Dynamics and rheology of a confined suspension of vesicles (a model for red blood cells) are studied numerically in two dimensions by using an immersed boundary lattice Boltzmann method. We pay particular attention to the link between the spatiotemporal organization and the rheology of the suspension. Besides confinement, we analyze the effect of concentration of the suspension, $\varphi$ (defined as the area fraction occupied by the vesicles in the simulation domain), as well as the viscosity contrast $\lambda$ (defined as the ratio between the viscosity of the fluid inside the vesicles, ${\eta }_{\mathrm{int}}$, and that of the suspending fluid, ${\eta }_{\mathrm{ext}}$). The hydrodynamic interaction between two vesicles is shown to play a key role in determining the spatial organization. For $\lambda =1$, the pair of vesicles settles into an equilibrium state with constant interdistance, which is regulated by the confinement. The equilibrium interdistance increases with the gap between walls, following a linear relationship. However, no stable equilibrium interdistance between two tumbling vesicles is observed for $\lambda =10$. A quite ordered suspension is observed concomitant with the existence of an equilibrium interdistance between a vesicle pair. However, a disordered suspension prevails when no pair equilibrium interdistance exists, as occurs for tumbling vesicles. We then analyze the rheology, focusing on the effective viscosity, denoted as $\eta$, as well as on normalized viscosity, defined as $\left[\eta \right]=(\eta -{\eta }_{\mathrm{ext}})/\left({\eta }_{\mathrm{ext}}\varphi \right)$. Ordering of the suspension is accompanied by a nonmonotonic behavior of $\left[\eta \right]$ with $\varphi$, while $\eta$ exhibits plateaus. The nonmonotonic behavior of $\left[\eta \right]$ is suppressed when a disordered pattern prevails.

• Received 20 June 2016

DOI:https://doi.org/10.1103/PhysRevFluids.2.103101