Mesohydrodynamics of membrane suspensions

Doi–Ohta rheological model of immiscible blends is extended by replacing the fluid interface with an elastic membrane. A symmetric tensor characterizing the in-membrane deformations joins the surface area and the orientation tensor (used in the Doi–Ohta theory) to provide morphological state variables. The governing equations of the model are solved numerically and the morphological and rheological predictions are presented. As an illustration, we regard the model as a first step in mesoscopic rheological modeling of suspensions of red blood cells. The material properties of the membrane enclosing the red blood cells, that are inferred from rheology, are indeed found to be close to the ones seen in direct experimental measurements. A more realistic model of human blood has to include additional morphological state variables describing larger structures (in particular whole red blood cells).