Tank treading and unbinding of deformable vesicles in shear flow: determination of the lift force

Deformation and tank-treading motion of flaccid vesicles in a linear shear flow close to a wall are quantitatively studied by light microscopy. Velocities of bounded vesicles obey Goldman's law established for rigid spheres. A progressive tilt and a transition of unbinding of vesicles are evidenced upon increasing the shear rate, gamma;. These observations disclose the existence of a viscous lift force, F(l), depending on the viscosity eta of the fluid, the radius R of the vesicle, its distance h from the substrate, and a monotonous decreasing function f(1-v) of the reduced volume v, in the following manner: F(l) = eta(gamma)(R(3)/h)f(1-v). This relation is valid for vesicles both close to and farther from the substrate.     

NMR velocimetry studies of the steady-shear rheology of a concentrated hard-sphere colloidal system

NMR velocimetry has been used to observe the steady-shear rheological behaviour of a concentrated suspension of hard-sphere like 370 nm diameter PMMA core-shell latex particles at the volume fraction Φ = 0.46, the liquid core of the spheres rendering possible NMR observation of the particles themselves. Rheological measurements in a cone-and-plate geometry indicate that when aged (i.e. left at rest for two weeks), the material exhibits yield stress behaviour at very low shear rates. For shear rates greater than 1 s ^{- 1} a transition to liquid-like behaviour was observed, leading to a rejuvenated fluid state which exhibits shear-thinning behaviour over a wide range of shear rates. A similar yield stress behaviour was reflected in NMR velocimetry measurements in a Couette geometry, where the solid-to liquid transition could be clearly observed. Under steady-state flow, the fluid state inside the radius at which yield stress was observed, exhibited shear-thinning behaviour with a power law exponent n slowly approaching unity with increasing shear rate. This behaviour has some similarities with a model of Derec et al. in which aging and rejuvenation effects compete. Substantial wall slip was observed both at the inner and at the outer wall, an effect which disappeared as the shear rate was increased. No radial particle migration from the high-shear region at the inner wall was observed.     

Pair-correlation function of a fluid undergoing a simple shear flow: Solution of the Kirkwood-Smoluchowski equation

Point of departure is an extended Kirkwood-Smoluchowski (K-S) equation for the pair-correlation function (PCF) which is applicable to a rather large range of shear rates. A solution procedure for the K-S equation in a stationary plane Couette-flow (simple shear flow) is outlined where the vorticity of the flow field is taken into account exactly and a perturbation calculation is made with respect to the deformation rate associated with the symmetric traceless part of the velocity gradient field. The first order solution is obtained explicitly and discussed in details. To obtain specific results, the intermolecular potential is assumed to consist of a hard core and a soft attractive force. Especially for hard spheres we obtain a completely explixit expression for the PCF, which is displayed graphically for some typical cases. It shows the ellipsoidal distrotion of the PCF (or the structure factor) observed by experiments^1,2) at lower shear rates and a twisted distortion at higher shear rates.     

Flow phase diagrams for concentration-coupled shear banding

After surveying the experimental evidence for concentration coupling in the shear banding of wormlike micellar surfactant systems, we present flow phase diagrams spanned by shear stress Σ (or strain rate ) and concentration, calculated within the two-fluid, non-local Johnson-Segalman (d-JS-φ) model. We also give results for the macroscopic flow curves Σ(ˉ,ˉφ) for a range of (average) concentrations ˉφ. For any concentration that is high enough to give shear banding, the flow curve shows the usual non-analytic kink at the onset of banding, followed by a coexistence “plateau” that slopes upwards, dΣ/dˉ > 0. As the concentration is reduced, the width of the coexistence regime diminishes and eventually terminates at a non-equilibrium critical point [Σ_c,ˉφ_c,ˉ_c]. We outline the way in which the flow phase diagram can be reconstructed from a family of such flow curves, Σ(ˉ,ˉφ), measured for several different values of ˉφ. This reconstruction could be used to check new measurements of concentration differences between the coexisting bands. Our d-JS-φ model contains two different spatial gradient terms that describe the interface between the shear bands. The first is in the viscoelastic constitutive equation, with a characteristic (mesh) length l. The second is in the (generalised) Cahn-Hilliard equation, with the characteristic length ξ for equilibrium concentration-fluctuations. We show that the phase diagrams (and so also the flow curves) depend on the ratio r ≡ l /ξ, with loss of unique state selection at r = 0. We also give results for the full shear-banded profiles, and study the divergence of the interfacial width (relative to l and ξ) at the critical point. Received: 20 December 2002 / Accepted: 24 April 2003 / Published online: 11 June 2003 RID="a" ID="a"e-mail: physf@irc.leeds.ac.uk RID="b" ID="b"e-mail: p.d.olmsted@leeds.ac.uk     

Does the Chapman-Enskog expansion for sheared granular gases converge?

The fundamental question addressed in this Letter is whether or not the partial Chapman-Enskog expansion P(xy)= [see text for formula] of the shear stress converges for a gas of inelastic hard spheres. By using a simple kinetic model it is shown that, in contrast to the elastic case, the above series does converge, the radius of convergence increasing with inelasticity. It is argued that this paradoxical conclusion is not an artifact of the kinetic model and can be understood in terms of the time evolution of the scaled shear rate in the uniform shear flow.     

Flow of wet granular materials

The transition from frictional to lubricated flows of a dense suspension of non-Brownian particles is studied. The pertinent parameter characterizing this transition is the Leighton number Le=eta(s)gamma / sigma, the ratio of lubrication to frictional forces. Le defines a critical shear rate below which no steady flow without localization exists. In the frictional regime the shear flow is localized. The lubricated regime is not simply viscous: the ratio of shear to normal stresses remains constant and the velocity profile has a universal form in both frictional and lubricated regimes. Finally, a discrepancy between local and global measurements of viscosity is identified, which suggests inhomogeneity of the material under flow.     

Dynamics of a tethered polymer in shear flow

The dynamics of a single polymer tethered to a solid surface in a shear flow was observed using fluorescently labeled DNA chains. Dramatic shear enhanced temporal fluctuations in the chain extension were observed. The rate of these fluctuations initially decreased for increasing shear rate gamma; and increased above a critical gamma;. Simulations revealed that these anomalous dynamics arise from a continual recirculating motion of the chain or cyclic dynamics. These dynamics arise from a coupling of the chain velocity in the flow direction to thermally driven fluctuations of the chain in the shear gradient direction.     

HEAT AND MASS TRANSFER AND WALL SHEAR STRESS IN VERTICAL GAS-LIQUID FLOW

Results of an experimental investigation of heat and mass transfer and wall shear stress at gas-liquid flow in a vertical tube are presented. Local wall shear stress and mass transfer coefficients were measured by an electrochemical method. Experiments were performed in the range of Reynolds number variation with respect to liquid Rc_i, = 8.5 × 10³-5.4 × 10⁴, gas Re_g = 3 × 10³-1.4 × 10⁵, pressure 0.1-1 MPa. The relationship between heat and mass transfer and wall shear at gas-liquid flows is shown to exist. The results of measuring heat and mass transfer coefficients are generalized by formulas applied to calculate heat and mass transfer in single-phase turbulent flow.     

Strengthened opposition control for skin-friction reduction in wall-bounded turbulent flows

An opposition control scheme with strengthened control input is proposed and tested in turbulent channel flows at friction Reynolds number Re_τ = 180 by direct numerical simulations. When the detection plane is located at less than 20 wall units, the drag reduction rate can be greatly enhanced by increasing the control amplitude parameter. The maximum drag reduction rate achieved in the present study is around 33%, which is much higher than the best value of 25% reported in literature. The strengthened control can be more efficient to attain a given drag reduction rate. Based on the total shear stress at the virtual wall established between the real wall and the detection plane by the control, a new friction velocity is proposed and the corresponding coordinate transform is made. Scaled by the proposed friction velocity, the wall-normal velocity fluctuation and the Reynolds shear stress of the controlled flows are collapsed well with those of the uncontrolled flow in the new coordinate. Based on the similarity, a relation between drag reduction rate and the effectiveness of the virtual wall is deduced, which disclosed that the elevation and residual Reynolds shear stress at the virtual wall are the key parameters to determine the drag reduction rate. The conclusion are also validated at Re_τ = 395 and 590. The decrease of the drag reduction rate with the increase of the Reynolds number is attributed to the enhanced residual Reynolds shear stress at the virtual wall.     

Influence of bubbly clusters on the characteristics of the two-phase gas-liquid flow in a flat channel

Results of experimental investigation of a bubbly gas-liquid flow in horizontal and weakly inclined (from −20° to +20°) flat channel are presented. These measurements were carried out within the 0.2–1 m/s range of superficial velocities and volumetric gas flow rate ratio of up to 0.2. The hydrodynamic structure was measured by the electrochemical method with application of wall shear stress and conductivity microprobes. During the experiments signals of shear stress on the upper channel wall and local gas flow rate ratio were recorded completely. After numerical treatment of recorded signals the profiles of local gas flow rate ratio were obtained, average shear stress and its relative mean square pulsations on the upper channel wall were determined. It is shown that under the studied regimes the bubbles are grouped into clusters, and the bubbly flow is presented by alternation of bubbly clusters and single-phase liquid with separate bubbles and without them. Average wall shear stress and absolute shear stress pulsations in the range of bubbly clusters and beyond them were determined. Histograms of probability density distribution were obtained for the wall shear stress on the upper wall. It is shown that average shear stress and absolute pulsations in clusters are significantly higher than those in the flow zone free from bubbles. The work was financially supported by the Russian Foundation for Basic Research (No. 07-08-00405a).     

A universal criterion for plastic yielding of metallic glasses with a (T/Tg) 2/3 temperature dependence

Room temperature (TR) elastic constants and compressive yield strengths of approximately 30 metallic glasses reveal an average shear limit gammaC=0.0267+/-0.0020, where tauY=gamma CG is the maximum resolved shear stress at yielding, and G the shear modulus. The gammaC values for individual glasses are correlated with t=TR/Tg , and gamma C for a single glass follows the same correlation (vs t=T/Tg). A cooperative shear model, inspired by Frenkel's analysis of the shear strength of solids, is proposed. Using a scaling analysis leads to a universal law tauCT/G=gammaC0-gammaC1(t)2/3 for the flow stress at finite T where gammaC0=(0.036+/-0.002) and gammaC1=(0.016+/-0.002).     

Wall Shear Stress and Heat Transfer of Downward Bubbly Flow at Low Flow Rates of Liquid and Gas

The effect of suppression of turbulence in a downward bubbly flow and its impact on the wall shear stress and heat transfer are discussed. Measurements were carried out for Reynolds numbers Re = 5000–10000, which were calculated from the velocity of the liquid phase and with the gas volumetric flow rate ratio β = 0–0.05. Data on the size of bubbles detaching from the edges of an array of capillaries in a liquid flow are given. The influence of the disperse phase dimensions on the wall shear stress and heat transfer is discussed. It is shown that change in the size of the dispersed phase can lead to both intensification and deterioration of heat transfer as compared with a single-phase flow at constant flow rates of liquid and gas at the channel inlet. The cause of the heat transfer deterioration is “laminarization” of the flow in the near-wall region. An analysis of the spectral power of signals is given.     

Crystal structure and interaction dependence of the crystal-melt interfacial free energy

We examine via molecular simulation the dependence of the crystal-melt interfacial free energy gamma on molecular interaction and crystal structure (fcc vs bcc) for systems interacting with inverse-power repulsive potentials, u(r)=epsilon(sigma/r)(n), 6< or =n< or =100. Both the magnitude and anisotropy of gamma are found to increase as the range of the potential increases. Also we find that gamma(bcc)相似文献   

Near-field laser Doppler velocimetry measures near-wall velocities

A new near-wall velocimetry technique is proposed, based on evanescent wave dynamic light scattering, which allows for the measurement of near-wall velocity profile (characterized by an apparent slip velocity and a shear rate) with a resolution of tens of nanometers. A full theoretical expression of the correlation function is derived for the case of linear flow with negligible Brownian motion. The technique is demonstrated for latex spheres dispersed in water-glycerol mixtures.     

Shear viscosity for inelastic hard spheres

The hydrodynamic equations of the Enskog theory for inelastic hard spheres is considered as a model for rapid flow granular fluids at finite densities. A detailed analysis of the shear viscosity of the granular fluid has been done using homogenous cooling state (HCS) and uniform shear flow (USF) models. It is found that shear viscosity is sensitive to the coefficient of restitution α and pair correlation function at contact. The collisional part of the Newtonian shear viscosity is found to be dominant than its kinetic part.     

Magnetic resonance visualisation of single- and two-phase flow in porous media.

Three-dimensional MRI and flow visualisation data are presented for single and two-phase flow occurring within packed beds of glass spheres. The initial motivation for this work has been to understand the operation of fixed-bed reactors used in many chemical processing operations; these systems also serve as model porous media in which to investigate the effect of the structure of a pore space on the flow phenomena occurring within it. For the case of single-phase flow, maps of the liquid shear rate components are calculated from which forces on individual spheres within the bed are obtained. The velocity histogram for flow transverse to the direction of superficial flow is exponential in both negative and positive directions. This form of the velocity histogram implies an exponential form for the displacement propagator, in contrast to the Gaussian distribution obtained by pulsed gradient spin echo measurements. This difference arises because the spatially resolved velocity imaging sequence measures only the average velocity within each voxel and is insensitive to the effects of incoherent (diffusive) motion. Visualisations of air-water flow through a sphere pack are also reported and the capability of MRI to yield information on rivulet formation and surface wetting characteristics is illustrated.     

Apparent viscosity and particle pressure of a concentrated suspension of non-Brownian hard spheres near the jamming transition

We consider the steady shear flow of a homogeneous and dense assembly of hard spheres suspended in a Newtonian viscous fluid. In a first part, a mean-field approach based on geometric arguments is used to determine the viscous dissipation in a dense isotropic suspension of smooth hard spheres and the hydrodynamic contribution to the suspension viscosity. In a second part, we consider the coexistence of transient solid clusters coupled to regions with free flowing particles near the jamming transition. The fraction of particles in transient clusters is derived through the Landau-Ginzburg concepts for first-order phase transition with an order parameter corresponding to the proportion of “solid” contacts. A state equation for the fraction of particle-accessible volume is introduced to derive the average normal stresses and a constitutive law that relates the total shear stress to the shear rate. The analytical expression of the average normal stresses well accounts for numerical or experimental evaluation of the particle pressure and non-equilibrium osmotic pressure in a dense sheared suspension. Both the friction level between particles and the suspension dilatancy are shown to determine the singularity of the apparent shear viscosity and the flow stability near the jamming transition. The model further predicts a Newtonian behavior for a concentrated suspension of neutrally buoyant particles and no shear thinning behavior in relation with the shear liquefaction of transient solid clusters.     

Towards a Landau–Ginzburg-Type Theory for Granular Fluids

In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical and unstable fluids. The granular fluid, which is usually modeled as a fluid of inelastic hard spheres (IHS), exhibits two instabilities: the spontaneous formation of vortices and of high density clusters. We suppress the clustering instability by imposing constraints on the system sizes, in order to illustrate how LG-equations can be derived for the order parameter, being the rate of deformation or shear rate tensor, which controls the formation of vortex patterns. From the shape of the energy functional we obtain the stationary patterns in the flow field. Quantitative predictions of this theory for the stationary states agree well with molecular dynamics simulations of a fluid of inelastic hard disks.     

Kinetic theory of nonlinear viscous flow in two and three dimensions

On the basis of a nonlinear kinetic equation for a moderately dense system of hard spheres and disks it is shown that shear and normal stresses in a steady-state, uniform shear flow contain singular contributions of the form ¦X¦^3/2 for hard spheres, or ¦X¦ log ¦X¦ for hard disks. HereX is proportional to the velocity gradient in the shear flow. The origin of these terms is closely related to the hydrodynamic tails t^–d/2 in the current-current correlation functions. These results also imply that a nonlinear shear viscosity exists in two-dimensional systems. An extensive discussion is given on the range ofX values where the present theory can be applied, and numerical estimates of the effects are given for typical circumstances in laboratory and computer experiments.Supported by National Science Foundation grant No. CHE-73-08856 (to HvB, JRD, and JS) and the Center for Theoretical Physics of the Univ. of Md. (to HvB).On leave from Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

剪切磁场位形下电阻壁模不稳定性的数值模拟

数值研究了平衡磁场位形对电阻壁模稳定性的影响。研究发现,磁场剪切对电阻壁模有解稳作用,对于不同的剪切磁场位形,最不稳定的电阻壁模的环向模数和极向模数不同。等离子流对电阻壁模的增长有抑制作用,稳定住电阻壁模的临界流速度随着磁场剪切率的增大而增大。电阻壁模经线性增长后,进入非线性演化阶段,最后达到饱和状态,剪切磁场位形下的扰动磁能比均匀磁场位形下的扰动磁能饱和度高。