Dynamic modes of microcapsules in steady shear flow: effects of bending and shear elasticities

Red blood cell motion and deformation in a curved microvessel

The flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications, such as red blood cells (RBCs) passing through the curved arteries in circulation, and cells sorting through a shear-induced migration in a curved channels. Most of past numerical studies focused on the cell deformation in small straight microvessels, or on the flow pattern in large curved vessels without considering the cell deformation. However, there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel. In this work, a particle-based method, smoothed dissipative particle dynamics (SDPD), is used to simulate the motion and deformation of a RBC in a curved microvessel of diameter comparable to the RBC diameter. The emphasis is on the effects of the curvature, the type and the size of the curved microvessel on the RBC deformation and the flow pattern. The simulation results show that a small curved shape of the microvessel has negligible effect on the RBC behavior and the flow pattern which are similar to those in a straight microvessel. When the microvessel is high in curvature, the secondary flow comes into being with a pair of Dean vortices, and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel. The RBC also loses the axisymmetric deformation, and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature. It is also found that a pair of Dean vortices arise only under the condition of De>1 (De is the Dean number, a ratio of centrifugal to viscous competition). The Dean vortices are more easily observed in the larger or more curved microvessels. Finally, it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel, i.e., the fluid close to the inner wall flows faster than that close to the outer wall. This is contrary to the common sense in large curved vessels. This velocity skewness was found to depend on the curvature of the microvessel, as well as the viscous and inertial forces.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

Micro-capsules in shear flow

This paper deals with flow-induced shape changes of elastic capsules. The state of the art concerning both theory and experiments is briefly reviewed starting with dynamically induced small deformation of initially spherical capsules and the formation of wrinkles on polymerized membranes. Initially non-spherical capsules show tumbling and tank-treading motion in shear flow. Theoretical descriptions of the transition between these two types of motion assuming a fixed shape are at odds with the full capsule dynamics obtained numerically. To resolve the discrepancy, we expand the exact equations of motion for small deformations and find that shape changes play a dominant role. We classify the dynamical phase transitions and obtain numerical and analytical results for the phase boundaries as a function of viscosity contrast, shear and elongational flow rate. We conclude with perspectives on time-dependent flow, on shear-induced unbinding from surfaces, on the role of thermal fluctuations and on applying the concepts of stochastic thermodynamics to these systems.

Dynamic modes of red blood cells in oscillatory shear flow

The dynamics of red blood cells (RBCs) in oscillatory shear flow was studied using differential equations of three variables: a shape parameter, the inclination angle θ, and phase angle ϕ of the membrane rotation. In steady shear flow, three types of dynamics occur depending on the shear rate and viscosity ratio. (i) tank-treading (TT): ϕ rotates while the shape and θ oscillate. (ii) tumbling (TB): θ rotates while the shape and ϕ oscillate. (iii) intermediate motion: both ϕ and θ rotate synchronously or intermittently. In oscillatory shear flow, RBCs show various dynamics based on these three motions. For a low shear frequency with zero mean shear rate, a limit-cycle oscillation occurs, based on the TT or TB rotation at a high or low shear amplitude, respectively. This TT-based oscillation well explains recent experiments. In the middle shear amplitude, RBCs show an intermittent or synchronized oscillation. As shear frequency increases, the vesicle oscillation becomes delayed with respect to the shear oscillation. At a high frequency, multiple limit-cycle oscillations coexist. The thermal fluctuations can induce transitions between two orbits at very low shear amplitudes. For a high mean shear rate with small shear oscillation, the shape and θ oscillate in the TT motion but only one attractor exists even at high shear frequencies. The measurement of these oscillatory modes is a promising tool for quantifying the viscoelasticity of RBCs, synthetic capsules, and lipid vesicles.