流场环境下复杂囊泡的动力学行为

采用非平衡态分子动力学方法研究了二维复杂囊泡在剪切流中的动力学行为. 模拟发现了复杂囊泡经典的翻滚(tumbling)、摇摆(trembling)和坦克履(tank-treading)行为, 还观察到由坦克履行为向平动行为(translating)的转变. 囊泡的平动行为与剪切率大小、复杂囊泡的形状密切相关. 当大囊泡均匀嫁接较多数目的小囊泡后, 其平动方式消失. 该研究有益于加深对囊泡在剪切流场中复杂性行为的理解.     

Swinging and tumbling of fluid vesicles in shear flow

The dynamics of fluid vesicles in simple shear flow is studied using mesoscale simulations of dynamically triangulated surfaces, as well as a theoretical approach based on two variables: a shape parameter and the inclination angle, which has no adjustable parameters. We show that, between the well-known tank-treading and tumbling states, a new "swinging" state can appear. We predict the dynamic phase diagram as a function of the shear rate, the viscosities of the membrane and the internal fluid, and the reduced vesicle volume. Our results agree well with recent experiments.     

Semiflexible polymers in shear flow

The dynamics of semiflexible polymers under the influence of shear flow is studied analytically. Power laws are derived for various conformational and dynamical quantities which are in agreement with experimental findings. In particular, the tumbling motion is analyzed and expressions are provided for the probability distributions of the orientation angles and the tumbling time. The calculations explain the similarities in the behavior of flexible and semiflexible polymers as well as free-draining and nondraining systems.     

Swinging of red blood cells under shear flow

We reveal that under moderate shear stress (etagamma[over ] approximately 0.1 Pa) red blood cells present an oscillation of their inclination (swinging) superimposed to the long-observed steady tank treading (TT) motion. A model based on a fluid ellipsoid surrounded by a viscoelastic membrane initially unstrained (shape memory) predicts all observed features of the motion: an increase of both swinging amplitude and period (1/2 the TT period) upon decreasing etagamma[over ], a etagamma[over ]-triggered transition toward a narrow etagamma[over ] range intermittent regime of successive swinging and tumbling, and a pure tumbling at low etagamma[over ] values.     

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.     

Characteristic periodic motion of polymers in shear flow

The motion of both free and tethered polymer molecules as well as rigid Brownian rods in unbound shear flow is found to be characterized by a clear periodicity or tumbling frequency. Periodicity is shown using a combination of single molecule DNA experiments and computer simulations. In all cases, we develop scaling laws for this behavior and demonstrate that the frequency of characteristic periodic motion scales sublinearly with flow rate.     

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.     

Polymer dynamics in chaotic flows with a strong shear component

We consider the dynamics of a polymer molecule injected into a chaotic flow with a strong mean shear component. The polymer experiences aperiodic tumbling in such flows. We consider a simplified model of the chaotic velocity field given by the superposition of a steady shear flow and a large-scale isotropic short-correlated random component. In the framework of this model, we present a detailed study of the statistical properties of single-polymer dynamics. We obtain the stationary probability distribution function of the polymer orientation, find the distribution of time periods between consequent events of tumbling, and find the tails of the polymer size distribution. The text was submitted by the author in English.     

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.     

Vacillating breathing and tumbling of vesicles under shear flow

The dynamics of vesicles under a shear flow are analyzed analytically in the small deformation regime. We derive two coupled nonlinear equations which describe the vesicle orientation in the flow and its shape evolution. A new type of motion is found, namely, a "vacillating-breathing" mode: the vesicle orientation undergoes an oscillation around the flow direction, while the shape executes breathing dynamics. This solution coexists with tumbling. Moreover, we provide an explicit expression for the tumbling threshold. A rheological law for a dilute vesicle suspension is outlined.     

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.      

Kayaking and wagging of rods in shear flow

For the first time, we have simulated the periodic collective orientational motions performed by rigid liquid-crystalline polymers with large aspect ratio in the nematic state in shear flow. In order to be able to do so, we developed a new, event-driven Brownian dynamics technique. We present the results of simulations of rods with aspect ratios L/d ranging from 20 to 60 at volume fractions phi given by Lphi/d = 3.5 and 4.5. By studying the path of the director, i.e., the average direction of the rods, we observe kayaking, wagging, flow aligning, and log-rolling type of orbits, depending on the parameters of the simulation and the initial orientation. We find that the tumbling periods depend on Lphi/d and the shear rate but not on the type of motion. Our simulation results qualitatively confirm theoretical predictions and are in good agreement with the experimental measurements of tumbling times of fd viruses.     

Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition

We consider the motion of red blood cells and other nonspherical microcapsules dilutely suspended in a simple shear flow. Our analysis indicates that depending on the viscosity, membrane elasticity, geometry, and shear rate, the particle exhibits either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behavior in which the two modes occur alternately. For red blood cells, we compute the complete phase diagram and identify a novel tank-treading-to-tumbling transition as the shear rate decreases. Observations of such motions coupled with our theoretical framework may provide a sensitive means of assessing capsule properties.     

均匀流中剪切变形加筋层合板声与振动特性研究

基于一阶剪切变形理论, 建立了分析均匀流中周期加筋层合板声振特性的理论模型. 该模型应用对流波动方程及边界条件精确考虑了均匀流与层合板的耦合作用, 加强筋通过法向线力及扭矩与层合板相互作用, 利用傅里叶波数变换和稳相法, 得到了位移谱和辐射声压的解析表达式. 计算结果与已有公开数据符合良好, 验证了模型的有效性. 数值结果表明, 在高频段不能忽略剪切变形和加强筋扭转运动的影响; 增大均匀流速度可降低结构的辐射声压; 适当调整板厚和加强筋间距可有效避开结构的辐射声压波峰. 关键词： 均匀流 第一阶剪切变形理论 层合板 波数变换     

Effects of oscillatory shear flow on chain-like cluster dynamics in ferrofluids without magnetic fields

Brownian dynamics simulations of interacting magnetic particles in a quasi-two-dimensional ferrofluid system are performed at zero temperature, under the influence of oscillatory shear flow in the absence of external magnetic fields. Starting from chain-like clusters of the particles, we study the time-dependent behavior of both magnetization and microstructures of the ferrofluid by changing values of two parameters, the shear rate strength and frequency of oscillatory shear flow. Simulation results show that there are three different dynamical regimes for the chain clusters dynamics, depending on these two parameters. Scaling behavior of the asymptotic magnetization is also observed for a certain range of parameters.     

Dense colloidal suspensions under time-dependent shear

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity), we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear stress as an example, we derive exactly a generalized Green-Kubo relation and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step strain.     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.     

A front-tracking method with Catmull–Clark subdivision surfaces for studying liquid capsules enclosed by thin shells in shear flow

This paper presents a front-tracking method for studying the large deformation of a liquid capsule enclosed by a thin shell in a shear flow. The interaction between the fluid and the shell body is accomplished through an implicit immersed boundary method. An improved thin-shell model for computing the forces acting on the shell middle surface during the deformation is described in surface curvilinear coordinates and within the framework of the principle of virtual displacements. This thin-shell model takes full account of in-plane tensions and bending moments developing due to the shell thickness and a preferred three-dimensional membrane structure. The approximation of the shell middle surface is performed through the use of the Catmull–Clark subdivision surfaces. The resulting limit surface is C²-continuous everywhere except at a small number of extraordinary nodes where it retains C¹ continuity. The smoothness of the limit surface significantly improves the ability of our method in simulating capsules enclosed by hyperelastic thin shells with different shapes and physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, ellipsoidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, swinging, tumbling and transition from tumbling to swinging have been studied over a range of shear rates, viscosity ratios and bending modulus.     

Shape dynamics and rheology of soft elastic particles in a shear flow

The shape dynamics of soft, elastic particles in an unbounded simple shear flow is investigated theoretically under Stokes flow conditions. Three types of motion-steady-state, trembling, and tumbling-are predicted, depending on the shear rate, elastic shear modulus, and initial particle shape. The steady-state motion is found to be always stable. In addition, the existence of a trembling regime is documented for the first time in nonvesicle systems, and a complete phase diagram is developed. The rheological properties of dilute suspensions of such soft particles generally exhibit shear-thinning behavior and can even display negative intrinsic viscosity for sufficiently soft particles.     

Molecular dynamics study of tethered polymers in shear flow

Single macromolecules can now be isolated and characterized experimentally using techniques such as optical tweezers and videomicroscopy. An interesting and important single-molecule problem is that of the dynamics of a polymer chain tethered to a solid surface and subjected to a shear flow. An experimental study of such a system was reported by Doyle et al. (Phys. Rev. Lett. 84, 4769 (2000)), and their results showed a surprising recirculating motion of the DNA chain. We explore this problem using molecular dynamics computer simulations with explicit hydrodynamic interactions. The dynamical properties of a Freely Jointed Chain (FJC) with Finitely Extensible Nonlinear Elastic (FENE) links are examined in similar conditions (i.e., confined between two surfaces and in the presence of a Poiseuille flow). We see the remarkable cyclic polymer motion observed experimentally, and we show that a simple cross-correlation function can be used to measure the corresponding period of motion. We also propose a new empirical equation relating the magnitude of the shear flow to the amount of chain deformation, an equation that appears to apply for both weak and strong flows. Finally, we report on packing effects near the molecularly flat wall, an associated chain-sticking phenomenon, and the impact of the chain hydrodynamic drag on the local fluid flow.