The Rheology of Non-Dilute Vesicle Suspensions

The extra particle shear stress and normal stresses in non-dilute vesicle suspensions are computed by direct numerical simulations of the suspension undergoing simple shear and/or pure extension. Each vesicle is modeled as a droplet enclosed by a lipid bilayer that by itself is a two-dimensional incompressible fluid with bending modulus. A Loop-subdivision based finite element method is used to model the membrane's bending deformation, and the flow is solved by a Stokes flow boundary-integral equation method, with the constraint of surface incompressibility strictly enforced. We show that the viscosity ratio between the fluid inside and outside of the membrane is the critical factor for the suspension rheology. Through a mechanism similar to that for an isolated vesicle in a simple shear flow, the viscosity ratio acts by affecting the vesicles' orientation angles, which in turn determine their resistance to the flow. The nondimensional shear viscosity however increases rapidly with volume fraction in a non-dilute suspension, and we discuss the physical mechanism for this effect by examining the membrane stresses during a vesicle-vesicle collision. Finally, we demonstrate that the reduced volume has a very important effect on the rheology of non-dilute vesicle suspensions.