Deformation and Motion of a Red Blood Cell in a Shear Flow Simulated by a Lattice Boltzmann Model

A lattice Boltzmann model is presented to simulate the deformation and motions of a red blood cell (RBC) in a shear flow. The curvatures of the membrane of a static RBC with different chemical potential drops calculated by our model agree with those computed by a shooting method very well. Our simulation results show that in a shear flow, a biconcave RBC becomes highly flattened and undergoes tank-treading motion. With intrinsically parallel dynamics, this lattice Boltzmann method is expected to find wide applications to both single and multi-vesicles suspension as well as complex open membranes in various fluid flows for a wide range of Reynolds numbers.     

Dynamics of viscous vesicles in shear flow

The dynamics of giant lipid vesicles under shear flow is experimentally investigated. Consistent with previous theoretical and numerical studies, two flow regimes are identified depending on the viscosity ratio between the interior and the exterior of the vesicle, and its reduced volume or excess surface. At low viscosity ratios, a tank-treading motion of the membrane takes place, the vesicle assuming a constant orientation with respect to the flow direction. At higher viscosity ratios, a tumbling motion is observed in which the whole vesicle rotates with a periodically modulated velocity. When the shear rate increases, this tumbling motion becomes increasingly sensitive to vesicle deformation due to the elongational component of the flow and significant deviations from simpler models are observed. A good characterization of these various flow regimes is essential for the validation of analytical and numerical models, and to relate microscopic dynamics to macroscopic rheology of suspensions of deformable particles, such as blood.     

Analysis of membrane tank-tread of nonspherical capsules and red blood cells

We present an analysis of membrane motion of deformable capsules and red blood cells suspended in a linear shear flow and undergoing swinging and tumbling motions using three-dimensional numerical simulations. This study is motivated by the theory of the shape-preserving cells which predicts that the direction of the membrane rotation depends on the cell orientation and reverses at every 45° inclination angle of the cell major axis with respect to the external flow direction. By considering large deformation of capsules and red blood cells, here we investigate how the shape oscillation affects the time dependence and the direction reversal of the membrane rotation. We find that the membrane tank-tread is highly time-dependent in nature and synchronized with the time-dependent deformation. The maximum and minimum of the tank-tread velocity occur at and near the minimum and maximum deformation, respectively. For the swinging capsules and red blood cells, the direction of the membrane rotation is always along the direction of the external fluid rotation; however, a direction reversal occurs during the tumbling motion in which case the membrane rotates in the direction of the external fluid rotation when the major axis is mostly in the extensional quadrant of the shear flow, and in the opposite direction when it is mostly in the compressional quadrant. Unlike the theory which predicts the direction reversal at every 45° inclination angle irrespective of the control parameters, namely, the capillary number, viscosity ratio, and asphericity, we find that the angle at which the direction reversal occurs depends on these parameters. In particular, if the tumbling motion occurs by decreasing the capillary number, the membrane rotation is in the direction of the external flow rotation in the entire extensional quadrant, but in the opposite direction in the compressional quadrant, irrespective of the specific values of the capillary number. If the tumbling motion occurs by increasing the viscosity ratio and asphericity, the angle at which the direction reversal occurs depends on the specific values of these two parameters. The spatial variation of the tank-tread velocity also is analyzed and attributed to the straining motion of the external flow.      

Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method

An improved penalty immersed boundary method (pIBM) has been proposed for simulation of flow-induced deformation of three-dimensional (3D) elastic capsules. The motion of the capsule membrane is described in the Lagrangian coordinates. The membrane deformation takes account of the bending and twisting effects as well as the stretching and shearing effects. The method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C¹ continuous. The membrane motion is then solved by the subdivision-surface based finite element method on the triangular unstructured mesh. On the other hand, the fluid motion is defined on the Eulerian domain, and is advanced by the fractional step method on a staggered Cartesian grid. Coupling of the fluid motion and the membrane motion is realized in the framework of the pIBM. Using the proposed method, deformation of 3D elastic capsules in a linear shear flow is studied in detail, and validations are examined by comparing with previous studies. Both the neo-Hookean membrane and the Skalak membrane are tested. For an initially spherical capsule the tank-treading motion is formed under various dimensionless shear rates and reduced bending moduli. It is found that buckling occurs near the equator of the capsule for small shear rates but near the tips for large shear rates, which is suppressed by including the bending rigidity of the membrane. Effects of the Reynolds number and the membrane density are investigated for an initially spherical capsule. For a non-spherical capsule, with the initial shape of the oblate spheroid or the biconcave circular disk as a model of the red blood cell, the swinging motion is observed due to the shape memory effect. By decreasing the dimensionless shear rate or increasing the reduced bending modulus, the swinging motion is transited into the tumbling motion.     

Dynamics of a compound vesicle in shear flow

The dynamics of a compound vesicle (a lipid bilayer membrane enclosing a fluid with a suspended particle) in shear flow is investigated by using both numerical simulations and theoretical analysis. We find that the nonlinear hydrodynamic interaction between the inclusion and the confining membrane gives rise to new features of the vesicle dynamics: The transition from tank treading to tumbling can occur in the absence of any viscosity mismatch, and a vesicle can swing if the enclosed particle is nonspherical. Our results highlight the complex effects of internal cellular structures have on cell dynamics in microcirculatory flows. For example, parasites in malaria-infected erythrocytes increase cytoplasmic viscosity, which leads to increase in blood viscosity.     

Fluid vesicles with viscous membranes in shear flow

The effect of membrane viscosity on the dynamics of vesicles in shear flow is studied. We present a new simulation technique, which combines three-dimensional multiparticle collision dynamics for the solvent with a dynamically triangulated membrane model. Vesicles are found to transit from steady tank treading to unsteady tumbling motion with increasing membrane viscosity. Depending on the reduced volume and membrane viscosity, shear can induce both discocyte-to-prolate and prolate-to-discocyte transformations. This behavior can be understood from a simplified model.     

Transition to tumbling and two regimes of tumbling motion of a vesicle in shear flow

Experimental results on the tank-treading-tumbling transition in the dynamics of a vesicle subjected to a shear flow as a function of a vesicle excess area, viscosity contrast, and the normalized shear rate are presented. Good agreement on the transition curve and scaling behavior with theory and numerical simulations was found. A new type of unsteady motion at a large degree of vesicle deformability was discovered and described as follows: a vesicle trembles around the flow direction, while the vesicle shape strongly oscillates.     

Using 3D fluid-structure interaction model to analyse the biomechanical properties of erythrocyte

This Letter presents a newly developed three-dimensional fluid-structure interaction model of the red blood cell (RBC). The model consists of a deformable liquid capsule modelled as Newtonian fluid enclosed by a hyperelastic membrane with viscoelastic property. Numerical results show that viscosity in the cytoplasm affects the deformed shape of RBC under loading. This observation is contrary to the earlier belief that viscosity of the cytoplasm can be neglected. Numerical simulations carried out to investigate large deformation induced on the RBC model using direct tensile forces show significant improvement in terms of correlation with experimental results. The membrane shear modulus estimated from the model ranges between 3.7 to compares well with results obtained from micropipette aspiration experiments.     

Microconfined flow behavior of red blood cells in vitro

The high red blood cell (RBC) deformability is essential to optimal gas exchange between gas and tissues in microcirculation in vivo. This review is focused on the flow behavior of RBCs in microconfined geometries in vitro, such as circular section capillaries, rectangular channels and pores, where at least one transverse dimension is comparable to cell size. Experimental results on RBC velocity and shape are reviewed together with modeling predictions and numerical simulations. In spite of the progress made so far, the pathophysiological implications of altered RBC deformability are still to be fully elucidated, and more data from clinically-relevant experimental methods and modeling-based interpretation are needed. Future directions include the emerging application of microfluidics techniques to investigate RBC flow in complex geometries. To cite this article: S. Guido, G. Tomaiuolo, C. R. Physique 10 (2009).     

An improved penalty immersed boundary method for fluid–flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid–flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid–flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.     

Margination of white blood cells in microcapillary flow

Margination of white blood cells (WBCs) towards vessel walls is an essential precondition for their efficient adhesion to the vascular endothelium. We perform numerical simulations with a two-dimensional blood flow model to investigate the dependence of WBC margination on hydrodynamic interactions of blood cells with the vessel walls, as well as on their collective behavior and deformability. We find WBC margination to be optimal in intermediate ranges of red blood cell (RBC) volume fractions and flow rates, while, beyond these ranges, it is substantially attenuated. RBC aggregation enhances WBC margination, while WBC deformability reduces it. These results are combined in state diagrams, which identify WBC margination for a wide range of flow and cell suspension conditions.     

Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed. Received 20 August 1998     

Orientation and dynamics of a vesicle in tank-treading motion in shear flow

Experimental results on mean inclination angle and its fluctuation due to thermal noise in tank-treading motion of a vesicle in shear flow as a function of vesicle excess area, normalized shear rate, viscosity, and viscosity contrast between inner and outer fluids, , are presented. Good quantitative agreement with theory made for was found. At the dependence is altered significantly. Dependence of the vesicle shape on shear rate is consistent with theory. A tank-treading velocity of the vesicle membrane is found to be a periodic function close to that predicted by theory.     

Viscoelastic theory for nematic interfaces

A complete macroscopic theory for compressible nematic-viscous fluid interfaces is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the interfacial stress tensor includes elastic and viscous components. Surface gradients of the interfacial elastic stress tensor generates tangential Marangoni forces as well as normal forces. The latter may be present even in planar surfaces, implying that in principle static planar interfaces may accommodate pressure jumps. The asymmetric interfacial viscous stress tensor takes into account the surface nematic ordering and is given in terms of the interfacial rate of deformation and interfacial Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic interfacial tension, which includes the interfacial tension and dilational viscosities. Viscous dissipation due to interfacial compressibility is described by the anisotropic dilational viscosity, and it is shown to describe the Boussinesq surface fluid appropriate for Newtonian interfaces when the director is homeotropic. Three characteristic interfacial shear viscosities are defined according to whether the surface orientation is along the velocity direction, the velocity gradient, or the unit normal. In the last case the expression reduces to the interfacial shear viscosity of the Boussinesq surface fluid. The theory provides a theoretical framework to study interfacial stability, thin liquid film stability and hydrodynamics, and any other interfacial rheology phenomena.     

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

微扩张管道内幂律流体非定常电渗流动

研究了电渗驱动下幂律流体在有限长微扩张管道内非稳态流动特性.基于Ostwald-de Wael幂律模型,采用高精度紧致差分离散二维Poisson-Nernst-Planck方程及修正的Cauchy动量方程,数值模拟了初始及稳态时刻微扩张管道内幂律流体电渗流流场分布情况,研究了管道截面改变对幂律流体无量纲剪切应变率及无量纲表观黏度的影响,以及无量纲表观黏度对拟塑性流体与胀流型流体流速分布的影响.数值模拟结果显示,当扩张角和无量纲电动宽度一定时,电场驱动下的幂律流体在近壁区域速度响应都很快;初始时刻,近壁处表观黏度的变化受到剪切应变率变化的影响,从而影响了三种幂律流体速度峰值的分布,出现拟塑性流体流速在扩张段上游及扩张段近壁处速度峰值均为幂律流体中最大、而在扩张段下游三种幂律流体速度峰值相近的现象;稳态时刻,幂律流体速度剖面呈现塞型分布,且满足连续性条件下,幂律流体流速随扩张管半径增大而减小,牛顿流体流动规律与宏观尺度下流动规律相同;初始时刻,在相同电动宽度、不同壁面电势作用下,幂律流体在扩张管近壁处剪切应变率分布的差异导致表观黏度分布的差异,并最终导致拟塑性流体与胀流型流体流速分布的差异.     

生物力学中片流的边界元分析

用边界元方法^[1,2]研究了生物力学中肺毛细血管血液的流动,并对肺毛细血管的SFH模型,SFC模型进行了数值模拟,给出血液流动的速度场及血管壁上的面力分布和压力分布.对肺毛细管内皮细胞受的切应力,数值计算表明,正常情况下,在0~4.64×10^-5N/cm²之间,这与Dewey实验结果^[8](0~5×10^-5N/cm²)相一致,肺胞的形态将按使呼吸膜受切应力值最小为原则构形.同时,本文方法还可为数值分析心血管内的血液流动提供一种有效的数值方法,这对生物力学和医学工程是有价值的.     

基于基液连续假设的大体系Cu-H2O纳米流体输运特性的模拟研究

分子动力学模拟是研究纳米流体的输运特性的重要手段, 但计算量庞大. 为研究能体现流动传热过程的大体系纳米流体的输运特性, 本文对基液采用连续介质假设, 将基液的势能拟合在纳米团簇的势能中, 大幅度减小了计算量, 使得大体系输运特性的模拟成为可能, 且模拟结果与多组实验结果吻合较好. 采用此方法模拟研究了速度梯度剪切对Cu-H₂O纳米流体颗粒聚集过程和聚集特性的影响, 进而对Cu-H₂O纳米流体在流动传热过程中的热导率和黏度进行了模拟计算, 定量揭示了宏观流动传热过程中不同的速度梯度、速度、平均温度和温度梯度对于Cu-H₂O纳米流体热导率和黏度的影响.     

Numerical simulation of flow in a screw-type blood pump

This study presents a numerical investigation of the flow field in a screw pump designed to circulate biological fluid such as blood. A simplified channel flow model is used to allow analysis using a Cartesian set of coordinates. Finite analytic (FA) numerical simulation of the flow field inside the channel was performed to study the influence of Reynolds number and pressure gradient on velocity distribution and shear stresses across the channel cross-section. Simulation results were used to predict flow rates, circulatory flow and the shear stresses, which are known to be related to the level of red blood cell damage (hemolysis) caused by the pump. The study shows that high shear levels are confined to small regions within the channel cross-section, but the circulatory nature of the flow causes an increased percentage of blood elements to pass through the high shear regions, and increases the likelihood of cell damage.