Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution

 The non-monotonic shear flow of a viscoelastic equimolar aqueous surfactant solution (cetylpyridinium chloride-sodium salicylate) is investigated rheologically and optically in a transparent strain-controlled Taylor Couette flow cell. As reported before, this particular wormlike micellar solution exhibits first a shear thinning and then a pronounced shear-thickening behavior. Once this shear-thickening regime is reached, a transient phase separation/shear banding of the solution into turbid and clear ring-like patterns orientated perpendicular to the vorticity axis, i.e., stacked like pancakes, is observed (Wheeler et al. 1998; Fischer 2000). The solution exhibit several unique features as no induction period of the shear induced phase, no structural build-up at the inner rotating cylinder, jumping pancake structure of clear and turbid ringlike phases, and oscillating shear stresses appear once the pancake structure is present. According to our analysis this flow phenomenon is not purely a mechanical or rheological driven hydrodynamic instability but one has to take into account structural changes of the oriented micellar aggregates (flow induced non-equilibrium phase transition) as proposed by several authors. Although this particular flow behavior and the underlying mixture of shear induced phases and mechanical instabilities is not fully understood yet, some classification characteristics based on a recent theoretical approach by Schmitt et al. (1995) and Porte et al. (1997) where a strong coupling between the flow instability (non-homogeneous flow profile due to the bands) and the structural changes causes the observed transient phenomena can be derived. In reference to the presented model the observed orientation of the rings is typical for complex fluids that undergo a spinodal phase separation coupled with a thermodynamic flow instability. In contrast to other shear banding phenomena, this one is observed in parallel plate, cone-plate, and Couette flow cell as well as under controlled stress and controlled rate conditions. Therefore, it adds an additional aspect to the present discussion on shear banding phenomena, i.e., the coupling of hydrodynamics and phase transition of rheological complex fluids. Received: 8 January 2001 Accepted: 15 May 2001     

A numerical simulation of suspension flow using a constitutive model based on anisotropic interparticle interactions

We report a Brownian configuration field implementation of a recent constitutive equation for suspensions, reported by Phan-Thien et al. 1999. The numerical method is a hybrid technique, which combines a modification of the Brownian configuration field method described by Hulsen et al. 1997 and the adaptive viscosity split stress formulation proposed by Sun et al. 1996. The implementation is used to examine the flow past a sphere in a tube. The relative viscosity derived from the drag force/sedimentation velocity agrees well with a well-known empiricism. In addition, the ratio of the pressure force to the drag on the sphere seems to be weakly dependent on the volume fraction, and is somewhat higher than Brenner's results of 1962, which were derived for Newtonian fluids. Received: 5 April 1999/Accepted: 27 September 1999     

Experimental study of flow past a square cylinder at high Reynolds numbers

 Measurements of two-components of velocity in the wake of a square cylinder using a hot-wire anemometer are reported. Two Reynolds numbers, namely 8700 and 17,625, have been considered. The measurements were carried out in a low-speed, low-turbulence wind tunnel. Benchmark experiments at much lower Reynolds numbers show good agreement between the present experiments and published results. At higher Reynolds numbers, the experimental data reveal anticipated trends in terms of wake recovery and turbulence decay. Both velocity and velocity fluctuations show symmetry about the wake axis. The experimental data have been compared with the large eddy simulation (LES) calculation reported by Wang et al. [University of Illinois at Urbana – Champaign (1996) Report CFD 96-03] and LDV measurements of Lyn et al. [J Fluid Mech (1995) 304: 285–319]. The agreement among the three sets is generally acceptable in terms of the time-averaged velocity components, but not the velocity fluctuations. The turbulence fluctuations in the present experiments are seen to be lower than in the referred work. The differences have been traced to factors such as the aspect ratio, blockage ratio and upstream turbulence. Experiments with increased upstream turbulence did show a reduction in the discrepancy between the present experiments and the published data. An assessment of the experimental data in terms of physical mechanisms revealed that (a) streamwise normal stresses were correlated with the vortex centers, and (b) the turbulence kinetic energy profiles are similar to the turbulence shear stress. Spectral analysis of the velocity signals was carried out in the present work. Energy transfer from the mean flow to the streamwise velocity fluctuation was confirmed in the near wake. A redistribution of the kinetic energy between the streamwise and transverse components of velocity over a longer distance downstream was subsequently observed. Received: 17 May 1999/Accepted: 29 December 1999     

Squeeze flow between plane and spherical surfaces

Experiments are described in which a constant force F squeezed a fluid, either between two parallel circular plates, or between a plate and convex spherical lens. Newtonian fluids obeyed the relation of Stefan (1874) for plates, and the relation of Adams et al. (1994) for plate and lens. The non-Newtonian yield stress fluids Brylcreem, Laponite and Sephadex were squeezed between plates of various diameter D to attain a stationary separation h. Only for separations greater than h ^* (which depended on the fluid) did Brylcreem and Laponite obey the relation F/D ³ ∝ h ⁻¹ of Scott (1931) and give a yield stress in agreement with the vane method. For Sephadex the dependence of F/D ³ on h disagreed with Scott's relation, but varied as h ^−5/2 for h > 0.6 mm and h ^−3/2 for h < 0.6 mm. On rotating one plate in its plane the yield stress fluids at a fixed F suffered a marked decrease of h. This, and the existence of h ^*, are discussed in terms of the soft glassy material model of Sollich et al. (1997) and Sollich (1998). Brylcreem and Laponite were squeezed between a plate and lenses of various curvature and their yield stress obtained using the relation of Adams et al. (1994) was compared with measurements by plate-plate squeeze-flow and vane methods. Received: 12 April 2000 Accepted: 26 October 2000     

Global Attractor for a Wave Equation with Nonlinear Localized Boundary Damping and a Source Term of Critical Exponent

The paper addresses long-term behavior of solutions to a damped wave equation with a critical source term. The dissipative frictional feedback is restricted to a subset of the boundary of the domain. This paper derives inverse observability estimates which extend the results of Chueshov et al. (Disc Contin Dyn Syst 20:459–509, 2008) to systems with boundary dissipation. In particular, we show that a hyperbolic flow under a critical source and geometrically constrained boundary damping approaches a smooth finite-dimensional global attractor. A similar result for subcritical sources was given in Chueshov et al. (Commun Part Diff Eq 29:1847–1876, 2004). However, the criticality of the source term in conjunction with geometrically restricted dissipation constitutes the major new difficulty of the problem. To overcome this issue we develop a special version of Carleman’s estimates and apply them in the context of abstract results on dissipative dynamical systems. In contrast with the localized interior damping (Chueshov et al. Disc Contin Dyn Syst 20:459–509, 2008), the analysis of a boundary feedback requires a more careful treatment of the trace terms and special tangential estimates based on microlocal analysis.      

Water in water emulsions: phase separation and rheology of biopolymer solutions

Partially miscible polymers in solution do not separate into two macroscopic phases; in general they behave as viscoelastic fluids containing droplets of the minority phase dispersed into a continuous majority phase (emulsion type systems). Both phases contain two types of polymers and solvent in variable amounts. With time, the smaller droplets tend to merge into larger ones and eventually sediment. Provided the time stability of the emulsion is long enough and the size of the droplets does not exceed a few tens of microns, the emulsion can be characterized by conventional rheological methods as an effective medium, both in the linear regime (viscoelasticity) and under flow. We investigated a ternary system composed by two biopolymers, a protein (caseinate) and a polysaccharide (alginate) in aqueous solution and established an analogy between these phase separated solutions and immiscible blends of polymers. We first characterized the biopolymers and determined the phase diagram at room temperature that we interpreted within the framework of the Edmond and Ogston model. For the rheological investigations, starting with an initial composition of the system, we separated the two phases by centrifugation. The individual phases were then characterized through their viscoelastic and flow behaviors. By recombining variable amounts of these phases, thereby varying only their volume fractions, we were able to prepare stable emulsions with constituents having constant compositions. The effect of shear on these emulsions was investigated. After different shearing protocols, the size of the droplets was derived from the Palierne model and the flow curves were analyzed. The droplet sizes were compared to the critical capillary numbers and coalescence predictions. The flow curves and the dynamic viscosities of the emulsions were interpreted with a model recently proposed by Kroy et al. that extends earlier work of Oldroyd (1953), Schowalter et al. (1968), and Frankel and Acrivos (1970). Received: 11 September 2000/Accepted: 21 December 2000     

Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow

An algorithm is derived for calculating flow-induced birefringence using a bead-spring model with and without excluded volume effects. The simulation results for the bead-spring model compare well with experimental results for stress and birefringence in extensional flows of dilute solutions of polystyrene molecular weight 2 million in a filament-stretching device in both “theta” and “good” solvents (Orr and Sridhar 1999; Sridhar et al. 2000). In a “good” solvent, both stress and birefringence rise much more rapidly with strain than in a “theta” solvent, making extensional rheology a very sensitive indicator of solvent quality. Received: 7 December 1999 Accepted: 23 May 2000     

Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel

An experimental study was conducted of incompressible, moderate Reynolds number flow of air over heated rectangular blocks in a two-dimensional, horizontal channel. Holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in self- sustained oscillatory flow. Experiments were conducted in the laminar, transitional and turbulent flow regimes for Reynolds numbers in the range from Re = 520 to Re = 6600. Interferometric measurements were obtained in the thermally and fluiddynamically periodically fully developed flow region on the ninth heated block. Flow oscillations were first observed between Re = 1054 and Re = 1318. The period of oscillations, wavelength and propagation speed of the Tollmien–Schlichting waves in the main channel were measured at two characteristic flow velocities, Re = 1580 and Re = 2370. For these Reynolds numbers it was observed that two to three waves span one geometric periodicity length. At Re = 1580 the dominant oscillation frequency was found to be around 26 Hz and at Re = 2370 the frequency distribution formed a band around 125 Hz. Results regarding heat transfer and pressure drop are presented as a function of the Reynolds number, in terms of the block-average Nusselt number and the local Nusselt number as well as the friction factor. Measurements of the local Nusselt number together with visual observations indicate that the lateral mixing caused by flow instabilities is most pronounced along the upstream vertical wall of the heated block in the groove region, and it is accompanied by high heat transfer coefficients. At Reynolds numbers beyond the onset of oscillations the heat transfer in the grooved channel exceeds the performance of the reference geometry, the asymmetrically heated parallel plate channel. Received on 26 April 2000     

Linear and nonlinear gravity-capillary water waves with a soluble surfactant

Naturally occurring soluble-surfactant slicks influence the properties of water waves. This paper describes results from wave tank experiments involving a soluble surfactant, and linear and nonlinear gravity- capillary waves. Instantaneous surface deflections were measured using optical techniques to determine the damping, phase speed, and the frequency content of the waves for wavemaker frequencies from 4 to 22 Hz. Measured linear-wave phase speed and damping agree well with existing theory at surfactant concentrations away from that leading to maximum damping. Under conditions leading to nonlinear waves, an as-yet-unexplained subharmonic wave with one-sixth the wavemaker frequency was found only with soluble surfactant present. Received: 3 September 2000/ Accepted: 8 August 2000     

An assessment of pressure drop and void fraction correlations with data from two-phase natural circulation loops

 Void fraction and pressure drop correlations play an important role in predicting the performance of natural circulation loops. Hence an assessment of the commonly used and often cited correlations for pressure drop and void fraction has been carried out with data from natural circulation loops. This assessment considered 33 void fraction correlations and 14 pressure drop correlations. The void fraction correlations were initially tested against the various limiting conditions. Only 14 correlations were found to satisfy at least two limiting conditions (i.e., at x = 0; α = 0 and at x = 1; α = 1) and were assessed against the data. This assessment showed that the Chexal et al. (1996) correlation is better than all the others considered. The assessment of pressure drop correlations were carried out with the Chexal et al. (1996) correlation for void fraction and Saha-Zuber model for the onset of subcooled boiling. This assessment showed that most correlations give predictions close to each other. Received on 17 January 2000     

Relaxation time spectra of star polymers

 The linear viscoelastic data for model star polymer melts with varying functionality and arm molecular weight were represented by means of a modified Baumgaertel-Schausberger-Winter (BSW) relaxation time spectrum, based on data analysis with the parsimonius model of Baumgaertel et al., reported in 1990. In the case of high arm functionality, the second slow terminal relaxation observed by Vlassopoulos et al. in 1997, was captured with a straightforward extension of the BSW model using broad cut-off functions. This study represents a potentially promising attempt to extend the applicability of this representation of viscoelastic data to more complex architectures, beyond simple linear chains which are characterized by self-similarity. The casting of linear viscoelastic data into spectra allows the exploration of star polymer behavior. It is a necessary step in preparation for large scale complex flow calculations in conjunction with constitutive models and for material databases. Received: 18 November 1998/Accepted: 12 August 1999     

Design of an oscillating flow apparatus for the study of low Reynolds number particle dynamics

An apparatus was designed and built to explore the effects of transient flow fluctuations on the dynamic behavior of particles in low Reynolds number (LRN) flows. While many experiments have been performed on LRN particle flows, relatively few have investigated periodic oscillations on the flow dynamics. The apparatus was oscillated at a frequency of 10 Hz with peak-to-peak displacements on the order of 10 mm. Particles of varying densities and diameters were placed into the oscillating flow. Video images of the particle dynamics were captured with both a personal video camcorder and high-speed digital camera. In parallel, computations were performed for the particle system in order to validate the experimental method and apparatus. Received: 25 February 2000/Accepted: 5 September 2000     

Dynamics of shear aligning of nematic liquid crystal monodomains

The equations of linear and angular momentum for nematic liquid crystals have been described with Ericksen's transversely isotropic fluid [TIF] model and solved for start-up of shear flow at constant rate and varying initial alignment conditions. An analytical solution for the rotation provides predictions of the nematic director which closely agree with experimental results of Boudreau et al. (1999), supporting the validity of Ericksen's TIF model. The solution is limited to flows where the effects of director gradients are negligible. Received: 13 September 1999/Accepted: 24 January 2000     

Sources of error and other difficulties in extensional rheometry revisited: commenting and complementing a recent paper by T. Schweizer

In a recent paper by T. Schweizer (Schweizer 2000) a large collection of experimental difficulties associated with the measurement of uniaxial extensional properties of polymer melts in the Rheometrics RME extensional rheometer is described. The work covers topics such as sample preparation for different types of polymers (sensitive or not to moisture) supplied in different shapes (pellets or powder), the necessary corrections to the tensile force, and the ever-present problem of determining the true strain rates of the experiments. The aim of the present paper is to complement and expand the work of Schweizer by pointing out other experimental problems that are the cause of errors in extensional rheometry of polymer melts. The present analysis, however, is not exclusively dedicated to the RME, unlike that of Schweizer, being directed instead to a general class of apparatus that work according to the principle of stretching a constant length sample between pairs of counter-rotating rollers; for example, all the data shown was obtained with our own extensional rheometer (Maia et al. 1999). This work will focus on the importance of the correct choice of the supporting media used for sample heating and support, the importance of end-effects, and the influence that the griping surfaces can have in such measurements. Received: 23 February 2001 Accepted: 15 May 2001     

The effect of roughness on separating flow over two-dimensional hills

Two new experimental data sets for turbulent flow over a steep, rough hill are presented. These include detailed laser Doppler anemometry measurements obtained at the separation and reattachment points and, in particular, within the reverse flow region on the lee side of the hill. These results allow the development of a new parametrization for rough wall boundary layers and validate the use of Stratford’s solution for a separating rough flow. The experiments were conducted in a water channel for two different Reynolds numbers. In the first set of rough wall experiments, the flow conditions and the hill shape are similar to those presented in Loureiro et al. (Exp. Fluids, 42:441–457, 2007a) for a smooth surface, leading to a much reduced separation region. In the second set of experiments, the Reynolds number is raised ten times. The region of separated flow is then observed to increase, but still to a length shorter than that recorded by Loureiro et al. (Exp. Fluids, 42:441–457, 2007a). Detailed data on mean velocity and turbulent quantities are presented. To quantify the wall shear stress, global optimization algorithms are used. The merit function is defined in terms of a local solution that is shown to reduce to the classical law of the wall far away from a separation point and to the expression of Stratford at a separation point. The flow structure at the separation point is also discussed.     

The Giesekus fluid in ω–D form for steady two-dimensional flows

Numerical results of the simulation of the Giesekus model in ω–D form, which has previously been introduced in Part I of this study, are presented. The model has been applied to the flow of a concentrated polymer solution through a planar 3.97:1 contraction. To obtain an accurate fit of the rheological properties of the fluid a four-mode model is used. The predictions of the numerical simulations are directly compared with the experimental results published by Quinzani et al. in 1994. For the velocity fields a good quantitative agreement is reached, especially in the upstream channel. Regarding the shear stress and first normal stress difference, qualitative predictions of the experimental profiles are obtained.     

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the approaching flow to separate and form a dynamically rich horseshoe vortex system (HSV) in the junction of the obstacle with the wall. The Reynolds number of the flow (Re) is one of the important parameters that control the rich coherent dynamics of the vortex, which are known to give rise to low-frequency, bimodal fluctuations of the velocity field (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). We carry out detached eddy simulations (DES) of the flow past a circular cylinder mounted on a rectangular channel for Re = 2.0 × 10⁴ and 3.9 × 10⁴ (Dargahi, Exp Fluids 8:1–12, 1989) in order to systematically investigate the effect of the Reynolds number on the HSV dynamics. The computed results are compared with each other and with previous experimental and computational results for a related junction flow at a much higher Reynolds number (Re = 1.15 × 10⁵) (Devenport and Simpson, J Fluid Mech 210:23–55, 1990; Paik et al., Phys Fluids 19:045107, 2007). The computed results reveal significant variations with Re in terms of the mean-flow quantities, turbulence statistics, and the coherent dynamics of the turbulent HSV. For Re = 2.0 × 10⁴ the HSV system consists of a large number of necklace-type vortices that are shed periodically at higher frequencies than those observed in the Re = 3.9 × 10⁴ case. For this latter case the number of large-scale vortical structures that comprise the instantaneous HSV system is reduced significantly and the flow dynamics becomes quasi-periodic. For both cases, we show that the instantaneous flowfields are dominated by eruptions of wall-generated vorticity associated with the growth of hairpin vortices that wrap around and disorganize the primary HSV system. The intensity and frequency of these eruptions, however, appears to diminish rapidly with decreasing Re. In the high Re case the HSV system consists of a single, highly energetic, large-scale necklace vortex that is aperiodically disorganized by the growth of the hairpin mode. Regardless of the Re, we find pockets in the junction region within which the histograms of velocity fluctuations are bimodal as has also been observed in several previous experimental studies.     

The origin of stress-oscillation damping during startup and reversal of torsional shearing of nematics

Using a controlled-temperature shear cell mounted on a polarizing microscope, we observe the behavior of nematic 4,4-n-octyl-cyanobiphenyl (8CB) during start-up and reversal of shearing in a torsional parallel-plate geometry and correlate this behavior with rheological measurements. During the start-up, a sequence of birefringent rings, or twist walls, are observed that originate at the sample edge and propagate radially inward. Each twist wall is a thin region in which the director is twisted out of the plane of the velocity and velocity-gradient directions. The radial variation of in-plane orientation can be explained by the variation of strain in the parallel-plate device. A high Ericksen-number solution of the Leslie-Ericksen equations predicts a damped oscillatory shear stress response which agrees quantitatively with the measured stress oscillations out to an edge strain of around 50. The damping of the stress oscillations is due to the nonuniformity of strain in the parallel-plate geometry. On reversal of the flow, if the strain, , is smaller than about 500 units, the damping of stress oscillations is reversed; this correlates with an outward radial migration of twist walls. When > 500, disclinations nucleate and spoil the reversibility of stress damping.Deceased     

Pseudo turbulence in PIV breaking-wave measurements

 The particle image velocimetry (PIV) technique was employed to measure the instantaneous velocity distribution under nonbreaking and breaking water waves. The corresponding turbulence intensity was calculated by the ensemble average of repeated measurements. The pseudo turbulence found was large enough to affect the accuracy of the turbulence measurements. We follow Prasad et al.'s (1992) approach to demonstrate that the pseudo turbulence is related to the bias error, which is the discrepancy between the true position of the particle image and the position calculated from the pixel array data with inadequate pixel resolution. To reduce the bias error (or the pseudo turbulence), we first calculate it from a turbulence-free flow with the same experimental set-up as that used for the targeted experiments (i.e., we use the same size of field of view, seeding particles, seeding density, lens aperture, and laser wavelength in both experiments). Then we minimize the bias error from the turbulence measurements in the actual experiments. To demonstrate the procedure, the evolution of a breaking wave is investigated. Received: 30 January 1998/Accepted: 28 October 1999     

Airfoil flow instabilities induced by background flow oscillations

 The effect of background flow oscillations on transonic airfoil (NACA 0012) flow was investigated experimentally. The oscillations were generated by means of a rotating plate placed downstream of the airfoil. Owing to oscillating chocking of the flow caused by the plate, the airfoil flow periodically accelerated and decelerated. This led to strong variations in the surface pressure and the airfoil loading. The results are presented for two angles of attack, α=4° and α=8.5°, which correspond to the attached and separated steady airfoil flows, respectively. Received: 6 June 2000 / Accepted: 18 October 2001