It has been recently reported in experiments that Drag Reducing Polymers (DRPs) significantly affect the distribution of red blood cells in blood capillaries. Physiologically, this has been shown to positively affect survival rates of rats subjected to severe loss of blood. Since capillary flow is laminar, the multiphase flow problem can be studied via low-Reynolds number hydrodynamics. Our work aims to understand the dynamics of deformable vesicles under flow, in both a Newtonain solvent and a polymer solution.

We report studies on dynamics of deformable spherical vesicles under flow. The vesicle is modeled as an elastic membrane surrounding a pocket of fluid. The membrane forces are calculated based on a finite element model and the hydrodynamic forces are calculated using the General Geometry Ewald-like Method (GGEM) (J.P. Hernandez-Ortiz et al., Physical Review Letters, 98, 140602, 2007). The viscoelastic fluid is modeled as a dispersion of FENE-P dumbbells.

The new model is first tested by observing the variation of the deformability parameter of a single spherical vesicle as a function of time for different non-dimensionalized shear rates (ηγa/Eh) and the obtained results are compared with earlier numerical and theoretical results.

We then report dynamics of both single vesicles and pairs of vesicles under shear flow. For single vesicles, we study the effect of viscoelasticity on the measured deformation parameter, and cross-stream migration velocity. For vesicle pairs, we observe trajectories of colliding vesicles to understand the effect of viscoelasticity on collision dynamics.