We simulate the cross-flow migration of rigid particles such as platelets in a red blood cell (RBC) suspension using the Stokes flow boundary integral equation method. Two types of flow environments are investigated: a suspension undergoing a bulk shear motion and a suspension flowing in a microchannel or duct. In a cellular suspension undergoing bulk shear deformation, the cross-flow migration of particles is diffusional. The velocity fluctuations in the suspension, which are the root cause of particle migration, are analyzed in detail, including their magnitude, the autocorrelation of Lagrangian tracer points and particles, and the associated integral time scales. The orientation and morphology of red blood cells vary with the shear rate, and these in turn cause the dimensionless particle diffusivity to vary non-monotonically with the flow capillary number. By simulating RBCs and platelets flowing in a microchannel of 34 lm height, we demonstrate that the velocity fluctuations in the core cellular flow region cause the platelets to migrate diffusively in the wall normal direction. A mean lateral velocity of particles, which is most significant near the edge of the cell-free layer, further expels them toward the wall, leading to their excess concentration in the cell-free layer. The calculated shear-induced particle diffusivity in the cell-laden region is in qualitative agreement with the experimental measurements of micron-sized beads in a cylindrical tube of a comparable diameter. In a smaller duct of 10 Â 15 lm cross section, the volume exclusion becomes the dominant mechanism for particle margination, which occurs at a much shorter time scale than the migration in the bigger channel. V

We perform single-molecule experiments and simulations to study the swelling of complex knots in linearly extended DNA molecules. We induce self-entanglement of DNA molecules in a microfluidic T-junction using an electrohydrodynamic instability and then stretch the molecules using divergent electric fields. After the chain is fully extended, the knot appears as a region of excess fluorescent brightness, and we shut off the field and observe the knot swelling over time. We find (1) the knot topologies created by the instability are more complex than what is expected from equilibrium simulations of knot formation, (2) the knot swells at a time scale comparable to the end-to-end relaxation of the chain, which indicates that the swelling is dictated by the chain’s global dynamics, and (3) knots are long-lived when the DNA is in the coiled state. These findings demonstrate the rich physics involved in the relaxation of knotted polymers which has not been examined heretofore.

Tubular vesicles in extensional flow can undergo 'pearling', i.e. the formation of beads in their central neck reminiscent of the Rayleigh-Plateau instability for droplets. In this paper, we perform boundary integral simulations to determine the conditions for the onset of this instability. Our simulations agree well with experiments, and we explore additional topics such as the role of the vesicle's initial shape on the number of pearls formed. We also compare our simulations to simple physical models of pearling that have been presented in the literature, where the vesicle is approximated as an infinitely long cylinder with a constant surface tension and bending modulus. We present a complete linear stability analysis of this idealized problem, including the effects of non-axisymmetric deformations as well as surface viscosity. We demonstrate that, while such models capture the essential physics of pearling, they cannot capture the stability of these transitions accurately, since finite length effects and non-uniform surface tension effects are important. We close our paper with a brief discussion of vesicles in compressional flows. Unlike quasi-spherical vesicles, we find that tubular vesicles can transition to a wide variety of permanent, buckled states under compression. The idealized problem mentioned above gives the essential physics behind these instabilities, which to our knowledge has not been examined heretofore.

Vesicles provide an attractive model system to understand the deformation of living cells in response to mechanical forces. These simple, enclosed lipid bilayer membranes are suitable for complementary theoretical, numerical, and experimental analysis. A recent study [Narsimhan, Spann, Shaqfeh, Journal of Fluid Mechanics, 2014, 750, 144] predicted that intermediate-aspect-ratio vesicles extend asymmetrically in extensional flow. Upon infinitesimal perturbation to the vesicle shape, the vesicle stretches into an asymmetric dumbbell with a cylindrical thread separating the two ends. While the symmetric stretching of high-aspect-ratio vesicles in extensional flow has been observed and characterized [Kantsler, Segre, Steinberg, Physics Review Letters, 2008, 101, 048101] as well as recapitulated in numerical simulations by Narsimhan et al., experimental observation of the asymmetric stretching has not been reported. In this work, we present results from microfluidic cross-slot experiments observing this instability, along with careful characterization of the flow field, vesicle shape, and vesicle bending modulus. The onset of this shape transition depends on two non-dimensional parameters: reduced volume (a measure of vesicle asphericity) and capillary number (ratio of viscous to bending forces). We observed that every intermediate-reduced-volume vesicle that extends forms a dumbbell shape that is indeed asymmetric. For the subset of the intermediate-reduced-volume regime we could capture experimentally, we present an experimental phase diagram for asymmetric vesicle stretching that is consistent with the predictions of Narsimhan et al.

When a flexible vesicle is placed in an extensional flow (planar or uniaxial), it undergoes two unique sets of shape transitions that to the best of the authors' knowledge have not been observed for droplets. At intermediate reduced volumes (i.e. intermediate particle aspect ratio) and high extension rates, the vesicle stretches into an asymmetric dumbbell separated by a long, cylindrical thread. At low reduced volumes (i.e. high particle aspect ratio), the vesicle extends symmetrically without bound, in a manner similar to the breakup of liquid droplets. During this 'burst' phase, 'pearling' occasionally occurs, where the vesicle develops a series of periodic beads in its central neck. In this paper, we describe the physical mechanisms behind these seemingly unrelated instabilities by solving the Stokes flow equations around a single, fluid-filled particle whose interfacial dynamics is governed by a Helfrich energy (i.e. the membranes are inextensible with bending resistance). By examining the linear stability of the steady-state shapes, we determine that vesicles are destabilized by curvature changes on its interface, similar to the Rayleigh-Plateau phenomenon. This result suggests that the vesicle's initial geometry plays a large role in its shape transitions under tension. The stability criteria calculated by our simulations and scaling analyses agree well with available experiments. We hope that this work will lend insight into the stretching dynamics of other types of biological particles with nearly incompressible membranes, such as cells.