Transition to turbulence in a shear flow

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.     

Solitons and defects in nematic liquid crystals under a simple shear flow and in a static external magnetic field

Under a simple shear flow and in a static external magnetic field, the production of defects in the director-aligning regime of nematic liquid crystals has been investigated in terms of the Leslie-Ericksen theory. The equation of motion of the nematic director, which conforms to the driven over-damped sine-Gordon equation, has a soliton solution of the amplitude w. We show that the stationary state with the director uniformly oriented at a Leslie angle is only a metastable state and the potential, which governs the motion of the director, has a nmnber of stable stationary states. For a strong magnetic field, the higher energy barrier between the stable and unstable states leads the director to be locked along the magnetic field direction. However, at the appropriate shear rate and magnetic field the defects, which appear as a stable solitary solution, can be nucleated from a uniformly aligned nematic liquid crystal. We have calculated the stationary travelling velocity of the solitary waves and the distance between a pair of defects.     

Flow of wet granular materials

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number Le=eta(s)gamma / sigma, the ratio of lubrication to frictional forces. Le defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant and the velocity profile has a universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.     

Shear-thinning-induced chaos in taylor-couette flow

The effect of weak shear thinning on the stability of the Taylor-Couette flow is explored for a Carreau-Bird fluid in the narrow-gap limit. The Galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow, becomes lower as the shear-thinning effect increases. That is, shear thinning tends to precipitate the onset of Taylor vortex flow. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows, which coincides with the onset of a supercritical bifurcation. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, a Hopf bifurcation emerges, which exists only for shear-thinning fluids.     

Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow

We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert et al., Phys. Rev. E 64, 051302 (2001)]. It is demonstrated that both the Bagnold scaling and the framework of kinetic theory are applicable in the bulk, which allows us to extract the constitutive relations from simulation data. The detailed comparison of our data with the kinetic theory shows quantitative agreement for the normal and shear stresses, but there exists a slight discrepancy in the energy dissipation, which causes a rather large disagreement in the kinetic theory analysis of the flow.     

A composite model of the plastic flow of amorphous covalent materials

A model based on the data available in the literature on the computer simulation of amorphous silicon has been proposed for describing the specific features of the plastic flow of amorphous covalent materials. The mechanism of plastic deformation involves homogeneous nucleation and growth of inclusions of a liquidlike phase under external shear stress. Such inclusions experience plastic shear, which is modeled by glide dislocation loops. The energy changes associated with the nucleation of these inclusions at room and increased temperatures have been calculated. The critical stress has been found, at which the barrierless nucleation of inclusions becomes possible. It has been shown that this stress decreases with an increase in temperature. According to the calculations, the heterogeneous (homogeneous) plastic flow of an amorphous material should be expected at relatively low (high) temperatures. Above the critical stress, the homogeneous flow is gradually replaced by the heterogeneous flow.     

Simulation of thermoelastic properties of solids in the framework of an ensemble of anharmonic oscillators

It has been shown that, in a classical ensemble of anharmonic oscillators, the mean value of the oscillator coordinate is a classical parameter in the sense that the statistical sum of the ensemble satisfies, to the second order in the anharmonicity constant, the stationary condition with respect to this parameter. This stationary condition is equivalent to the classical condition for the balance of external and internal forces acting on the oscillator. This equivalence is justified by the fact that the statistical sum, which is stationary with respect to the mean oscillator coordinate, agrees within this accuracy with the usual statistical sum of independent anharmonic oscillators. After introducing the classical parameter into a large thermodynamic system, the energy balance under the mechanical deformation of the system is realized through the exchange between two scale levels: the energy of oscillations at the microlevel and the macroscopic potential energy of deformation of the sample as a whole.     

Lyapunov Instability of the Boundary-Driven Chernov–Lebowitz Model for Stationary Shear Flow

We report on the computation of full Lyapunov spectra of the boundary-driven Chernov–Lebowitz model for stationary planar shear flow. The Lyapunov exponents are calculated with a recently developed formalism for systems with elastic hard collisions. Although the Chernov–Lebowitz model is strictly energy conserving, any phase-space volume is subjected to a contraction due to the reflection rules of the hard disks colliding with the walls. Consequently, the sum of Lyapunov exponents is negative. As expected for an inhomogeneously driven system, the Lyapunov spectra do not obey the conjugate pairing rule. The external driving makes the system less chaotic, which is reflected in a decrease of the Kolmogorov–Sinai entropy if the driving is increased.     

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     

Asymptotic stability of stationary states in the wave equation coupled to a nonrelativistic particle

We consider the Hamiltonian system consisting of a scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subjected to an external potential. The stationary solutions of the system are a Coulomb type wave field centered at those particle positions for which the external force vanishes. It is assumed that the charge density satisfies the Wiener condition, which is a version of the “Fermi Golden Rule.” We prove that in the large time approximation, any finite energy solution, with the initial state close to the some stable stationary solution, is a sum of this stationary solution and a dispersive wave which is a solution of the free wave equation.     

非均匀剪切流场中液晶聚合物微观结构的无网格模拟

基于宏观流场控制方程与微观分子取向扩散方程耦合的微-宏观双尺度模型,率先采用无网格方法对液晶聚合物在非均匀剪切流场中的微观结构进行了模拟研究.无网格方法精度高、稳定性好的特性保证了模拟结果的可靠性.研究了Deborah数对平板Poiseuille流中液晶聚合物微观结构的影响,预测出非均匀剪切流场中液晶聚合物的一种单一结构和五种复合结构.指出在复合结构的过渡区,分子运动具有不稳定性,可能产生瑕疵. 关键词： 液晶 微观结构 双尺度 无网格     

Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.     

Nonlinear dynamics of transport barrier relaxations in tokamak edge plasmas

A new mechanism for intermittent relaxations of transport barriers is found by using three dimensional fluid turbulence simulations. This mechanism is generic since it only requires a stationary E x B shear flow. It is found here that if the flow shear increases faster than linearly with heating power, the relaxation frequency decreases with power. An analytical study reveals that this nonlinear dynamics is governed by a time delay for effective velocity shear stabilization.     

Fluctuation background due to incompressible disturbances in laminar shear flows

The incompressible fluctuation background in laminar shear flows with a smooth velocity profile is investigated. Concrete calculations are performed for parallel Couette flow using nonmodal analysis of the linear dynamics of the disturbances. Nonmodal analysis makes it possible to grasp phenomena that could not be grasped in the early investigations, and thereby makes it possible to represent the fluctuation background in a completely new light: In incompressible shear flows the spatial spectral energy density of the fluctuation background is anisotropic, and furthermore in certain regions of wave-number space it is higher than that of the thermal noise. It is also shown that in the stationary state of the nonequilibrium system studied there exists a new, indirect channel for thermalization of the energy of the mean flow—energy is constantly transferred from the mean flow into the spatial Fourier harmonics of vortex pertubations and ultimately into heat. Possible manifestations of the fluctuation background described in this paper are listed. Zh. éksp. Teor. Fiz. 112, 1664–1674 (November 1997)     

Non-linear oscillatory rheological properties of a generic continuum foam model: Comparison with experiments and shear-banding predictions

The occurrence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarios in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e. the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary whose amplitude is history dependent and thus depends on the sample preparation.     

Low-frequency potential structures in a nonuniform dusty magnetoplasma

The linear and nonlinear properties of a modified convective cell (MCC) in a nonuniform dusty magnetoplasma with a perpendicular plasma flow are investigated. It is shown that the free energy of the equilibrium plasma flow can drive the MCC at nonthermal levels. By choosing some specific profiles for the sheared plasma flow and the dust number density, we analyze the eigenvalue equation for deducing the growth rate and the threshold of a convective mode instability which arises due to its interaction with the shear plasma flows. Our analytical results show that a Rayleigh-type instability sets in provided that the characteristic width of the flow does not exceed a certain value. On the other hand, the nonlinear equation, which governs the dynamics of the nonlinearly interacting convective modes, admits stationary solutions in the form of a vortex chain associated with zonal flows, as well as tripolar and global vortices. The relevance of our investigation to a laboratory experiment is discussed.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Impact of the external energy supply to the shock layer region on the shock wave parameters

A system of equations describing supersonic gas flow in the presence of a heat source near the shock front is obtained. Relations between the gas parameters in disturbed and undisturbed regions, which generalize the classical Hugoniot-Rankine relations, are derived. Formulas for calculation of the flow parameters in the presence of an energy supply to the shock layer region are presented. It is demonstrated that there exists a critical intensity of energy supply at which the system of equations of the conservation laws for the gas parameters on both sides of the shock layer possesses no stationary solution.     

An analysis of flow-induced miscibility of polymer blends

The phase behavior of blends of polystyrene and poly(vinyl methyl ether) undergoing shearing flow was examined. Experiments conducted at a constant level of flow-induced strain found that such flow elevates the phase boundary and pro-motes miscibility. In the framework of the Cahn-Hilliard model for spinodal decomposition, an expression was developed which predicts the effect of an external flow field on the spinodal. The basis for this expression is the minimization of strain energy in a two-component polymer system that is in a thermodynamic state near its phase-separation point. The zero shear viscosities of the blends were measured and demonstrated to be an indication of one- or two-phase flow.