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.     

Viscosity of liquid metal suspensions — experimental approaches and open issues

Knowing the viscosity of metal melts with suspended particles is necessary to interpret experimental results and to simulate fluid flow in such materials. At present, reliable viscosity data is only available for pure metals and alloys. In order to study the viscosity behavior of metal melts with suspended solid particles in detail, samples with defined particle amounts are needed. Various methods of incorporating particles into the metallic melts were evaluated, and viscosity was experimentally determined using an oscillating cup technique. It was shown that solid particles in suspension change the melts’ viscosities dramatically, far beyond the effects expected from normal colloidal rheology.     

Rheology of nanosized hairy grain suspensions

Suspensions of nanosized hairy grains have been prepared by grafting long polydimethylsiloxane chains (molecular weight ) onto silica particles (radius ), dispersed into a good solvent of PDMS. Depending on the particle volume fraction, different rheological behaviors are observed. In the very dilute regime, the suspensions are perfectly stable and the particles behave almost as hard spheres: flow penetration inside the corona is then very weak. When the particle volume fraction goes to the close packing volume fraction, the suspension viscosity does not diverge as for hard spheres due to the increase of flow penetration inside the corona and to corona entanglements. The particles have then the same behavior as polymer stars having an intermediate number of arms (). Finally, in the concentrated regime (), the suspensions form irreversible gels. We shown that this unexpected gelation phenomenon is related to the presence of the silica cores: grafted PDMS chains can adsorb onto different particles and form irreversible bonds between the cores. The viscosity and elastic modulus evolutions during gelation are well described by the scalar percolation model of sol-gel transition. Received 23 March 1998     

Viscosity minimum in bimodal concentrated suspensions under shear

We study a model of concentrated suspensions under shear in two dimensions. Interactions between suspended particles are dominated by direct-contact viscoelastic forces and the particles are neutrally bouyant. The bimodal suspensions consist of a variable proportion between large and small droplets, with a fixed global suspended fraction. Going beyond the assumptions of the classical theory of Farris (R.J. Farris, Trans. Soc. Rheol. 12, 281 (1968)), we discuss a shear viscosity minimum, as a function of the small-to-large-particle ratio, in shear geometries imposed by external body forces and boundaries. Within a linear-response scheme, we find the dependence of the viscosity minimum on the imposed shear and the microscopic drop friction parameters. We also discuss the viscosity minimum under dynamically imposed shear applied by boundaries. We find a reduction of macroscopic viscosity with the increase of the microscopic friction parameters that is understood using a simple two-drop model. Our simulation results are qualitatively consistent with recent experiments in concentrated bimodal emulsions with a highly viscous or rigid suspended component. Received 28 June 2002 RID="a" ID="a"e-mail: ernesto@pion.ivic.ve     

Viscosity and dispersion state of magnetic suspensions

We investigate the viscosity behavior of a magnetic suspension in which magnetic particles are dispersed in a mixture of polyacrylic liquids. The size of magnetite particles is nearly 300 nm and the volume fraction of the magnetic particles is in the range of 0.003-0.03. The particle concentration dependence of the suspension viscosity yields the intrinsic viscosity [η], which varies from 25.6 at 5 s⁻¹ to 5.1 at 400 s⁻¹. The yield stress and the infinite shear viscosity of the suspension increase non-linearly as the particle concentration ? increases. We examine the effect of process conditions such as milling time and amount of dispersant on the viscosity behavior of the suspension. As milling time elapses, yield stress and low shear viscosity decrease and then reach constant values while the infinite shear viscosity remains constant. When oleic acid is added as a dispersant, the yield stress and low shear viscosity of the suspension show minimum values as the amount of oleic acid increases. These results agree with experimental results of sedimentation tests, which enable us to estimate the aggregate size of magnetic suspension. The yield stress and the low shear viscosity of the magnetic suspension are found to be useful in evaluating the dispersion state of the magnetic suspension.     

Modeling effective viscosity reduction behaviour of solid suspensions

Under a simple shearing flow, the effective viscosity of solid suspensions can be reduced by controlling the inclusion particle size or the number of inclusion particles in a unit volume. Based on the Stokes equation, the transformation field method is used to model the reduction behaviour of effective viscosity of solid suspensions theoretically by enlarging the particle size at a given high concentration of particles. With a lot of samples of random cubic particles in a unit cell, our statistical results show that at the same higher concentration, the effective viscosity of solid suspensions can be reduced by increasing the particle size or reducing the number of inclusion particles in a unit volume. This work discloses the viscosity reduction mechanism of increasing particle size, which is observed experimentally.     

Shear flows and shear viscosity in a two-dimensional Yukawa system (dusty plasma)

The shear viscosity of a two-dimensional liquid-state dusty plasma was measured experimentally. A monolayer of highly charged polymer microspheres, with a Yukawa interaction, was suspended in a plasma sheath. Two counterpropagating Ar+ laser beams pushed the particles, causing shear-induced melting of the monolayer and a shear flow in a planar Couette configuration. By fitting the particle velocity profiles in the shear flow to a Navier-Stokes model, the kinematic viscosity was calculated; it was of order 1 mm(2) s(-1), depending on the monolayer's parameters and shear stress applied.     

Shape dynamics and rheology of soft elastic particles in a shear flow

The shape dynamics of soft, elastic particles in an unbounded simple shear flow is investigated theoretically under Stokes flow conditions. Three types of motion-steady-state, trembling, and tumbling-are predicted, depending on the shear rate, elastic shear modulus, and initial particle shape. The steady-state motion is found to be always stable. In addition, the existence of a trembling regime is documented for the first time in nonvesicle systems, and a complete phase diagram is developed. The rheological properties of dilute suspensions of such soft particles generally exhibit shear-thinning behavior and can even display negative intrinsic viscosity for sufficiently soft particles.     

On the orientational characteristics and transport coefficients of an oblate spheroidal hematite particle in a simple shear flow

We have developed the basic equation of the orientational distribution function of oblate spheroidal hematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. An oblate spheroidal hematite particle has an important characteristic in that it is magnetized in a direction normal to the particle axis. Since a dilute dispersion is addressed in the present study, we have taken into account only the friction force (torque) whilst neglecting the hydrodynamic interactions among the particles. This basic equation has been solved numerically in order that we may investigate the dependence of the orientational distribution on the magnetic field strength, shear rate and rotational Brownian motion and the relationship between the orientational distribution and the transport coefficients such as viscosity and diffusion coefficient. We found that if the effect of the magnetic field is more dominant, the particle inclines in such a way that the oblate surface aligns in the magnetic field direction. If the Peclet number increases and the effect of the shear flow becomes more dominant, the particle inclines such that the oblate surface tilts in the shear flow direction. The viscosity due to the magnetic torque is shown to increase as the magnetic field increases, since the magnetic torque due to the applied magnetic field becomes the more dominant effect. Moreover, the viscosity increase is shown to be more significant for a larger aspect ratio or for a more oblate hematite particle. We have applied the analysis to the problem of particle sedimentation under gravity in the presence of a magnetic field applied in the sedimentation direction. The particles are found to sediment with the oblate surface aligning more significantly in the sedimentation direction as the applied magnetic field strength increases.     

Study on Steady Shear Rheological Behavior of Concentrated Suspensions of Sulfonated Polyacrylamide/Na-Montmorillonite Nanoparticles

Concentrated suspensions of sulfonated polyacrylamide (SPA)/Na⁺-montmorillonite (Na-MMT) were prepared and their stability and steady shear rheological properties were described as a function of nanoparticle and polymer concentration and temperature. The results showed that the Na-MMT nanoparticles suspensions were stable in the absence and presence of SPA and no sedimentation was seen. The Z-average particle sizes for the SPA/Na-MMT suspensions increased in the presence of SPA. Rheological investigations showed that the SPA solutions and SPA/Na-MMT suspensions displayed non-Newtonian behavior in almost the whole range of shear rate. All the suspensions exhibited a shear-thinning flow character as shear rate increased. The flow curves indicated the shear viscosity and stress of the samples were decreased with increasing nanoparticles concentration up to 1.5 wt%, but for Na-MMT loading greater than 1.5 wt% there was an increase in shear viscosity and stress of the suspensions. Increasing of SPA concentration had more effect on increasing the rheological properties of SPA/Na-MMT suspensions than increasing of nanoclay content. Shear viscosity and stress of the suspensions increased with increasing SPA concentration and decreased with increasing temperature from 50°C to 70°C.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Negative viscosity due to magnetic properties of a non-dilute suspension composed of ferromagnetic rod-like particles with magnetic moment normal to the particle axis

The negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis, have been investigated. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rod-like particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.     

Lattice Boltzmann simulation of solid particles suspended in fluid

The lattice Boltzmann method, an alternative approach to solving a fluid flow system, is used to analyze the dynamics of particles suspended in fluid. The interaction rule between the fluid and the suspended particles is developed for real suspensions where the particle boundaries are treated as no-slip impermeable surfaces. This method correctly and accurately determines the dynamics of single particles and multi-particles suspended in the fluid. With this method, computational time scales linearly with the number of suspensions,N, a significant advantage over other computational techniques which solve the continuum mechanics equations, where the computational time scales asN ³. Also, this method solves the full momentum equations, including the inertia terms, and therefore is not limited to low particle Reynolds number.     

纳米TiO2颗粒对电流变悬浮液中硅油的挥发增强效应

物理化学性能稳定的二甲基硅油常作为电流变液分散相, 当与纳米量级的介电颗粒混合组成电流变悬浮液时, 在非密闭环境下极易挥发, 时间足够长时, 可完全挥发. 本文通过实验研究了纳米二氧化钛颗粒对二氧化钛和硅油组成的悬浮液中硅油挥发增强现象, 分析表明, 纳米颗粒在电流变悬浮液的硅油气-液界面上形成纳米尺度的凸型曲面, 使液面上蒸气压大大提高, 导致挥发增强. 本文还对颗粒浓度, 环境温度和硅油黏度等对硅油挥发增强效应的影响进行了系统的研究和分析.     

Effect of the bulk viscosity on the sound propagation in nonequilibrium suspensions of microparticles in gas

The sound propagation in a mixture of gas with uniformly dispersed solid particles, whose temperature is maintained above that of the gas by an external source, is considered. The dispersion properties of this kind of suspensions are studied, and expressions for the second viscosity and the sound velocity in such suspensions are derived. It is shown that, in a nonequilibrium suspension, the second viscosity may be negative. The ranges of the suspension parameters, for which the propagation of low-frequency sound is impossible, are determined.     

Electrorheological effects in carbon, barium titanate, and nickel coated with barium titanate suspensions

Effects of the electric field on the rheology, electrorheological (ER) effects, are investigated on carbon, barium titanate (BaTiO₃) and BaTiO₃-coated nickel (BT-Ni) suspensions. Among some electroreological properties, electric field frequency dependence of the induced shear stress (yield stress) observed for three suspensions shows a contrasting behavior. With increase in the electric field frequency, the yield stress decreases above 100 Hz in the carbon suspension, monotonously increases in the BaTiO₃ suspension, and is almost constant in the BT-Ni suspension. The difference in the frequency dependence and magnitude of the yield stress is discussed on the basis of the magnitude and relaxation time of the interfacial polarization and the effect of the particle rotation under the shear flow.     

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.     

Pattern formation in flowing electrorheological fluids

A two-fluid continuum model is developed to describe mass transport in electro- and magnetorheological suspensions. The particle flux is related to the field-induced stresses. Solutions of the resulting mass balance show column formation in the absence of flow, and stripe formation when a suspension is subjected simultaneously to an applied electric field and shear flow.     

Shear Stress in a Couette Flow of Liquid-Particle Suspensions

The mechanisms of momentum transfer and shear stress of liquid-particle suspensions in two-dimensional Couette flow are studied using direct numerical simulation by lattice-Boltzmann techniques. The results obtained display complex flow phenomena that arise from the two-phase nature of the fluid including a nonlinear velocity profile, layering of particles, and apparent slip near the solid walls. The general rheological behaviour of the suspension is dilatant. A detailed study of the various momentum transfer mechanisms that contribute to the total shear stress indicates that the observed shear thickening is related to enhanced relative solid phase stress for increasing shear rates.