Showing papers on "Shear flow published in 2002"

Determining the shear viscosity of model liquids from molecular dynamics simulations

Abstract: Several methods are available for calculating shear viscosities of liquids from molecular dynamics simulations. There are equilibrium methods based on pressure or momentum fluctuations and several nonequilibrium methods. For the nonequilibrium method using a periodic shear flow, all relevant quantities, including the accuracy, can be estimated before performing the simulation. We compared the applicability, accuracy and efficiency of this method with two equilibrium methods and another nonequilibrium method, using simulations of a Lennard-Jones fluid and the SPC and SPC/E [(extended) simple point charge] water models.

On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities

Abstract: Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier–Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin–Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin–Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.

Viscosity bifurcation in thixotropic, yielding fluids

Abstract: Most concentrated colloidal suspensions such as cement, drilling fluids, paints, muds, etc., have been considered until now thixotropic fluids with a flow curve of an ideal yield stress fluid. We start by showing from inclined plane tests, intended to determine the yield stress, that these systems in fact exhibit peculiar properties. Unlike ideal yield stress fluids, they stop flowing abruptly below a critical stress, and start flowing at a high velocity beyond a critical stress, which in addition increases with the time of preliminary rest. In order to clarify these features we carried out a complete set of rheometrical tests with a model fluid, a bentonite suspension. Our results show that under controlled stress, in some cases after significant flow, there is bifurcation of the behavior towards either stoppage or rapid shear, depending on the relative values of the imposed and critical stresses. As an immediate consequence, we find that no (homogeneous) steady state flows at a shear rate below a critical value can be obtained. These results can be qualitatively predicted by a simple theoretical model that assumes that the viscosity of the material results from the competition between aging and shear rejuvenation, associated to, respectively, the organization or disorganization of the network of particle interactions. This shows that the flow curve in the steady state of concentrated colloidal suspensions and, more generally, of structured fluids, is strongly affected by their thixotropy.

INTERNAL GRAVITY WAVES: From Instabilities to Turbulence

Abstract: ▪ Abstract We review the mechanisms of steepening and breaking for internal gravity waves in a continuous density stratification. After discussing the instability of a plane wave of arbitrary amplitude in an infinite medium at rest, we consider the steepening effects of wave reflection on a sloping boundary and propagation in a shear flow. The final process of breaking into small-scale turbulence is then presented. The influence of those processes upon the fluid medium by mean flow changes is discussed. The specific properties of wave turbulence, induced by wave-wave interactions and breaking, are illustrated by comparative studies of oceanic and atmospheric observations, as well as laboratory and numerical experiments. We then review the different attempts at a statistical description of internal gravity wave fields, whether weakly or strongly interacting.

Transient phenomena in thixotropic systems

Abstract: A nonlinear rheological model which accounts for the time-dependent elastic, viscous and yielding phenomena is developed in order to describe the flow behavior of thixotropic materials which exhibit yield stress. A key feature of the formulation is a smooth transition from an ‘elastically’ dominated response to a ‘viscous’ response without a discontinuity in the stress–strain curve. The model is phenomenological and is based on the kinetic processes responsible for structural changes within the thixotropic material. As such, it can predict thixotropic effects, such as stress overshoot during start-up of a steady shear flow and stress relaxation after cessation of flow. Thus this model extends a previously proposed viscoplastic model [J. Rheol. 34 (1991) 647] to include thixotropy. An analysis and comparison to experimental data involving oscillatory shear flow are provided to evaluate the accuracy of the model and to estimate the model parameters in a prototype concentrated suspension. The experiments were conducted using a series of concentrated suspensions of silicon particles and silicon carbide whiskers in polyethylene. The data obtained with this experimental system indicated much better agreement between the theory and experiments that obtained in earlier work.

Rheology and microstructure in concentrated noncolloidal suspensions

Abstract: The rheological behavior of a monodisperse suspension of non-Brownian particles undergoing simple shear flow in the presence of a weak interparticle force is studied using accelerated Stokesian dynamics. The availability of a faster numerical algorithm permits the investigation of larger systems (typically of 512 particles), and accurate results for the suspension viscosity, first and second normal stress differences, and the particle pressure are determined as a function of the volume fraction. The system microstructure, expressed through the pair-distribution function, is also studied and it is demonstrated how the resulting anisotropy in the pair-distribution function is correlated with the suspension non-Newtonian behavior. The ratio of the normal to excess shear stress is found to be an increasing function of the volume fraction, suggesting different volume fraction scalings for different elements of the stress tensor. The relative strength and range of the interparticle force is varied and its effec...

Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

Abstract: We present a fully parametrized bead–spring chain model for stained λ-phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions (HI). Parameters are determined from equilibrium experimental data for 21 μm stained λ-phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 μm. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regi...

Severe plastic deformation: simple shear versus pure shear

Abstract: The paper analyzes an effect of deformation mode on structure evolution under severe plastic deformation. From a continuum standpoint, all possible strain states range from pure shear to simple shear and can be described by a single parameter. The microstructure evolution at large strains is linked with successive steps of continuous flow and flow localization. It is shown that simple shear conforms to the optimal deformation mode for development of spatial networks of high angle boundaries and fine grains during flow localization both for monotonic loading and cross loading. Using this approach, different deformation techniques for simple shear processing are considered with the emphasis on equal channel angular extrusion.

Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation

Abstract: Three constitutive laws (Skalak et al.'s law extended to area-compressible interfaces, Hooke's law and the Mooney-Rivlin law) commonly used to describe the mechanics of thin membranes are presented and compared. A small-deformation analysis of the tension-deformation relation for uniaxial extension and for isotropic dilatation allows us to establish a correspondence between the individual material parameters of the laws. A large-deformation analysis indicates that the Mooney-Rivlin law is strain softening, whereas the Skalak et al. law is strain hardening for any value of the membrane dilatation modulus. The large deformation of a capsule suspended in hyperbolic pure straining flow is then computed for several membrane constitutive laws. A capsule with a Mooney-Rivlin membrane bursts through the process of continuous elongation, whereas a capsule with a Skalak et al. membrane always reaches a steady state in the range of parameters considered. The small-deformation analysis of a spherical capsule embedded in a linear shear flow is modified to account for the effect of the membrane dilatation modulus.

Three‐dimensional particle simulations of collisionless magnetic reconnection

Abstract: [1] Three-dimensional (3-D) particle simulations are performed in a double current layer configuration to investigate the stability of current sheets and boundary layers which develop during magnetic reconnection of antiparallel fields in collisionless plasma. The strong current layers that develop near the x line remain surprisingly laminar, with no evidence of turbulence and associated anomalous resistivity or viscosity. Neither the electron shear flow instabilities nor kink-like instabilities, which have been observed in these current layers in earlier simulations, are present. The sharp boundary layers which form between the inflow and outflow regions downstream of the x line are unstable to the lower hybrid drift instability. The associated fluctuations, however, do not strongly impact the rate of reconnection. As a consequence, magnetic reconnection in the 3-D system remains nearly two dimensional.

Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid

Abstract: The nonequilibrium dynamics of a binary Lennard-Jones mixture in a simple shear flow is investigated by means of molecular dynamics simulations. The range of temperature T investigated covers both the liquid, supercooled, and glassy states, while the shear rate γ covers both the linear and nonlinear regimes of rheology. The results can be interpreted in the context of a nonequilibrium, schematic mode-coupling theory developed recently, which makes the theory applicable to a wide range of soft glassy materials. The behavior of the viscosity η(T,γ) is first investigated. In the nonlinear regime, strong shear-thinning is obtained, η∼γ−α(T), with α(T)≃23 in the supercooled regime. Scaling properties of the intermediate scattering functions are studied. Standard “mode-coupling properties” of factorization and time superposition hold in this nonequilibrium situation. The fluctuation-dissipation relation is violated in the shear flow in a way very similar to that predicted theoretically, allowing for the definit...

Large-scale finite-wavelength modulation within turbulent shear flows.

Abstract: We show that turbulent "spirals" and "spots" observed in Taylor-Couette and plane Couette flow correspond to a turbulence-intensity modulated finite-wavelength pattern which in every respect fits the phenomenology of coupled noisy Ginzburg-Landau (amplitude) equations with noise. This suggests the existence of a long-wavelength instability of the homogeneous turbulence regime.

Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re

Abstract: The effect of free rotation on the drag and lift forces on a solid sphere in unbounded linear shear flow is investigated. The sphere Reynolds number, Re=|ur|d/ν, is in the range 0.5–200, where ur is the slip velocity. Direct numerical simulations of three-dimensional flow past an isolated sphere are performed using spectral methods. The sphere is allowed to rotate and translate freely in the shear flow in response to the hydrodynamic forces and torque acting on it. The effect of free rotation is studied in a systematic way by considering three sets of simulations. In the first set of simulations, we study how fast a pure rotational or translational motion of the sphere approaches steady state. The “history” effect of rotational and translational motions are compared. Results at high Re are found to be significantly different from the analytical prediction based on low Re theory. In steady simulations, the sphere is allowed to rotate in a torque-free condition. The torque-free rotation rate and the drag an...

Dynamical phenomena in liquid-crystalline materials

Abstract: ▪ Abstract Recent progress in modeling and simulation of the flow of nematic liquid crystals is presented. The Leslie-Ericksen (LE) theory has been successful in elucidating the flow of low molar-mass nematics. The theoretical framework for the flow of polymeric nematic liquid crystals is still evolving; extensions of the Doi theory capture qualitative features of the flow of polymeric nematics in simple geometries, but these theories have not been shown to predict texture development in flow. Mesoscopic theories for textured materials based on spatial averaging capture only some qualitative features of nonrectilinear liquid-crystalline polymer flow. Interfacial effects in liquid-crystalline systems have begun to receive attention in the context of interfacial viscoelasticity and the dynamics of dispersed liquid-crystalline polymers in immiscible blends.

Measurements of the turbulent energy dissipation rate

Abstract: The one-dimensional surrogate for the dimensionless energy dissipation rate Ce is measured in shear flows over a range of the Taylor microscale Reynolds number Rλ, 70≲Rλ≲1217. We recommend that Ce should be defined with respect to an energy length scale derived from the turbulent energy spectrum. For Rλ≳300, a value of Ce≈0.5 appears to be a good universal approximation for flow regions free of strong mean shear. The present results for Ce support a key assumption of turbulence—the mean turbulent energy dissipation rate is finite in the limit of zero viscosity.

Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

Abstract: . A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.

Shear flow and Kelvin-Helmholtz instability in superfluids.

Abstract: The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.

A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio

Abstract: A numerical algorithm for the linear equation of state is developed for the volume-of-fluid interface-tracking code SURFER++, using the continuous surface stress formulation for the description of interfacial tension. This is applied to deformation under simple shear for a liquid drop in a much more viscous matrix liquid. We choose a Reynolds number and capillary number at which the drop settles to an ellipsoidal steady state, when there is no surfactant. The viscosity ratio is selected in a range where experiments have shown tip streaming when surfactants are added. Our calculations show that surfactant is advected by the flow and moves to the tips of the drop. There is a threshhold surfactant level, above which the drop develops pointed tips, which are due to surfactant accumulating at the ends of the drop. Fragments emitted from these tips are on the scale of the mesh size, pointing to a shortcoming of the linear equation of state, namely that it does not provide a lower bound on interfacial tension. One outcome is the possibility of an unphysical negative surface tension on the emitted drops.

Emergence of intense jets and jupiter's Great Red Spot as maximum-entropy structures

Abstract: We explain the emergence and robustness of intense jets in highly turbulent planetary atmospheres, like that on Jupiter, by a general statistical mechanics approach to potential vorticity patches. The idea is that potential vorticity mixing leads to the formation of a steady organized coarse-grained flow, corresponding to the statistical equilibrium state. Our starting point is the quasi-geostrophic 1-1/2 layer model, and we consider the relevant limit of a small Rossby radius of deformation. Then narrow jets are obtained, in the sense that they scale like the radius of deformation. These jets can be either zonal, or closed into a ring bounding a vortex. Taking into account the beta-effect and a sublayer deep shear flow, we predict organization of the turbulent atmospheric layer into an oval-shaped vortex within a background shear. Such an isolated vortex is centred over an extremum of the equivalent topography, combining the interfacial geostrophic tilt due to the deep shear flow and the planetary beta-effect (the resulting effective beta-effect is locally quadratic). This prediction is in agreement with an analysis of wind data in major Jovian vortices (Great Red Spot and Oval BC).

Small-Angle Neutron Scattering from Viscoelastic Polymer−Clay Solutions

Abstract: The influence of shear on viscoelastic polymer−clay solutions was investigated by means of small-angle neutron scattering (SANS) under shear. SANS was used to measure the shear-induced orientation of polymer and platelets. With increasing shear rate an anisotropic scattering pattern developed. At higher shear rates, the scattering anisotropy increased due to the enhanced orientation of the clay platelets in the shear field. The clay platelets aligned by the flow in an unusual direction, with the surface normal parallel to the vorticity direction. SANS on regular samples (contrast between D2O and solution components) measured the shear-induced orientation of polymer and platelets. However, with contrast matching the orientation of the polymer alone could be detected. With increasing shear rate, clay particles oriented first (SANS on regular samples) and then polymer chains started to stretch (SANS on contrast matched samples). Cessation of shear led to fast recovery, demonstrating the system to be highly e...

Free surface flows of polymer solutions with models based on the conformation tensor

Abstract: A computational method is presented for analyzing free surface flows of polymer solutions with the conformation tensor. It combines methods of computing Newtonian free surface flows [J. Comp. Phys. 99 (1992) 39; V.F. deAlmeida, Gas–Liquid Counterflow Through Constricted Passages, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 1995 (Available from UMI, Ann Arbor, MI, order number 9615160); J. Comp. Phys. 125 (1996) 83] and viscoelastic flows [J. Non-Newtonian Fluid Mech. 60 (1995) 27; J. Non-Newtonian Fluid Mech. 59 (1995) 215]. Modifications are introduced to compute a traceless velocity gradient, to impose inflow boundary conditions on the conformation tensor that are independent of the specific model adopted, and to include traction boundary conditions at free surfaces and open boundaries. A new method is presented for deriving and coding the entries of the analytical Jacobian for Newton’s method by keeping the derivatives of the finite element weighted residual equations with respect to the finite element basis functions in their natural vector and tensor forms, and then by mapping such vectors and tensors into the elemental Jacobian matrix. A new definition of extensional and shear flow is presented that is based on projecting the rate of strain tensor onto the principal basis defined by the conformation tensor. The method is validated with two benchmark problems: flow around a cylinder in a channel, and flow under the downstream section of a slot or knife coater. Regions of molecular stretch—determined by monitoring the eigenvalues of the conformation tensor—and molecular extension and shear rate—determined by projecting the rate of strain dyadic onto the eigenvectors of the conformation tensor—are shown in the flow around a cylinder of an Oldroyd-B liquid. The free surface coating flow between a moving rigid boundary and a parallel static solid boundary from which a free surface detaches is analyzed with several models of dilute and semidilute solutions of polymer of varying degree of stiffness based on the conformation tensor approach [J. Non-Newtonian Fluid Mech. 23 (1987) 271; A.N. Beris, B.J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure, 1st ed., Oxford University Press, Oxford, 1994; J. Rheol. 38 (1994) 769; M. Pasquali, Polymer Molecules in Free Surface Coating Flows, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 2000 (Available from UMI, Ann Arbor, MI, order number 9963019)]. Although the boundary conditions at the static contact line introduce a singularity, that singularity does not affect the computation of flows at high Weissenberg number when a recirculation is present under the static boundary. In this case, a steep layer of molecular stretch develops under the free surface downstream of the stagnation point. Here the polymer aligns with its principal stretching axis parallel to the free surface. When the recirculation is absent, the singularity at the contact line strongly affects the computed velocity gradient, and the computations fail at moderate Weissenberg number irrespective of the polymer model and of whether the polymer is affecting the flow or not.

The influence of developed cavitation on the flow of a turbulent shear layer

Abstract: Developed cavitation in a shear layer was studied experimentally in order to determine the effect that the growth and collapse of cavitation have on the dynamics of shear flows. Planar particle imaging velocimetry (PIV) was used to measure the velocity field, the vorticity, strain rates, and Reynolds stresses of the flow downstream of the cavitating and noncavitating shear layer; the flow pressures and void fraction were also measured. The flow downstream of a cavitating shear flow was compared to the noncavitating shear flow. For cavitating shear layers with void fractions of up to 1.5%, the growth rate of the shear layer and the mean flow downstream of the shear layer were modified by the growth and collapse of cavitation bubbles. The cross-stream velocity fluctuations and the Reynolds stresses measured downstream of the cavitating shear layer were reduced compared to the entirely noncavitating flow. This result is inconsistent with a scaling of the shear stress within the shear flow based on the mean flow. The decrease in the cross-stream fluctuations and Reynolds stresses suggests that the cavitation within the cores of strong streamwise vortices has decreased the coupling between the streamwise and cross-stream velocity fluctuations.

Anisotropic velocity correlation spectrum at small scales in a homogeneous turbulent shear flow.

Abstract: A simple theoretical analysis and direct numerical simulations on ${512}^{3}$ grid points suggest that the velocity correlation spectrum tensor in the inertial subrange of homogeneous turbulent shear flow at high Reynolds number is given by a simple form that is an anisotropic function of the wave vector. The tensor is determined by the rate of the strain tensor of the mean flow, the rate of energy dissipation per unit mass, the wave vector, and two nondimensional constants.

Microstructure from simulated Brownian suspension flows at large shear rate

Abstract: Pair microstructure of concentrated Brownian suspensions in simple-shear flow is studied by sampling of configurations from dynamic simulations by the Stokesian Dynamics technique. Simulated motions are three dimensional with periodic boundary conditions to mimic an infinitely extended suspension. Hydrodynamic interactions through Newtonian fluid and Brownian motion are the only physical influences upon the motion of the monodisperse hard-sphere particles. The dimensionless parameters characterizing the suspension are the particle volume fraction and Peclet number, defined, respectively, as φ=(4π/3)na3 with n the number density and a the sphere radius, and Pe=6πηγa3/kT with η the fluid viscosity, γ the shear rate, and kT the thermal energy. The majority of the results reported are from simulations at Pe=1000; results of simulations at Pe=1, 25, and 100 are also reported for φ=0.3 and φ=0.45. The pair structure is characterized by the pair distribution function, g(r)=P1|1(r)/n, where P1|1(r) is the conditional probability of finding a pair at a separation vector r. The structure under strong shearing exhibits an accumulation of pair probability at contact, and angular distortion (from spherical symmetry at Pe=0), with both effects increasing with Pe. Flow simulations were performed at Pe=1000 for eight volume fractions in the range 0.2⩽φ⩽0.585. For φ=0.2–0.3, the pair structure at contact, g(|r|=2)≡g(2), is found to exhibit a single region of strong correlation, g(2)≫1, at points around the axis of compression, with a particle-deficient wake in the extensional zones. A qualitative change in microstructure is observed between φ=0.3 and φ=0.37. For φ⩾0.37, the maximum g(2) lies at points in the shear plane nearly on the x axis of the bulk simple shear flow Ux=γy, while at smaller φ, the maximum g(2) lies near the compressional axis; long-range string ordering is not observed. For φ=0.3 and φ=0.45, g(2)∼Pe0.7 for 1⩽Pe⩽1000, a slower increase than the g(2)∼Pe predicted theoretically for φ≪1 [Brady and Morris, J. Fluid Mech. 348, 143 (1997)]. Spherical harmonic decomposition of g(r) was performed, and for Pe=1000, expansion convergence is found to be nearly complete when harmonics Ylm to the level l=10 are included.

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

Abstract: 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.

Modeling of oscillatory shear flow of emulsions under small and large deformation fields

Abstract: A model for a mixture of two Newtonian liquids that undergo oscillatory shear flow is presented. The model expresses qualitatively the relationship between the oscillating stress and the oscillating shape of the drops characterized by a second order symmetric tensor called a morphology tensor. The governing equations of the model are solved analytically in small-amplitude oscillatory shear (SAOS) flow and, to the second order of the capillary number, in large-amplitude oscillatory shear (LAOS) flow. Maxwell-type dynamic moduli under SAOS are found to give quite similar predictions as those of Palierne [J. F. Palierne, Rheol, Acta 29, 204 (1990)] and Bousmina [M. Bousima, Rheol, Acta 38, 73 (1999)] emulsion models. Nonlinear dependence of the shear stress and the difference in first normal stress on strain are predicted for LAOS. The predictions of the model are found to be in agreement with the experimental results of Cavallo et al. [R. Cavallo et al., Rheol. Acta (in press, 2002)].