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.     

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.     

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     

Phase-ordering dynamics of binary mixtures with field-dependent mobility in shear flow

The effect of shear flow on the phase-ordering dynamics of a binary mixture with field-dependent mobility is investigated. The problem is addressed in the context of the time-dependent Ginzburg-Landau equation with an external velocity term, studied in self-consistent approximation. Assuming a scaling ansatz for the structure factor, the asymptotic behavior of the observables in the scaling regime can be analytically calculated. All the observables show log-time periodic oscillations which we interpret as due to a cyclical mechanism of stretching and break-up of domains. These oscillations are damped as consequence of the vanishing of the mobility in the bulk phase. Received 13 April 1999     

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.     

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.     

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.     

Ripple formation in weakly turbulent flow

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.     

A Monte-Carlo study of equilibrium polymers in a shear flow

We use an off-lattice microscopic model for solutions of equilibrium polymers (EP) in a lamellar shear flow generated by means of a self-consistent external field between parallel hard walls. The individual conformations of the chains are found to elongate in flow direction and shrink perpendicular to it while the average polymer length decreases with increasing shear rate. The Molecular Weight Distribution of the chain lengths retains largely its exponential form in dense solutions whereas in dilute solutions it changes from a power-exponential Schwartz distribution to a purely exponential one upon an increase of the shear rate. With growing shear rate the system becomes increasingly inhomogeneous so that a characteristic variation of the total monomer density, the diffusion coefficient, and the center-of-mass distribution of polymer chains of different contour length with the velocity of flow is observed. At higher temperature, as the average chain length decreases significantly, the system is shown to undergo an order-disorder transition into a state of nematic liquid crystalline order with an easy direction parallel to the hard walls. The influence of shear flow on this state is briefly examined. Received 22 October 1998 and Received in final form 12 April 1999     

Shear-driven heat flow in absence of a temperature gradient

Jaynesian statistical inference is used to predict that steady, non-uniform Couette flow in a simple liquid will generate a heat flux proportional to the gradient of the square of the strain-rate when the temperature gradient is negligible. The heat flux is divided into phonon and self-diffusion components, with the latter coupling to the elastic strain and inelastic strain-rate. Operators for all these are substituted into the information-theoretic phase-space distribution. By taking moments of an exact equation for this distribution derived by Robertson, one obtains an evolution equation for the self-diffusion component of the heat flux which, in a steady state, predicts shear-driven heat flow. Received 10 September 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.     

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     

On the orientational characteristics and transport coefficients of an oblate spheroidal hematite particle in a simple shear flow

We have developed the basic equation of the orientational distribution function of oblate spheroidal hematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. An oblate spheroidal hematite particle has an important characteristic in that it is magnetized in a direction normal to the particle axis. Since a dilute dispersion is addressed in the present study, we have taken into account only the friction force (torque) whilst neglecting the hydrodynamic interactions among the particles. This basic equation has been solved numerically in order that we may investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion and the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. We found that if the effect of the magnetic field is more dominant, the particle inclines in such a way that the oblate surface aligns in the magnetic field direction. If the Peclet number increases and the effect of the shear flow becomes more dominant, the particle inclines such that the oblate surface tilts in the shear flow direction. The viscosity due to the magnetic torque is shown to increase as the magnetic field increases, since the magnetic torque due to the applied magnetic field becomes the more dominant effect. Moreover, the viscosity increase is shown to be more significant for a larger aspect ratio or for a more oblate hematite particle. We have applied the analysis to the problem of particle sedimentation under gravity in the presence of a magnetic field applied in the sedimentation direction. The particles are found to sediment with the oblate surface aligning more significantly in the sedimentation direction as the applied magnetic field strength increases.     

Stretching of polymers in a random three-dimensional flow

Behavior of a dilute polymer solution in a random three-dimensional flow with an average shear is studied experimentally. Polymer contribution to the shear stress is found to be more than 2 orders of magnitude higher than in a laminar shear flow. The results indicate that the polymer molecules are strongly stretched by the random motion of the fluid.     

A minimal model for vorticity and gradient banding in complex fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions. Received 1 April 2001 and Received in final form 16 June 2001     

Mechanical behavior of pathological and normal red blood cells in microvascular flow based on modified level-set method

The research of the motion and deformation of the RBCs is important to reveal the mechanism of blood diseases. A numerical method has been developed with level set formulation for elastic membrane immersed in incompressible fluid. The numerical model satisfies mass and energy conservation without the leaking problems in classical Immersed Boundary Method(IBM), at the same time, computing grid we used can be much smaller than the general literatures. The motion and deformation of a red blood cell(including pathological normal status) in microvascular flow are simulated. It is found that the Reynolds number and membrane's stiffness play an important role in the transmutation and oscillation of the elastic membrane. The normal biconcave shape of the RBC is propitious to create high deformation than other pathological shapes. With reduced viscosity of the interior fluid both the velocity of the blood and the deformability of the cell reduced. With increased viscosity of the plasma both the velocity of the blood and the deformability of the cell reduced. The tank treading of the RBC membrane is observed at low enough viscosity contrast in shear flow. The tank tread fixed inclination angle of the cell depends on the shear ratio and viscosity contrast, which can be compared with the experimental observation well.     

Parametric resonance with a point-vortex pair in a nonstationary deformation flow

The movement of a pair of point vortices with arbitrary intensities, embedded in a nonstationary shear and rotational flow, is studied. The expression for the vorticity center is shown to be reduced to a Riccati equation. In the particular case of harmonic oscillations, parametric resonance, which results in unbounded motion of the vortex pair, is found and analyzed. Using the fast oscillation averaging, an analytical estimate for the main zone in the parametric space is obtained. With the help of numerical calculations, the reliability of the estimate is asserted and a family of the minor zones is obtained.     

Encapsulated drop breakup in shear flow

We investigate the deformation and breakup in shear flow of an encapsulated drop in which both the core and shell are Newtonian fluids. The equations of motion are solved numerically using a level set method to track interface motion. We consider the case of a drop stretched to a given length in constant shear and then allowed to relax. A range of morphologies is produced, and novel kinematics occur, due to the interaction of the core and outer interfaces. A phase diagram is presented to describe the morphologies produced over a range of capillary numbers and core interfacial tensions.     

A lattice Boltzmann method for a two-phase flow containing solid bodies with viscoelastic membranes

A lattice Boltzmann method (LBM) for two-phase flows containing solid bodies with viscoelastic membranes is proposed. The method is based on the two-phase LBM, in which one phase is regarded as the solid phase. In the present model, the membrane is assumed to be composed of identical particles that are connected to their neighboring particles by elastic springs to take account of stretching and compression effects. The method is applied to two representative problems, namely the behavior of a viscoelastic body under shear flow and the motion of a viscoelastic body in a Poiseuille flow. Tank-tread motion and axial migration, which are both characteristic of the motion of viscoelastic bodies, are simulated by using the method. These results indicate that the method is capable of simulating the complex behavior of viscoelastic bodies in capillaries, such as the motion of red blood cells in blood flows.