Shear Flow Of Fluid Research Articles

On control of shear flow of an upper convected Maxwell fluid

AbstractWe consider parallel shear flow of an upper convected Maxwell fluid. A control is available in the form of a body force. The system of equations governing the velocity and shear stress is equivalent to a damped linear wave equation, and well known results imply that it is controllable if the time interval is sufficiently long for waves to propagate back and forth across the uncontrolled region. On the other hand, the issue of controlling normal stresses is far more difficult. If the control is available in the entire flow region, then normal stresses can be controlled, subject to a necessary positive definiteness constraint. On the other hand, if the control is confined to a subinterval, then the normal stresses are not controllable.

Numerical methods for solid particles in particulate flow simulations

The flow motion of solid particle suspensions is a fundamental issue in many problems of practical interest. The velocity field of a such system is computed by a finite element method with a multi-domain approach of two phases (namely a viscous fluid and rigid bodies), whereas the particle displacement is made by a particulate method. We focus our paper on a simple shear flow of Newtonian fluid.

Time‐dependent mixing in stratified Kelvin‐Helmholtz billows: Experimental observations

Quantitative time‐dependent laboratory measurements are made of the irreversible mixing caused by the development, saturation and turbulent breakdown of Kelvin‐Helmholtz (KH) billows in an initially stable two‐layer stratified shear flow of miscible fluids. The measurements are obtained using a light attenuation technique. Irreversible mixing is found to be strongly dependent on the life‐cycle of the flow, in particular the characteristics of large‐scale, quasi‐two‐dimensional billow merging events, which stir the flow and then trigger mixing during turbulent transition.

Unsteady shear flow of fluids with pressure-dependent viscosity

We study the unsteady shear flow of fluids with pressure-dependent viscosity, situated between two parallel horizontal plates with the upper plate moving while the flow is subjected to an oscillating pressure gradient. The dimensionless form of the momentum equation is solved numerically using a central difference approximation for the spatial derivative terms and a forward difference approximation for the time derivative term. In addition to providing the velocity profiles at the midsection between the two plates, the values of shear stress at the lower (stationary) plate for various values of the dimensionless numbers are also plotted.

Theory of steady waves in horizontal flow with a linear velocity profile

The structure and characteristics of nonlinear steady waves on the surface of horizontal shear flow of an ideal homogeneous incompressible fluid of finite depth with a linear velocity profile are studied using two-dimensional theory and the Euler approach. The wave motion is considered irrotational. A modification of the first Stokes method is proposed that allows algebraic calculations of terms of perturbation series. Nonlinear dispersion relations are obtained and analyzed for both upstream and downstream traveling waves.

Simulations of magnetorheological suspensions in Poiseuille flow

Particle-level simulations are conducted to study magnetorheological fluids in plane Poiseuille flow. The importance of the boundary conditions for the particles at the channel walls is examined by considering two extreme cases: no friction and infinite coefficient of friction. The inclusion of friction produces Bingham fluid behavior, as commonly observed experimentally for MR suspensions. Lamellar structures, similar to those reported for electrorheological fluids in shear flow, are observed in the post-yield region for both particle boundary conditions. The formation of these lamellae is accompanied by an increase in the bulk fluid velocity. The slip boundary condition produces higher fluid velocities and thicker lamellar structures.

Shear flow of viscoelastic fluids as a control problem

We consider a homogeneous parallel shear flow of a viscoelastic fluid with a single relaxation time. This problem results in a set of ordinary differential equations for the stresses. In this system, we view the shear rate as a control and consider the problem of steering the system to a given state of stress. For several popular constitutive models, we characterize the stresses which can be reached.

Parallel shear flows of fluids with a temperature dependent viscosity

We investigate whether parallel shear flows of an incompressible Newtonian fluid with a viscosity which depends linearly on temperature is possible in situations where the temperature changes along the flow direction. It is shown that parallel flow is possible only in planar or axisymmetric geometries. These two situations are investigated further. For either a plane channel or a circular pipe, we show that the temperature variation in the flow direction must be exponential.

Effects of body forces on electro- and magnetorheological fluids

Body forces in electro- and magnetorheological fluids are typically small compared to the magnitudes of the field-induced electric and magnetic forces. Using particle-level simulations, we show that these relatively small forces can have large effects on the rheological response of these fluids in shear flow.

Attractor dimension estimate for plane shear flow of micropolar fluid with free boundary

This research is motivated by a problem from lubrication theory. We consider a free boundary problem of a two-dimensional boundary-driven micropolar fluid flow. The existence of a unique global-in-time solution of the problem and the global attractor for the associated semigroup are known. In this paper we estimate the dimension of the global attractor in terms of the given data and the geometry of the domain of the flow by establishing a new version of the Lieb–Thirring inequality with constants depending explicitly on the geometry of the domain. We also obtain some new estimates for the Navier–Stokes shear flows. Copyright © 2005 John Wiley & Sons, Ltd.

Fall velocity of particles in shear flow of drilling fluids

Viscoplastic drilling fluids discharge excavated solid particles in soft soil tunnelling. Deposition of particles in pipes and boreholes should be kept to a minimum. To quantify the fall velocity of particles in shear flow different combinations of fluid properties and particle sizes were tested. It is shown that co-rotation of the particles with the flow and vertical equilibrium of forces determine the fall velocity in these fluids. The use of a Stokes type formula for fall velocity in shear flow of tunnelling fluids is justified.

Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames

We present a new finite element scheme for direct simulation of inertialess particle suspensions in simple shear flows of Oldroyd-B fluids. The sliding bi-periodic frame concept of Lees & Edwards [J. Phys. C 5 (1972) 1921] has been combined with the DEVSS/DG finite element scheme, by introducing constraint equations along the domain boundary. The force-free, torque-free rigid body motion of a particle is described by the rigid-ring problem and implemented by Lagrangian multipliers only on the particle boundary, which allows general treatments for boundary-crossing particles. In our formulation, the bulk stress is obtained by simple boundary integrals of Lagrangian multipliers along the domain and particles. Concentrating on 2-D circular disk particles, we discuss the bulk rheology of suspensions as well as the micro-structural developments through the numerical examples of single-, two- and many-particle problems, which represent a large number of such systems in simple shear flow. We report the steady bulk viscosity and the first normal stress coefficient, from very dilute to highly concentrated systems. The results show shear-thickening behavior for both properties and the common experimental observation of the scaling of the first normal stress to the shear stress has been reproduced. Unlike Newtonian systems, two particles in an Oldroyd-B fluid result in kissing-tumbling-tumbling phenomena: they keep rotating around each other, when they are closely located. Many-particle problems reveal the occurrence of strong elongational flows between separating particles.

Imaging the shear flow of complex fluids using high-frequency ultrasound

Complex fluids show fascinating properties under flow due to the existence of a mesoscopic scale located between the microscopic and the macroscopic scales. For instance, uncoiling of polymer molecules under flow leads to well-documented shear-thinning behaviors. More surprisingly, inhomogeneous flows of visco-elastic fluids are observed in simple shear experiments even at very low Reynolds numbers. Indeed, due to strong coupling between the flow and the fluid microstructure, shear may induce new structural organizations that coexist in the flow leading to shear localization or to shear bands. Whereas classical rheology only yields global data such as the viscosity averaged over the whole sample, the present work is devoted to local ultrasonic velocimetry in sheared complex fluids. A 1D high-frequency (36 MHz) speckle tracking technique is presented that allows the spatio-temporal study of various inhomogeneous unsteady flows. Moreover, preliminary results using a 2D ultrafast flow imaging technique at 12 MHz show that images of the flow can be obtained with an unprecedented temporal resolution.

Local entropy production in turbulent shear flows: a high-Reynolds number model with wall functions

Entropy production in incompressible turbulent shear flows of Newtonian fluids is analysed systematically and incorporated into a CFD code. There are four different mechanisms of entropy production: dissipation in a mean and fluctuating velocity field and heat flux in a mean and fluctuating temperature field. Based on asymptotic considerations wall functions for the four production terms are developed. These wall functions are mandatory when high-Reynolds number turbulent models are used since peak values of entropy production occur in the immediate vicinity of a wall. As an example pipe flow with heat transfer is analysed and compared to results from a direct numerical simulation with special emphasis on the entropy production in the near wall region.

Constitutive equation of co-rotational derivative type for anisotropic-viscoelastic fluid

A constitutive equation theory of Oldroyd fluid B type, i.e. the co-rotational derivative type, is developed for the anisotropic-viscoelastic fluid of liquid crystalline (LC) polymer. Analyzing the influence of the orientational motion on the material behavior and neglecting the influence, the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation, retardation times and anisotropic viscosities are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid. Using the equation for the shear flow of LC polymer fluid, the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al. For the fiber spinning flow of the fluid, the analytical expression of the extensional viscosity is given.

Effect of the orientation of the magnetic field on the flow of a magnetorheological fluid. I. Plane channel

Shear flow and Poiseuille flow of magnetorheological fluids in a plane channel under an inclined magnetic field are studied. The proposed theoretical model is based on stability analysis of chain-like clusters of dipolar magnetic particles. Hydrodynamic and magnetic torque acting on aggregates balances each other such that some misalignment between orientations of chains and the field takes place. Two magnetic field directions symmetric relative to the velocity gradient influence the aggregate behavior in different ways. In one case, the aggregates tend to turn along the flow whereas in the other case, they tend to turn transverse to the flow. The predicted peak value of the yield stress arises for θ0=−π/4 (where θ0 is the clockwise angle between the velocity gradient and the direction of the field) and is 1.8 times the value for θ0=0. If we consider Poiseuille flow between two parallel plates, the velocity gradient, being positive on one side and negative on the other, the stress is no longer symmetric r...

Parallel shear flows of fluids with a pressure-dependent viscosity

We consider parallel shear flows of an incompressible Newtonian fluid with a pressure-dependent viscosity. It is proved that pressure driven parallel flow in the plane is possible only if the dependence of the viscosity on the pressure is linear. In this case, a parallel flow exists for a pipe of arbitrary cross-section. For the special case of axisymmetric flow, we identify three cases for which pressure driven parallel flow exists.

Inertial effects in Brownian motion of a trapped particle in shear flow

The Brownian motion of a bound particle in shear flow is a basic problem in colloid and polymer science. Since the flow has a rotational component, the description cannot be cast in the usual equilibrium statistical mechanics framework of particle motion in a potential well. Instead, the property of local equilibrium may be exploited which necessitates the inclusion of the particle's inertia. Accordingly, a fluctuation dissipation relation is derived which contains a correction due to the interplay between particle inertia and shear flow. The result shows that at very high shear rates, local equilibrium cannot prevail. Having established the relation between drift and diffusion matrices the full stochastic description of the particle dynamics in phase space is obtained from the Langevin equation. Possibilities to measure the predicted inertia effects and implications for computer simulations of complex fluids in shear flows are discussed.

On the Origin of Irregular Structure in Saturn's Rings

We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal forces and the yield stress of these assemblies; the required tensile strength of ~10^5 dyn/cm^2 is consistent with the sticking forces observed in laboratory simulations of frosted ice particles. These assemblies could be the nonlinear outcome of a linear instability that occurs in a rotating fluid disk in which the shear stress is a decreasing function of the shear. We show that a simple model of an incompressible, non-Newtonian fluid in shear flow leads to the Cahn-Hilliard equation, which is widely used to model the formation of structure in binary alloys and other systems.

PTV measurement on interaction between two immiscible droplets and turbulent uniform shear flow of carrier fluid

A flow visualization and a particle-tracking-velocimetry measurement have been conducted for a turbulent water plane Couette flow with two oil droplets in the central region in order to elucidate the effect of secondary flow induced by the droplets on the modification of shear-dominant turbulence. The diameters of these droplets are about 80 times larger than the micro scale of turbulence. The tracer particles coated with fluorescence color and the optical filter for the video camera is found to be effective for diminishing the reflected light from the interface and the moving wall. The experimental results show that zero-velocity regions exist near the interface around the axis because the direction of the wall-normal secondary flow is opposite to that of water moving with the rotating droplets. It is also found that the turbulence intensities in the region between the two droplets and in the small regions for the confluence and stagnation are attenuated due to the weakening of the wall-normal secondary flow particularly in the case where the distance between the centers of the two droplets is twice as long as the droplet diameter.