Showing papers on "Shear flow published in 2008"

New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear

Abstract: Characterizing purely viscous or purely elastic rheological nonlinearities is straightforward using rheometric tests such as steady shear or step strains. However, a definitive framework does not exist to characterize materials which exhibit both viscous and elastic nonlinearities simultaneously. We define a robust and physically meaningful scheme to quantify such behavior, using an imposed large amplitude oscillatory shear (LAOS) strain. Our new framework includes new material measures and clearly defined terminology such as intra-/intercycle nonlinearities, strain-stiffening/softening, and shear-thinning/thickening. The method naturally lends a physical interpretation to the higher Fourier coefficients that are commonly reported to describe the nonlinear stress response. These nonlinear viscoelastic properties can be used to provide a “rheological fingerprint” in a Pipkin diagram that characterizes the material response as a function of both imposed frequency and strain amplitude. We illustrate our new ...

Shear thickening of cornstarch suspensions as a reentrant jamming transition.

Abstract: We study the rheology of cornstarch suspensions, a non-Brownian particle system that exhibits shear thickening. From magnetic resonance imaging velocimetry and classical rheology it follows that as a function of the applied stress the suspension is first solid (yield stress), then liquid, and then solid again when it shear thickens. For the onset of thickening we find that the smaller the gap of the shear cell, the lower the shear rate at which thickening occurs. Shear thickening can then be interpreted as the consequence of dilatancy: the system under flow wants to dilate but instead undergoes a jamming transition because it is confined, as confirmed by measurement of the dilation of the suspension as a function of the shear rate.

Three-dimensional instabilities in compressible flow over open cavities

Abstract: Direct numerical simulations are performed to investigate the three-dimensional stability of compressible flow over open cavities. A linear stability analysis is conducted to search for three-dimensional global instabilities of the two-dimensional mean flow for cavities that are homogeneous in the spanwise direction. The presence of such instabilities is reported for a range of flow conditions and cavity aspect ratios. For cavities of aspect ratio (length to depth) of 2 and 4, the three-dimensional mode has a spanwise wavelength of approximately one cavity depth and oscillates with a frequency about one order of magnitude lower than two-dimensional Rossiter (flow/acoustics) instabilities. A steady mode of smaller spanwise wavelength is also identified for square cavities. The linear results indicate that the instability is hydrodynamic (rather than acoustic) in nature and arises from a generic centrifugal instability mechanism associated with the mean recirculating vortical flow in the downstream part of the cavity. These three-dimensional instabilities are related to centrifugal instabilities previously reported in flows over backward-facing steps, lid-driven cavity flows and Couette flows. Results from three-dimensional simulations of the nonlinear compressible Navier–Stokes equations are also reported. The formation of oscillating (and, in some cases, steady) spanwise structures is observed inside the cavity. The spanwise wavelength and oscillation frequency of these structures agree with the linear analysis predictions. When present, the shear-layer (Rossiter) oscillations experience a low-frequency modulation that arises from nonlinear interactions with the three-dimensional mode. The results are consistent with observations of low-frequency modulations and spanwise structures in previous experimental and numerical studies on open cavity flows.

Shear banding and yield stress in soft glassy materials.

Abstract: Shear localization is a generic feature of flows in yield stress fluids and soft glassy materials but is incompletely understood. In the classical picture of yield stress fluids, shear banding happens because of a stress heterogeneity. Using recent developments in magnetic resonance imaging velocimetry, we show here for a colloidal gel that even in a homogeneous stress situation shear banding occurs, and that the width of the flowing band is uniquely determined by the macroscopically imposed shear rate rather than the stress. We present a simple physical model for flow of the gel showing that shear banding (localization) is a flow instability that is intrinsic to the material, and confirm the model predictions for our system using rheology and light scattering.

Turbulence in Fluids

Abstract: to Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards "Real World Turbulence".

Tensorial hydrodynamic slip

Abstract: We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as a constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful for extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.

Linear and nonlinear shear flow behavior of monodisperse polyisoprene melts with a large range of molecular weights

Abstract: Shear rheological data for a wide range of nearly monodisperse linear polyisoprene melts are reported herein using the results of linear and nonlinear measurements. The number of entanglements per chain ranges from about 0.5 to 230. In order to extend the range of available frequencies and shear rates the procedure of time-temperature superposition is improved and validated in both the linear and the nonlinear regime. In the linear flow regime a detailed comparison with the tube theory by Likhtman and McLeish [Macromolecules 35, 6332–6343 (2002)] was performed. The overall agreement was found to be satisfactory but several minor disagreements, e.g., at the crossover regime and for the steady-state compliance, were observed and have been discussed. Until now, most nonlinear models for entangled polymers were compared with shear data on solutions. However, the equivalence between solutions and melts is not well established. In this paper the results of a series of nonlinear start-up shear experiments are co...

Shear flow and formation of Nugget zone during friction stir welding of aluminium alloy 5083-O

Abstract: The flow of the shear layer around the tool pin and how it deposits into the cavity at the trailing end of the pin to form the weld Nugget zone during friction stir welding (FSW) had not been fully understood. In this study, FSW experiments were conducted to result in pins broken and embedded in the workpiece of a work-hardened aluminium alloy during FSW, followed by metallography analysis of the weld samples. Evidence has suggested that a portion of the shear zone formed a layer and detached in a trailing–retreating location of the pin, one in each revolution. The shear layer detached from the pin leaving little material to rotate with the pin. The detached layers continued to flow, pushed by the incoming material in the shear zone, filling the stable and forward moving cavity afterward. The velocity of the freshly deposited shear layer was very low in comparison to the pin periphery velocity.

Tensorial hydrodynamic slip

Abstract: We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as an constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful to extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.

Vesicles and red blood cells in shear flow

Abstract: We describe the similarities and the specificities of the behaviour of individual soft particles, namely, drops, lipid vesicles and red blood cells subjected to a shear flow. We highlight that their motion depends in a non-trivial way on the particle mechanical properties. We detail the effect of the presence of a wall with or without wall-particle attractive interaction from a biological perspective.

Turbulence Structures in Flow over Two-Dimensional Dunes

Abstract: This paper presents a large eddy simulation (LES) of turbulent open channel flow over two-dimensional periodic dunes. The Reynolds number R based on the bulk velocity U (bulk) and the maximum flow depth h , is approximately 25,000. The instantaneous flow field is investigated with special emphasis on the occurrence of coherent structures. Instantaneous vortices were visualized and it is shown that separated vortices are formed downstream of the dune crest due to Kelvin–Helmholtz instabilities. Near the point of reattachment the so-called kolk-boil vortex evolves in form of a hairpin vortex. Also present are previously separated vortices, which are convected along the stoss side of the downstream dune and elevated toward the water surface. The existence of near wall streaks which reform shortly after reattachment is also shown. The spacing between two low-speed streaks is very similar to that observed previously over smooth and rough walls. For validation, profiles of the time-averaged velocities, streamwise, and wall-normal turbulent intensities and the Reynolds shear stress calculated by the LES are presented and compared with available laser Doppler velocimetry measurements and overall good agreement is found.

Suspension properties at finite Reynolds number from simulated shear flow

Abstract: This work examines the role of particle-scale inertia in a monodisperse suspension of non-Brownian and neutrally buoyant spherical particles subjected to simple-shear flow. The dimensionless parameters governing the problem are the solid-volume fraction ϕ and the Reynolds number defined Re=ργa2∕μ, where a is the sphere radius, γ is the shear rate, and μ and ρ are the viscosity and density of the fluid, respectively. Using numerical simulations in a wall-bounded domain via the lattice-Boltzmann method, the bulk rheological properties of relative viscosity, normal stress differences, and particle pressure are reported for 0.01⩽Re<5 and 0.05⩽ϕ⩽0.3. The anisotropy in microstructure at finite Re is studied through the pair distribution function g(r). Also presented are the probability density functions of particle velocity fluctuations in gradient and vorticity directions. Comparisons to low Reynolds number theory and simulations are provided wherever possible.

Dynamic motion of red blood cells in simple shear flow

Abstract: A three-dimensional numerical model is proposed to simulate the dynamic motion of red blood cells (RBCs) in simple shear flow. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes which take into account the membrane shear elasticity and the membrane area incompressibility. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to have the same physical properties as the matrix fluid. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the cells are found to carry out a swinging motion, in which periodic inclination oscillation and shape deformation superimpose on the membrane tank treading motion. With the shear rate decreasing, the swinging amplitude of the cell increases, and finally triggers a transition to tumbling motion. This is the first direct numerical simulation that predicts both the swinging motion of the RBCs and the shear rate induced transition, which have been observed in a recent experiment. It is also found that as the mode changes from swinging to tumbling, the apparent viscosity of the suspension increases monotonically.

Settling of an isolated spherical particle in a yield stress shear thinning fluid

Abstract: We visualize the flow induced by an isolated non-Brownian spherical particle settling in a shear thinning yield stress fluid using particle image velocimetry. With Re<1, we show a breaking of the fore-aft symmetry and relate this to the rheological properties of the fluid. We find that the shape of the yield surface approximates that of an ovoid spheroid with its major axis approximately five times greater than the radius of the particle. The disagreement of our experimental findings with previous numerical simulations is discussed.

Swinging and tumbling of elastic capsules in shear flow

Abstract: The deformation of an elastic micro-capsule in an infinite shear flow is studied numerically using a spectral method. The shape of the capsule and the hydrodynamic flow field are expanded into smooth basis functions. Analytic expressions for the derivative of the basis functions permit the evaluation of elastic and hydrodynamic stresses and bending forces at specified grid points in the membrane. Compared to methods employing a triangulation scheme, this method has the advantage that the resulting capsule shapes are automatically smooth, and few modes are needed to describe the deformation accurately. Computations are performed for capsules with both spherical and ellipsoidal unstressed reference shape. Results for small deformations of initially spherical capsules coincide with analytic predictions. For initially ellipsoidal capsules, recent approximate theories predict stable oscillations of the tank-treading inclination angle, and a transition to tumbling at low shear rate. Both phenomena have also been observed experimentally. Using our numerical approach we can reproduce both the oscillations and the transition to tumbling. The full phase diagram for varying shear rate and viscosity ratio is explored. While the numerically obtained phase diagram qualitatively agrees with the theory, intermittent behaviour could not be observed within our simulation time. Our results suggest that initial tumbling motion is only transient in this region of the phase diagram.

Slip at high shear rates.

Abstract: There are contradictory published data on the behavior of fluid slip at high shear rates. Using three methodologies (molecular dynamics simulations, an analytical theory of slip, and a Navier-Stokes-based calculation) covering a range of fluids (bead-spring liquids, polymer solutions, and ideal gas flows) we show that as shear rate increases, the amount of slip, as measured by the slip length, asymptotes to a constant value. The results clarify the molecular mechanics of how slip occurs. Furthermore, they indicate that in this limit, molecular dynamics simulations must accurately account for heat transfer to the solid.

On the linear stability of weakly ionized, magnetized planar shear flows

Abstract: We investigate the effects of ambipolar diffusion and the Hall effect on the stability of weakly ionized, magnetized planar shear flows. Employing a local approach similar to the shearing-sheet approximation, we solve for the evolution of linear perturbations in both streamwise-symmetric and non-streamwise-symmetric geometries using Wentzel-Kramers-Brillouin techniques and/or numerical methods. We find that instability arises from the combination of shear and non-ideal magnetohydrodynamic processes and is a result of the ability of these processes to influence the free energy path between the perturbations and the shear. They turn what would be simple linear-in-time growth due to current and vortex stretching from shear into exponentially growing instabilities. Our results aid in understanding previous work on the behaviour of weakly ionized accretion discs. In particular, the recent finding that the Hall effect and ambipolar-diffusion destabilize both positive and negative angular velocity gradients acquires a natural explanation in the more general context of this paper. We construct a simple toy model for these instabilities based upon transformation operators (shears, rotations and projections) that captures both their qualitative and, in certain cases, exact quantitative behaviour.

Viscoelasticity and shear flow of concentrated, non-crystallizing colloidal suspensions: Comparison with Mode-Coupling Theory

Abstract: We present a comprehensive rheological study of a suspension of thermosensitive particles dispersed in water. The volume fraction of these particles can be adjusted by the temperature of the system in a continuous fashion. Due to the finite polydispersity of the particles (standard deviation: 17%), crystallization is suppressed and no fluid-crystal transition intervenes. Hence, the moduli $G'$ and $G"$ in the linear viscoelastic regime as well as the flow curves (shear stress $\sigma(\dot{\gamma})$ as the function of the shear rate $\dot{\gamma}$) could be measured in the fluid region up to the vicinity of the glass transition. Moreover, flow curves could be obtained over a range of shear rates of 8 orders of magnitude while $G'$ and $G"$ could be measured spanning over 9 orders of magnitude. Special emphasis has been laid on precise measurements down to the smallest shear rates/frequencies. It is demonstrated that mode-coupling theory generalized in the integration through transients framework provides a full description of the flow curves as well as the viscoelastic behavior of concentrated suspensions with a single set of well-defined parameters.

Hydrodynamic lift of vesicles under shear flow in microgravity

Abstract: The dynamics of a vesicle suspension in a shear flow between parallel plates has been investigated under microgravity conditions, where vesicles are only submitted to hydrodynamic effects such as lift forces due to the presence of walls and drag forces. The temporal evolution of the spatial distribution of the vesicles has been recorded thanks to digital holographic microscopy, during parabolic flights and under normal gravity conditions. The collected data demonstrates that vesicles are pushed away from the walls with a lift velocity proportional to , where is the shear rate, R the vesicle radius and z its distance from the wall. This scaling as well as the dependence of the lift velocity upon the vesicle aspect ratio are consistent with the theoretical predictions by Olla (J. Phys. II 7 (1997) 1533).