The dynamics of a non-dilute vesicle suspension in a simple shear flow

Abstract

AbstractWe simulate multivesicle suspensions undergoing simple shear deformation by using the Stokes-flow boundary-integral equation method to quantify the effect of vesicle–vesicle interactions on the microstructure and rheology of the suspension. The binary collisions between vesicles are found to cause a vesicle’s instantaneous inclination angle to deviate considerably from its stationary tank-treading angle. The strength of the binary interaction becomes significant when the distance between centroids is less than three vesicle radii, which is consistent with observations from experiments. Vesicle interactions in the suspension delay the transition from tank-treading (TT) to trembling (TR)/tumbling (TU), which can be explained by the augmentation of the inclination angles in a binary collision when the viscosity ratio $\lambda $ is close to its critical value. Accordingly, in a non-dilute suspension the global minimum of the particle shear viscosity occurs at higher values of $\lambda $ due to the close correlation between the vesicle’s orientation and particle shear stress. In the high-$\lambda $ regime, collisions in a suspension disrupt the TU cycles of individual vesicles, resulting in intermittent TU/TR motions. In addition, an entangled state is observed to occur for an interacting vesicle pair in the TR/TU regime, where the centroids are aligned approximately parallel to the vorticity direction and rotates about it. The persistence of this close-range interaction results in two distinct peaks in the pair distribution of vesicles. However, their existence is limited to suspensions at low volume fraction, as they are otherwise disrupted by the three-body interactions that occur more frequently in a dense suspension.