly and dominates because the larger inertia makes the arrangement more random. For concentrated cases, we observe that the optimal volume fraction, at which the transport of capsules is a maximum, increases with Re. This study may help to understand the collective behavior of capsules in Poiseuille flows.
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