Shear-induced gradient diffusivity of a red blood cell suspension: effects of cell dynamics from tumbling to tank-treading.

Hydrodynamic interactions generate a diffusive motion in particulates in a shear flow, which plays seminal roles in overall particulate rheology and its microstructure. Here we investigate the shear induced diffusion in a red-blood cell (RBC) suspension using a numerical simulation resolving individual motion and deformation of RBCs. The non-spherical resting shape of RBCs gives rise to qualitatively different regimes of cell dynamics in a shear flow such as tank-treading, breathing, tumbling and swinging, depending on the cell flexibility determined by the elastic capillary number. We show that the transition from tumbling to tank-treading causes a reduction in the gradient diffusivity. The diffusivity is computed using a continuum approach from the evolution of a randomly packed cell-layer width with time as well as by the dynamic structure factor of the suspension. Both approaches, although operationally different, match and show that for intermediate capillary numbers RBCs cease tumbling accompanied by a drop in the coefficient of gradient diffusivity. A further increase of capillary number increases the diffusivity due to increased deformation. The effects of bending modulus and viscosity ratio variations are also briefly investigated. The computed shear induced diffusivity was compared with values in the literature. Apart from its effects in margination of cells in blood flow and use in medical diagnostics, the phenomenon broadly offers important insights into suspensions of deformable particles with non-spherical equilibrium shapes, which also could play a critical role in using particle flexibility for applications such as label free separation or material processing.

Mechanisms of spontaneous chain formation and subsequent microstructural evolution in shear-driven strongly confined drop monolayers.

It was experimentally demonstrated by Migler and his collaborators [Phys. Rev. Lett., 2001, 86, 1023; Langmuir, 2003, 19, 8667] that a strongly confined drop monolayer sheared between two parallel plates can spontaneously develop a flow-oriented drop-chain morphology. Here we show that the formation of the chain-like microstructure is driven by far-field Hele-Shaw quadrupolar interactions between drops, and that drop spacing within chains is controlled by the effective drop repulsion associated with the existence of confinement-induced reversing streamlines, i.e., the swapping trajectory effect. Using direct numerical simulations and an accurate quasi-2D model that incorporates quadrupolar and swapping-trajectory contributions, we analyze microstructural evolution in a monodisperse drop monolayer. Consistent with experimental observations, we find that drop spacing within individual chains is usually uniform. Further analysis shows that at low area fractions all chains have the same spacing, but at higher area fractions there is a large spacing variation from chain to chain. These findings are explained in terms of uncompressed and compressed chains. At low area fractions most chains are uncompressed (spacing equals lst, which is the stable separation of an isolated pair). At higher area fractions compressed chains (with tighter spacing) are formed in a process of chain zipping along y-shaped structural defects. We also discuss the relevance of our findings to other shear-driven systems, such as suspensions of spheres in non-Newtonian fluids.