Light scattering by critical fluids under shear flow

Our theory of critical fluids under shear flow is used to analyze the light scattering experiments of Beysens et al. on a critical fluid mixture flowing through a capillary pipe. The scattered light intensity integrated over frequency, the turbidity, and the transmittency are calculated numerically and found to be in good agreement with the experiments. Various critical amplitudes are also calculated to order ? where ? = 4 ? d, d being the spatial dimensionality of the system. They are found to be considerably different from those near equilibrium in the case of strong shear.     

Yieldlike constitutive transition in shear flow of entangled polymeric fluids

We describe an unexpected constitutive transition in entangled polymer solutions. At and beyond a critical stress, the initial spatially homogeneous and well-entangled sample transforms from its entangled (coiled) state into a fully disentangled (stretched) state over a period during which the resulting shear rate increases in a spatially inhomogeneous fashion. In the mode of controlled shear rate, the sample exhibits a stress plateau over three decades. Flow birefringence and normal stress observations unravel additional features of these flow phenomena.     

Anisotropic thermal conduction in a polymer liquid subjected to shear flow

Flow-induced anisotropic thermal conduction in a polymer liquid is studied using force Rayleigh scattering. Time-dependent measurements of the complete thermal diffusivity tensor, which includes one off-diagonal and three diagonal components, are reported on an entangled polymer melt subjected to a uniform shear deformation. These data, in conjunction with mechanical measurements of the stress, provide the first direct evidence that the thermal conductivity tensor and the stress tensor are linearly related in a deformed polymer liquid.     

Calculation of the intrinsic viscosity for dilute polymer solutions undergoing shear flow

Starting from a set of coupled Langevin equations describing the dynamics of flexible (Gaussian) polymer chains in the presence of hydrodynamic interactions and undergoing a weak shear flow, the stress tensor is determined using Kramers formula. With the aid of renormalization group techniques the steady state intrinsic viscosity is extracted toO() (4–d,d being the spatial dimensionality) and to lowest nontrivial order in the flow strength. Within the preaveraging approximation we find a numerically small effect of shear thinning.     

Nonlocal shear stress for homogeneous fluids

It has been suggested that for fluids in which the rate of strain varies appreciably over length scales of the order of the intermolecular interaction range, the viscosity must be treated as a nonlocal property of the fluid. The shear stress can then be postulated to be a convolution of this nonlocal viscosity kernel with the strain rate over all space. In this Letter, we confirm that this postulate is correct by a combination of analytical and numerical methods for an atomic fluid out of equilibrium. Furthermore, we show that a gradient expansion of the nonlocal constitutive equation gives a reasonable approximation to the shear stress in the small wave vector limit.     

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     

Light scattering by critical fluids in the presence of a uniform shear flow

Some predictions are made on dynamic light scattering by critical fluids in the presence of a shear flow. A Doppler shift broadening is predicted to occur whenever the scattering vector has a component along the direction of flow.     

Pair-correlation function of a fluid undergoing a simple shear flow: Solution of the Kirkwood-Smoluchowski equation

Point of departure is an extended Kirkwood-Smoluchowski (K-S) equation for the pair-correlation function (PCF) which is applicable to a rather large range of shear rates. A solution procedure for the K-S equation in a stationary plane Couette-flow (simple shear flow) is outlined where the vorticity of the flow field is taken into account exactly and a perturbation calculation is made with respect to the deformation rate associated with the symmetric traceless part of the velocity gradient field. The first order solution is obtained explicitly and discussed in details. To obtain specific results, the intermolecular potential is assumed to consist of a hard core and a soft attractive force. Especially for hard spheres we obtain a completely explixit expression for the PCF, which is displayed graphically for some typical cases. It shows the ellipsoidal distrotion of the PCF (or the structure factor) observed by experiments^1,2) at lower shear rates and a twisted distortion at higher shear rates.     

Dynamo quenching due to shear flow

We provide a theory of dynamo (alpha effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the alpha effect is reduced by the shear even in the absence of magnetic field. The alpha effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun.     

An iterative algorithm for computing aeroacoustic integrals with application to the analysis of free shear flow noise

An iterative algorithm is developed for the computation of aeroacoustic integrals in the time domain. It is specially designed for the generation of acoustic images, thus giving access to the wavefront pattern radiated by an unsteady flow when large size source fields are considered. It is based on an iterative selection of source-observer pairs involved in the radiation process at a given time-step. It is written as an advanced-time approach, allowing easy connection with flow simulation tools. Its efficiency is related to the fraction of an observer grid step that a sound-wave covers during one time step. Test computations were performed, showing the CPU-time to be 30 to 50 times smaller than with a classical non-iterative procedure. The algorithm is applied to compute the sound radiated by a spatially evolving mixing-layer flow: it is used to compute and visualize contributions to the acoustic field from the different terms obtained by a decomposition of the Lighthill source term.     

一种计算剪切模量温度系数的方法

采用理论计算与动高压实验相结合的方法，提出了一个计算剪切模量温度系数G′T的新方法.首先用理论方法计算一个中间数据G(PS)，然后再与动高压实验数据G(PH)结合在一起计算出G′T,并针对93钨合金材料进行了计算.计算结果表明剪切模量温度系数G′T开始是随温度和压力变化的，但在高温高压下，它趋近于一常数.对于93钨合金，这个常数约为-004GPa／℃.同时，这也是对Steinberg本构模型中的剪切模量温度系数为常数的一个证明.并且，当把这一常数代入剪切模量温度系数的计算式中，将重新计算出的剪切模量与实验测得的剪切模量结果进行了比较，结果表明二者符合得很好，从而证明了本计算的剪切模量温度系数的正确性. 关键词： 有限应变物态方程 剪切模量温度系数 Steinberg本构模型 动高压实验     

Stable dynamic states at the nematic liquid crystals in weak shear flow

We study stable equilibria of liquid crystals in the flow being at rest and the stable dynamic states for nematic liquid crystals under weak shear flow for the Doi model [M. Doi, S.F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, 1986]. It is first theoretically proven that there is a hysteresis phenomenon in the flow being at rest when the non-dimensional potential intensity among particles changes. Furthermore, in the weak shear flow, we show that there exist many stable dynamic states: flow aligning, tumbing, log-rolling and kayaking, which depend on the initial concentrated orientation of liquid crystal particles. The results are consistent with those of numerical simulation [M.G. Forest, Q. Wang, R. Zhou, The weak shear kinetic phase diagram for nematic polymers, Rheol. Acta 43 (2004) 17-37; M.G. Forest, R. Zhou, Q.Wang, Full-tensor alignment criteria for sheared nematic polymers, J. Rheol. 47 (2003) 105-127] and experimental discoveries [W.R. Burghardt, Molecular orientation and rheology in sheared lyotropic liquid crystalline polymers, Macromol. Chem. Phys. 199 (1998) 471-488; Ch. Gähwiller, Temperature dependence of flow alignment in nematic liquid crystals, Phys. Rev. Lett. 28 (1972) 1554-1556]. Theoretical analysis is reported the first time that the Kayaking state does not circulate around a fixed direction but the asymmetric axis will periodically change.     

Elastic capsules in shear flow: Analytical solutions for constant and time-dependent shear rates

We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent behaviour, have been identified using numerical methods. In this paper, we integrate the equations of motion in the quasi-spherical limit analytically for time-constant and time-dependent shear flow using matched asymptotic expansions. Using this method, we find analytical expressions for the mean tumbling rate in general time-dependent shear flow. The capsule dynamics is studied in more detail when the inverse shear rate is harmonically modulated around a constant mean value for which a dynamic phase diagram is constructed. By a judicious choice of both modulation frequency and phase, tumbling motion can be induced even if the mean shear rate corresponds to the swinging regime. We derive expressions for the amplitude and width of the resonance peaks as a function of the modulation frequency.     

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.     

Variational principle for flow of non-Newtonian fluids

A variational principle is formulated for finding stationary solutions of the equations of motion for an incompressible non-Newtonian fluid with constitutive equation of the Reiner-Rivlin type. The basic functional is related, but not identical to the rate of energy dissipation. It can be used for analyzing the stability of the stationary state against small perturbations.     

Wall shear stress around a stationary gas slug in a downward liquid flow

A single cell of the gas-liquid slug flow was studied. The flow around an immobile gas slug in a downflow of liquid and under its bottom was measured. The values of the wall shear stress and its pulsations were measured by the electrodiffusion method depending on a distance from the slug nose. It is shown that in a liquid film around a slug, turbulent pulsations are damped in comparison with a single-phase liquid flow. In the bottom part of a slug, where vortices are detached, turbulent pulsations exceed significantly the single-phase ones. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 07-08-00405a).     

The effect of shear in self-assembled fluids: The large-N limit

The dynamics of self-assembled fluids subjected to a uniform shear are solved for large-N component model of microemulsions. The dynamical structure factor S(k, t) is studied for quenches from an uncorrelated high temperature state into the Lifshitz line within the microemulsion phase. The structure factor shows multiscaling behavior with characteristic length scales (t7/ ln t)1/6 in the flow direction and (t/ ln t)1/6 in directions perpendicular to the flow. The structure factor shows two parallel ridges in the shear-flow plane.     

Using relative entropy to find optimal approximations: An application to simple fluids

We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist of (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and (b) to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry. As an illustration we apply our method to simple fluids. The “exact” canonical distribution is approximated by that of a fluid of hard spheres. The proposed method first determines the preferred value of the hard-sphere diameter, and then obtains an optimal hard-sphere approximation by a suitably weighed average over different hard-sphere diameters. This leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a numerical demonstration, the radial distribution function and the equation of state for a Lennard-Jones fluid (argon) are compared with results from molecular dynamics simulations.