Molecular orientation of a commercial thermotropic liquid crystalline polymer in simple shear and complex flow

In-situ X-ray scattering methods have been used to measure the average degree of molecular orientation in the commercial thermotropic copolyesteramide, Vectra B. Experiments were conducted in both homogeneous shear flow and in extrusion-fed channel flows that provided mixed shear/extensional deformations. In the channel flows, extension has a dramatic effect on the average orientation state in the vicinity of stagnation points or expansions/contractions in cross-sectional area. Of particular note, a temporary increase and subsequent decay in orientation observed in a 4:1 slit-contraction flow provides additional indirect evidence supporting the hypothesis that Vectra B exhibits director tumbling. This is consistent with results from other fully aromatic copolyesters but contrasts with findings in model thermotropes incorporating flexible spacers. Thus, it seems that the stiffer backbone of commercial main chain LCPs is the main feature which, apparently, leads to tumbling. Measurements of average molecular orientation in transient shear flows show some connections with the corresponding mechanical response, but fail to show the distinctive characteristics that have previously been associated with either tumbling or aligning in LCPs using similar procedures. These experiments might be adversely affected by the comparatively slow rate of data acquisition, which leads to lengthy experiments in which the sample is more prone to degradation.     

Orientation and rheology of rodlike particles with weak Brownian diffusion in a second-order fluid under simple shear flow

An analysis of particle orientation in a dilute suspension of rodlike particles in a second-order fluid was performed to examine the effects of the elasticity of the fluid and of weak Brownian diffusion of the particle on its orientation. Distributions of particle orientation under a simple shear flow with rate of shearg have been obtained as a function of a single nondimensional parameter, ^* =/r _e ² (D/g), which combines the effects of the particle aspect ratior _e , the weak fluid elasticity, and the weak Brownian rotation diffusion coefficientD of the particle. In the limit of larger _e , when the fluid elasticity is strong enough to overcome the rotational diffusion effect on the particle motion, most of the particles will orient close to the vorticity axis. A new shear-thinning mechanism of the shear viscosity of such systems is predicted by the theory.     

Comparative rheological studies of polyamide-6 and its low loaded nanocomposite based on layered silicates

We study some rheological properties for polyamide-6 (PA-6) and a low concentrated clay nanocomposite melt based on polyamide-6 and montmorillonite. Simple shear experiments, carried out for both the neat system and nanocomposite at two different temperatures, include start up shear flows, stress relaxation after cessation of steady flow and oscillatory shear. The dynamic data for the neat PA-6 matrix differ markedly from that of the nanocomposite system, even if it has very low nanofiller concentration. Thermal stability of the PA-6 matrix imposed many restrictions on rheological studies of our systems. Therefore an experimental window was established via rheological and thermal characterization of the materials, wherein the polymer matrix was confirmed to be thermally stable. The relaxation spectra for both polymer systems were determined from linear dynamic experiments using the Pade-Laplace procedure. A rough estimation of nanocomposite volume fraction at percolation allowed us to attribute the occurrence of extra (relative to the neat polymer) Maxwell modes observed for the nanocomposite to the formation of a particulate network above the percolation threshold.     

Coarse-grained model of entangled polymer melts in non-equilibrium

A coarse-grained model developed for entangled polymeric systems and calibrated to represent melts in equilibrium (Rakshit, Picu, J Chem Phys 125:164907(1)–(10), 2006) is used to model shear flows. The model is a hybrid between multimode and mean-field representations: chain inner blobs are constrained to move along the chain backbone and the end blobs are free to move in 3D and continuously redefine the diffusion path for the inner blobs. Therefore, contour length fluctuations and reptation are captured. Constraint release is implemented by tracing the position of chain ends and performing a local relaxation of the chain backbones once end retraction is detected. This algorithm takes advantage of the multi-body nature of the model and requires no phenomenological parameters other than the length of an entanglement segment. The model is used to study start-up and step strain shear flows and reproduces features observed experimentally such as the overshoot during start-up shear flow, the Lodge–Meissner law, the monotonicity of the steady state shear stress with the strain rate, and shear thinning at large . These simulations are performed in conditions in which using a fully refined model of the same system would have been extremely computationally demanding or simply impossible with the current methods.     

Application of the integral diffusion equations to the investigation of turbulent transport

In recent years there have appeared several experimental studies [1–5] which have shown that there are cases of turbulent flow with an asymmetric distribution of the flow velocity and in which at the point where the velocity derivative is zero the turbulent shear stress is not zero. This raises the question of the connection of the Reynolds stress tensor with the characteristics of the average flow. The relationships used in the usual mixing length theory connect the shear stress with the local value of the flow velocity derivative and are not consistent with the experimental results mentioned above. These relationships are based on the assumption that the mixing length is small in comparison with the characteristic length of the flow. Experiment shows that this assumption is not justified [6].Thus, turbulent diffusion refers to the case of diffusion with a large mean free path. In addition to the concept of gradient diffusion, there is also the concept of bulk convection or integral diffusion [10], which means a transfer mechanism in which the shear stress is not expressed in terms of the velocity gradient. The generalization of mixing length theory proposed in [11–14] is based on the very simple kinetic equation which was used for the examination of turbulent transfer problems in [8] and which is encountered in the treatment of transport problems in gases, neutron diffusion, and radiative energy transfer.The proposed generalization of mixing length theory employs an analogy with the indicated processes and permits the derivation of formulas which are valid for large mean free paths. In the case of small mean free paths the obtained relationships lead to the relationships for diffusion in a continuous medium and, in particular, to the relationships of the Prandtl mixing length theory. The integral diffusion model is a phenomenological semiempirical theory in which empirical constants and several hypotheses common in mixing length theory are used. A very general analysis of the expression for the shear stress leads to the conclusion that if the flow is asymmetric over a distance comparable with the mixing length the points at which the velocity derivative and the turbulent shear stress are zero do not coincide [12]. Hence, it is to be hoped that the integral diffusion model will allow treatment of the above questions, which cause difficulty in the case of ordinary mixing length theory. Incompressible turbulent flow is considered.     

Two-scale semiempirical theory of turbulent boundary layers and jets

To characterize the turbulence of boundary layers in the energy-bearing interval of wave numbers several turbulence scales are sometimes used (for example, [1, 2]). In particular, the universality of the semiempirical model of turbulence [2] can be extended in this way. A turbulence model with one equation (energy balance of the turbulence) has been constructed and used [3–6] and it has been established that the number of problems that can be solved for a universal choice of the values of the empirical coefficients increases appreciably if not one but two turbulent scales are used. In the present paper, it is shown that the introduction of a second scale makes it possible to take into account the interaction of shear layers in flows with two shear layers (for example, a channel or jet), and also to take into account the influence of turbulence of an external flow on a boundary layer. The interaction of shear layers is taken into account in theories containing a transport equation for the turbulent frictional stress _t (for example, [7]), in which the essence of the interaction reduces to diffusion of _t from layer to layer. In the present paper, a predominant volume interaction effect is assumed. It takes the form of a difference between the interaction of large-scale vortices with a shear deformation motion in flows with one and two shear layers, and also in the presence of turbulence in an external flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 17–25, November–December, 1982.     

Spots and turbulent domains in a model of transitional plane Couette flow

A review of the globally subcritical transition to turbulence in shear flows is presented, with an emphasis on the cases of plane and circular Couette flows (pCf and cCf, respectively). A Swift–Hohenberg-like model is next proposed to interpret the behavior of plane Couette flow in the vicinity of its global stability threshold. We present results of numerical simulations supporting this proposal and helping us to raise good questions about the growth and decay of intermittent turbulent domains in this precise context, and more generally about the coexistence of laminar flow and turbulence in other spatio-temporally intermittent flows. PACS 47.27.-i, 47.54.-r, 05.45.-a     

Oscillatory and simple shear flows of a flour-water dough: a constitutive model

We reported some dynamic and viscometric data on an Australia strong flour-water dough. In oscillatory shear flow experiments, we found the linear viscoelastic strain limit is extremely low, of O(10^–3), consistent with other published data on doughs. The relaxation spectrum derived from the dynamic data is broad, indicating the blend nature of dough. In the start-up of a simple shear flow, we found the shear stress increases nonlinearly with time to a peak value and then decreases rapidly, with no steady-state response. The concept of steady-state viscosity is not very meaningful here, unless the strain at which the measurements are taken is also specified. The stress peaks are strain-rate dependent; but they occur at a strain of O(10), for the strong flour/water dough used, over four decades of strain rates. The experimental data were used to construct a phenomenological model for dough, consisting of an hyperelastic term (representing the elastic gluten network of permanent cross-linked long chain polymers), and a viscoelastic contribution (representing the suspension of starch globules and other long-chain components in dough that are not parts of the permanent cross-linked gluten network). The model predictions compared favourably with experimental data in oscillatory and shear flows.     

Orienting properties of discotic nematic liquid crystals in Jeffrey-Hamel flows

The orienting properties of incompressible discotic nematic liquid crystals for creeping flows between converging and diverging planar walls (Jeffrey-Hamel) are analyzed using the Leslie-Ericksen theory. The dependence of director orientation on the reactive parameter and the flow kinematics is presented. Closed form stationary solutions for the director orientation are found when elastic effects are neglected. Stationary numerical solutions for the velocity and director fields using the full Leslie-Ericksen theory are presented. The director field in converging flow is characterized by azimuthal (radial) centerline orientation, by being asymmetric with respect to the azimuthal (radial) direction, and by having an allowed orientation range that spans two half-quadrants (full quadrants). In the limiting case of perfectly flat disk ( –) the flow-induced director orientation in converging flow is the azimuthal direction, while in diverging flow the director rotates by a full n radians. By reducing the vertex angle between the walls to vanishingly small values, converging flow solutions properly reduce to those of flow between parallel plates, but diverging flows are expected to lead to a new instability.     

Modelling of the pressure-velocity correlation in turbulence diffusion

Most current computations of trubulent flows with second-moment closure adopt the diffusion models which neglect the effect of pressure-velocity correlation. In the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the second-moment closures. Through the relation between and , established by Lumley, we propose here a new turbulence diffusion model which takes into consideration the pressure effect. Applications of this new model in the computation of shearless turbulence mixing layer and plane and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.     

Polydomain model predictions of liquid crystalline polymer orientation in mixed shear/extensional channel flows

 The Larson-Doi (LD) polydomain model is used to simulate orientation development along the centerline of slit-expansion and slit-contraction flows of liquid crystalline polymers (LCPs). Orientation is computed using the LD structural evolution equations, subject to an imposed velocity field that accounts for the spatial variation of both shear and extension rates characteristic of this class of flows. Computed axial distributions of orientation averaged through the sample thickness are qualitatively similar to birefringence and X-ray scattering measurements of molecular orientation in similar flows of lyotropic and thermotropic LCPs. In slit-expansion flows, the simulations predict a 90^∘ flip in orientation direction near the midplane due to transverse stretching in the expansion region. Far away from the midplane where shear gradients dominate, orientation remains primarily along the flow direction. Within the LD model, tumbling and flow aligning materials respond in a qualitatively similar manner to mixed shear and extension, although tumbling materials are systematically more susceptible to the effects of extension. Received: 22 October 1999/Accepted: 13 January 2000     

A novel approach to high shear rate rheometry

A procedure is presented for converting torque-speed plots obtained from experiments using discs rotating rapidly in shear thinning materials into information on the viscosity function. The method is based on an exact boundary-layer solution for the power-law model and on the concept of pseudo-similarity of non-Newtonian flows. It enables the rheological behaviour to be evaluated at very high shear rates. Experimental data for concentrated shear-thinning kaolin suspensions at shear rates from 400 to 2 10⁵s^–1 are compared with values of the viscosity function obtained from customary viscometers of the Brookfield and Couette type.     

Feasability study of wall shear stress imaging using microstructured surfaces with flexible micropillars

A new optical sensor technique based on a sensor film with arrays of hair-like flexible micropillars on the surface is presented to measure the temporal and spatial wall shear stress field in boundary layer flows. The sensor principle uses the pillar tip deflection in the viscous sublayer as a direct measure of the wall shear stress. The pillar images are recorded simultaneously as a grid of small bright spots by high-speed imaging of the illuminated sensor film. Two different ways of illumination were tested, one of which uses the fact that the transparent pillars act as optical microfibres, which guide the light to the pillar tips. The other method uses pillar tips which were reflective coated. The tip displacement field of the pillars is measured by image processing with subpixel accuracy. With a typical displacement resolution on the order of 0.2 m, the minimum resolvable wall friction value is _w20 mPa. With smaller pillar structures than those used in this study, one can expect even smaller resolution limits.     

Experiments on the nonlinear stages of excited and natural planar jet shear layer transition

An experimental investigation focusing on the nonlinear stages of planar jet shear layer transition is presented. Experimental results for transition under both natural and low level artificial forcing conditions are presented and compared. The local spectral dynamics of the jet shear layer is modeled as a nonlinear system based upon a frequency domain, second-order Volterra functional series representation. The local linear and nonlinear wave coupling coefficients are estimated from time-series streamwise velocity fluctuation data. From the linear coupling coefficient, the mean dispersion characteristics and spatial growth rates may be obtained. With the estimation of the nonlinear power transfer function, the total, linear and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and linear-quadratic coupling bicoherency, the local system output power may be completely characterized and the effect of nonlinearity on local mean flow distortion assessed. Particular attention is focused upon quantifying the linear and nonlinear power transfer that characterizes the different stages of the jet shear layer transition for both natural and excited flows. The quadratic power transfer that occurs with deviation from the perfect resonant wavenumber matching condition is clarified as is the dynamic mechanism of subharmonic resonance. The mechanism of spectral broadening is described and contrasted for natural and artificially excited flows.     

Rheological influences on the consolidation process of soils

Summary Consolidation of soils occurs when the imposed loading produces strains accompanied by the slow escape of pore-water from the voids between the particles. This straining is accompanied by rolling and sliding of the particles into a more dense packing.Terzaghi realized that the plastic resistance to deformation, in the case of clay consolidation, was so small that the consolidation process could be considered as a hydrodynamic problem; in this way, he used simplifying assumptions which led to the development of a time-settlement relationship for clays based entirely on the escape of pore-water; this is a linear equation.Consolidation theory gives a unique stress-strain-time relationship — provided that the strains are not sufficiently large to overcome the shear strength of the soil, with the consequence that rheological considerations govern the deformation process.In the case of soft soils, especially organic soils, the volume of water expelled during consolidation is very large and the shear strength of the soils small. The experimental results indicated that, at low stresses, the strain rates were low indicating plastic deformation of the material with the process governed by the hydrodynamic theory — while at higher stresses, the strain rates increased causing the soil to flow in viscous form and the rheological behaviour predominated over the hydrodynamic process.A further complication to theTerzaghi theory arises with soft soils having high water contents; during the consolidation process, the permeability is reduced as the particles assume a more dense packing.A Flow-Loading parameter was obtained for the soils which incorporated the changes in permeability as a function of loading. This parameter was incorporated in the consolidation theory and provided a non-linear second-order differential equation which can predict the settlement-time behaviour as a function of both loading and changing soil properties.With 6 figures     

Using the anisotropy of magnetic susceptibility to infer flow-induced orientation of anisotropic particles: feasibility and sensitivity

In this paper, the use of anisotropy of magnetic susceptibility (AMS) measurements has been investigated in order to check the sensitivity of this technique versus the flow conditions. The orientation of anisotropic magnetic particles during the flow of a polystyrene $/$ magnetite blend through a capillary rheometer has been studied. Thanks to the magnetic properties of the magnetite, AMS measurements are possible. Different values of the filler concentration, viscosity, and shear rate were used. It is shown that the AMS technique is able to detect accurately particle orientation and that sensitivity decreases when increasing the concentration of magnetite grains. In addition, the rectangular-shaped sample imposed by the rheological device does not affect measures of AMS significantly. The results give reasons to consider that the measure of AMS is an accurate and sensitive method to access the mean local rheological behavior in filled or non-filled systems containing anisotropic tracers.     

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.     

Velocity and spanwise vorticity measurements in an excited mixing layer of a plane jet

The mixing layer of a plane jet was subjected to periodic weak excitation at two different frequencies corresponding to shear layer mode (St =0.012) and preferred mode (St _D =0.36). The nozzle exit boundary layer was identical for the unexcited and excited flows. Measurements of mean velocity, longitudinal and lateral velocity fluctuations, Reynolds shear stress and spanwise component of fluctuating vorticity were made over a longitudinal distance x/D of 6 for both the unexcited and the excited flows. Even weak excitation was observed to influence the development of the mixing layer. Under shear layer mode of excitation, the width of the layer and longitudinal turbulence level decrease compared to the naturally developing (unexcited) flow whereas preferred mode of excitation results in increase in the width and turbulence levels. The rms spanwise vorticity showed an increase for shear layer mode of excitation whereas the preferred mode of excitation resulted in a decrease compared to the values in an unexcited flow. Spectra of velocity and vorticity fluctuations exhibited subharmonic peaks, suggesting the possible occurrence of vortex pairing in both unexpected and excited flows. The influence of excitation is found to decrease as x/D increases and is not significant at x/D=6.This study was partly supported by a grant from the Research Grant Council, Hong Kong. The support and hospitality of the Department of Mechanical Engineering, University of Hong Kong are gratefully acknowledged by SR. The authors are grateful the referees for valuable comments.     

Axisymmetric Vortex Fluid Flow in a Long Elastic Tube

A mathematical model for axisymmetric eddy motion of a perfect incompressible fluid in a long tube with thin elastic walls is proposed. Necessary and sufficient conditions for hyperbolicity of the system of equations of motion for flows with monotonic radial velocity profiles are formulated. The propagation velocities of the characteristics of the system under study and the characteristic shape of this system are calculated. The existence of simple waves continuously attached to a given steady shear flow is proved. The group of transformations admitted by the system is found, and submodels that determine invariant solutions are given. By integrating factorsystems, new classes of exact solutions of equations of motion are found.