Microstructural investigations of the yielding behaviour of bidisperse magnetorheological fluids

Particle level simulations were used to investigate the effects of size bidispersity and particle size ratios on the static and yielding behaviour of magnetorheological fluids (MRF). The MRF were treated as linearly magnetisable, neutrally buoyant particles dispersed in a viscous carrier liquid. In the quiescent mode (static structures), the bidisperse suspensions were found to have a higher tendency to form straight chains than the monodisperse suspensions; this is consistent with previous findings. Under steady shearing, the bidisperse suspensions exhibited higher stress enhancement than the monodisperse systems. The stress enhancement in bidisperse suspensions is likely to be due to the population and orientation of interacting large particles in the bidisperse suspensions.     

Modeling of colloid and colloid-facilitated contaminant transport in a two-dimensional fracture with spatially variable aperture

Mathematical models are developed for two-dimensional transient transport of colloids, and cotransport of contaminant/colloids in a fracture-rock matrix system with spatially variable fracture aperture. The aperture in the fracture plane is considered as a lognormally distributed random variable with spatial fluctuations described by an exponential autocovariance function. Colloids are envisioned to irreversibly deposit onto fracture surfaces without penetrating the rock matrix; whereas, the contaminant is assumed to decay, sorb onto fracture surfaces and onto colloidal particles, as well as to diffuse into the rock matrix. The governing stochastic transport equations are solved numerically for each realization of the aperture fluctuations by a fully implicit finite difference scheme. Emphasis is given on the effects of variable aperture on colloid and colloid-facilitated contaminant transport. Simulated breakthrough curves of ensemble averages of several realizations show enhanced colloid transport and more pronounced fingering when colloids are subject to size exclusion from regions of small aperture size. Moreover, it is shown that an increase in the fracture aperture fluctuations leads to faster transport and increases dispersion. For the case of contaminant/colloids cotransport it is shown, for the conditions considered in this work, that colloids enhance contaminant mobility and increase contaminant dispersion.Nomenclature b fracture aperture, L - c contaminant concentration in the fracture, M/L³ - c _m contaminant concentration in the rock matrix, M/L³ - c _o source contaminant concentration, M/L³ - c ^* contaminant concentration adsorbed onto fracture surfaces, M/L² - c _m ^* contaminant concentration adsorbed inside the rock matrix, M/M - d _p colloidal particle diameter, L - D hydrodynamic dispersion coefficient dyadic, L²/t - D Brownian diffusion coefficient for colloids and molecular diffusion coefficient for contaminants, L²/t - D _m effective diffusion coefficient in the rock matrix, L²/t - h total head potential in the fracture, L - K _f partition coefficient for contaminant sorption onto fracture surfaces, L - K _m contaminant partition coefficient in the rock matrix, L³/M - K _n partition coefficient for contaminant sorption onto suspended colloids, L - K _n* partition coefficient for contaminant sorption onto deposited colloids, L³/M - _x fracture length in thex-direction, L - _y fracture length in they-direction, L - n colloid concentration in the liquid phase, M/L³ - n _o source colloid concentration, M/L³ - n ^* colloid concentration adsorbed onto fracture surfaces, M/L² - n _max ^* maximum deposited colloid concentration on fracture surfaces, M/L² - N ^* number of deposited colloidal particles per unit surface area of the fracture, 1/L² - N _max ^* maximum number of deposited colloidal particles per unit surface area of the fracture, 1/L² - q ^* diffusive mass flux into the rock matrix, M/L²t - R retardation factor in the fracture - R _m retardation factor in the rock matrix - s contaminant concentration adsorbed on colloids in the liquid phase, M/M - s _o source solid-phase contaminant concentration onto suspended colloids, M/M - s ^* contaminant concentration adsorbed on deposited colloids, M/M - t time, t - U interstitial velocity vector, L/t - x coordinate along the fracture length, L - y coordinate along the fracture width, L - z coordinate perpendicular to the fracture plane, L - area blocked by a deposited colloidal particle, L² - _L longitudinal dispersivity, L - _T transversal dispersivity, L - fluid specific weight, M/L²t² - fraction of the fracture surface physically covered by colloids - gz dummy integration variable - porosity of the rock matrix - colloid deposition coefficient, L - first-order decay coefficient, 1/t - fluid dynamic viscosity, M/Lt - defined in (18) - _b bulk density of the rock matrix, M/L³ - _p colloidal particle density, M/L³ - standard deviation of the lognormally distributed fluctuations of the fracture aperture     

Non-Newtonian Flow in a Variable Aperture Fracture

The transmissivity of a variable aperture fracture for flow of a non-Newtonian, purely viscous power-law fluid with behavior index n is studied. The natural logarithm of the fracture aperture is considered to be a two-dimensional, spatially homogeneous and correlated Gaussian random field. We derive an equivalent fracture aperture for three flow geometries: (1) flow perpendicular to aperture variation; (2) flow parallel to aperture variation; (3) flow in an isotropic aperture field. Under ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the geometric mean of cases 1 and 2. When n=1 all our expressions for the equivalent aperture reduce to those derived in the past for Newtonian flow and lognormal aperture distribution. As log-aperture variance increases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3.     

An automated single-particle tracker: application to characterization of non-azimuthal motion in Couette flows at low Reynolds number

We describe an experiment that allows us to record 3-dimensional trajectories of single particles in Couette shear flows, at low Reynolds number. The core of the apparatus is a Couette cell with transparent contra-rotating cylinders. Fluorescent spherical particles are used as tracers. A single tracer is imaged onto a webcam, equipped with a home-made autofocus system. For a given average shear rate, tracking of an individual tracer is performed automatically by driving the amount of contra-rotation between both cylinders and the position of the webcam. The performance of the tracker is illustrated through examples of trajectories of neutrally buoyant tracers in a Newtonian fluid. The setup is mostly aimed at characterizing complex flows in non-colloidal concentrated suspensions and wet granular materials. We show examples of 3d trajectories in a dense suspension of 200 μm spherical grains, revealing details of the short-scale diffusive-like particle motion, together with flow localization and large-scale non-azimuthal flow patterns.     

Rheology of concentrated suspensions containing mixtures of spheres and fibres

Optimising flow properties of concentrated suspensions is an important issue common for many industries. The rheology of concentrated suspensions has therefore been studied intensively both experimentally and theoretically. Most studies have focused on monodisperse and polydisperse suspensions of either spheres or fibres. In practice, most suspensions contain particles that are polydisperse both in size and shape. A mixing rule for such systems is expected to be a powerful tool for engineers and product designers. Therefore in this work, suspensions of spheres, fibres and mixtures thereof were characterised using rotational shear rheometry and in-line image analyses. Thereby, total solids volume concentration and fibre fraction was varied. Results from transient and steady-state shear rheometry are discussed with respect to concentration, fibre fraction, and shear induced microstructure. Experimentally obtained viscosity data were accurately fitted using the model proposed by Farris (T Soc Rheol 12:281, 1968) for mixtures of monodisperse non-interacting spheres of different sizes.Originally presented at the Annual European Rheology Conference 2003, AERC 2003     

页岩气和致密砂岩气藏微裂缝气体传输特性

页岩气和致密砂岩气藏发育微裂缝,其开度多在纳米级和微米级尺度且变化大,因此微裂缝气体传输机理异常复杂.本文基于滑脱流动和努森扩散模型,分别以分子之间碰撞频率和分子与壁面碰撞频率占总碰撞频率的比值作为滑脱流动和努森扩散的权重系数,耦合这两种传输机理,建立了微裂缝气体传输模型. 该模型考虑微裂缝形状和尺度对气体传输的影响. 模型可靠性用分子模拟数据验证.结果表明:(1)模型能够合理描述微裂缝中所有气体传输机理,包括连续流动,滑脱流动和过渡流动;(2)模型能够描述不同开发阶段,微裂缝中各气体传输机理对传输贡献的逐渐变化过程;(3)微裂缝形状和尺度影响气体传输,相同开度且宽度越大的微裂缝,气体传输能力越强,且在高压和微裂缝大开度的情况下表现更明显.      

Dynamic simulation of non-spherical particulate suspensions

Particle-level simulation has been employed to investigate rheology and microstructure of non-spherical particulate suspensions in a simple shear flow. Non-spherical particles in Newtonian fluids are modeled as three-dimensional clusters of neutrally buoyant, non-Brownian spheres linked together by Hookean-type constraint force. Rotne–Prager correction to velocity disturbance has been employed to account for far-field hydrodynamic interactions. An isolated rod-like particle in simple shear flow exhibits a periodic orientation distribution, commonly referred to as Jeffery orbit. Lubrication-like repulsive potential between clusters have been included in simulation of rod-like suspensions at various aspect ratios over dilute to semi-dilute volume fractions. Shear viscosity evaluated by orientation distribution qualitatively agrees with one obtained by direct computation of shear stress.     

Numerical study on the shear-flow behavior and transport process in rough rock fractures

This paper presents a systematic research for understanding mechanical shearing effects on the fluid flow and the solute transport behavior of rough fractures through a numerical simulation approach. The aperture fields were modeled based on a real rock fracture geometry and the normal displacement obtained from the shear-flow test. The fluid flow through the rough fracture under shear was simulated using a finite element code that solves the Reynolds equation, and the transport behavior through the rough fracture under shear was simulated calculating the advection–dispersion equation. The results show that the fracture apertures increase as the shear displacement increases, with a few major flow channels detected through the fracture. The shear-induced flow channels increase both flow connectivity and transport connectivity, which accelerate the movement of solutes in a particular direction and lead to early breakthrough of the contaminants. Adsorption, acting as a retardation term, has a decisive influence on the transport process. These results can give a basic knowledge of the hydromechanical and solute transport progress through fracture, and will be helpful to safety assessment for high-level radioactive waste disposal facilities.     

Effects of the Correlation Length on the Hydraulic Parameters of a Fracture Network

We consider the influences of correlation length and aperture variability on the REV, the equivalent permeability of a fracture network, and the uncertainty in the equivalent permeability using a two-dimensional orthogonal bond percolation model. The percolation threshold, correlation length, effective conductivity, and coefficient of variation of the effective conductivity are investigated over statistically representative multiple realizations with Monte Carlo simulations in 2D fracture networks that have log-normally distributed individual fracture permeabilities. We show that although the aperture variability is large, the REV and the correlation length are similar near the percolation threshold. In contrast, when the fracture density is much larger than the percolation threshold they diverge as the aperture variability increases. We characterize the effects of correlation length and aperture variability on effective conductivity with a simple function. From the coefficient of variation analysis, the correlation length can be a criterion for evaluating which conceptual model is appropriate for describing the flow system for a given fracture network when aperture variability is sufficiently small. However, discrete fracture network models are recommended for flow simulation models because of the difficulty of REV estimation and the uncertainty in equivalent hydraulic parameters when aperture variability is large.     

Free-surface flow of concentrated suspensions

Free-surface flows of concentrated suspensions exhibit many interesting phenomena such as particle segregation and surface corrugation. In this work the flow structures associated with free-surface has been studied experimentally. The free-surface velocity for neutrally buoyant suspension of uniform spheres in a gravity driven inclined channel flow was determined by particle imaging velocimetry (PIV) technique. Experiments were carried out for concentrated suspensions with particle fractions ? ranging from 0.40 to 0.50. The measured velocities show blunted profile in the channel. The blunting of the velocity profile increases with the particle concentration. The rms velocity fluctuations measured at the free-surface progressively increase with particle fraction ? and are linear in shear rate γ. The surface roughness were characterized by analyzing the power spectral density of the refracted light from the free-surface. The characteristics observed are in support of earlier findings.     

Comparison of Kinetic and Hybrid-Equilibrium Models Simulating Colloid-Facilitated Contaminant Transport in Porous Media

The presence of colloidal particles in groundwater can enhance contaminant transport by reducing retardation effects and carrying them to distances further than predicted by a conventional advective/dispersive equation with normal retardation values. When colloids exist in porous media and affect contaminant migration, the system can best be simulated as a three-phase medium. Mechanisms of mass transfer from one phase to another by colloids and contaminants can be kinetic or equilibrium-based, depending on the sorption–desorption reaction rate between the aqueous and solid phases. When the rate of sorption between the water phase and the solid phase(s) is not much greater than the rate of change in contaminant concentration in the water phase, kinetic sorption models may better describe the phenomenon. In some cases of modeling one or more mass transfer processes, a useful simplification may be to introduce the local equilibrium assumption. In this study, the local equilibrium assumption for sorption processes on colloidal surfaces (hybrid equilibrium model) was compared with kinetic-based models. Sensitivity analyses were conducted to deduce the effect of major parameters on contaminant transport. The results obtained from the hybrid equilibrium model in predicting the transport of colloid-facilitated groundwater contaminant are very similar to those of the kinetic model, when the point of interest is not at contaminant and colloid source vicinities and the time of interest is sufficiently long for imposed sources.     

Existence,Uniqueness, and Stability of Generalized Traveling Waves in Time Dependent Monostable Equations

The current paper is devoted to the study of traveling wave solutions of spatially homogeneous monostable reaction diffusion equations with ergodic or recurrent time dependence, which includes periodic and almost periodic time dependence as special cases. Such an equation has two spatially homogeneous and time recurrent solutions with one of them being stable and the other being unstable. Traveling wave solutions are a type of entire solutions connecting the two spatially homogeneous and time recurrent solutions. Recently, the author of the current paper proved that a spatially homogeneous time almost periodic monostable equation has a spreading speed in any given direction. This result can be easily extended to monostable equations with recurrent time dependence. In this paper, we introduce generalized traveling wave solutions for time recurrent monostable equations and show the existence of such solutions in any given direction with average propagating speed greater than or equal to the spreading speed in that direction and non-existence of such solutions of slower average propagating speed. We also show the uniqueness and stability of generalized traveling wave solutions in any given direction with average propagating speed greater than the spreading speed in that direction. Moreover, we show that a generalized traveling wave solution in a given direction with average propagating speed greater than the spreading speed in that direction is unique ergodic in the sense that its wave profile and wave speed are unique ergodic, and if the time dependence of the monostable equation is almost periodic, it is almost periodic in the sense that its wave profile and wave speed are almost periodic.     

The effect of sphere–wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells

A new method for simulating the motion of particles in viscoelastic Boger fluids is extended to problems with bounded geometries. Viscoelasticity is incorporated into the Stokesian dynamics method by modeling a viscoelastic fluid as a suspension of finite-extension nonlinear-elastic (FENE) dumbbells. Wall–particle and wall–bead interactions are included by using the image system method of Blake; particle–particle and particle–bead interactions are also modified by the presence of the wall. The method of incorporating sphere–wall interactions is verified by doing calculations for several problems involving particle–wall interactions in Newtonian fluids. The method is then used to study particle–wall interactions in viscoelastic dumbbell suspensions by examining several problems of interest: the sedimentation of a spherical particle near vertical and tilted walls; the sedimentation of a nonspherical particle between two flat plates; and the migration of a neutrally buoyant sphere in plane Poiseuille flow. We find that a single sphere falling near a wall moves toward the wall and exhibits anomalous rotation. When the wall is tilted by an amount less than a few degrees, the sphere still moves toward the wall, but tilting the wall greater than an angle of approximately 1.5° results in the sphere falling away from the wall. A nonspherical particle settling in a channel exhibits an oscillatory motion, but ultimately becomes centered in the channel with its long axis parallel to gravity. Finally, it is shown that a neutrally buoyant sphere in plane Poiseuille flow migrates to the channel center in wide channels, but migrates to the walls when the sphere is sufficiently large relative to the channel width.     

Lateral migrations of solid spheres in tube flow

Cross-flow displacements of neutrally buoyant solid spheres under Poiseuille-type flow conditions in narrow channels, at low volume fraction, are described by a phenomenological model within the framework of the Fokker-Planck equation. In this model, the effects of particle-particle and particle-wall interactions are taken into account. In addition to the classical wall effect (depleted layer near the wall), numerical solutions of the derived equations display two opposite lateral migrations towards the wall and the tube axis, and an alignment of the particles in adjacent layers parallel to the flow. These numerical results are then compared with experimental results obtained by Goldsmith and Marlow [18] for erythrocyte suspensions. A good qualitative agreement is observed.     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Measurements of single spherical particle trajectories with lateral migration in a slit with one porous wall under laminar flow conditions

Lateral migration of spherical, neutrally buoyant particles moving in Poiseuille flow was measured in a slit with a porous membrane at one wall. Neutrally buoyant particles with diameters of 226 μm were injected into 22% glycerol-water solution flowing vertically in a slit channel (1.6 × 50 × 152 mm). The particles were illuminated with a strobe at 25 flashes/sec and photographed with a 4 × 5 camera under dark field conditions. Measured particle trajectories are compared with theoretically predicted trajectories based on Altena and Belfort's (1984) model. The theoretical trajectories are within the limits of error in the measured trajectories. By confirming the Altena and Belfort (1984) model within the range of experimental conditions tested here, inertial interactions should be included when modeling membrane fouling of dilute suspensions (Belfort et al. 1982).     

Colloid Transport in Porous Media: A Review of Classical Mechanisms and Emerging Topics

To celebrate the tenth anniversary of InterPore, we present an interdisciplinary review of colloid transport through porous media. This review aims to explore both classical colloid transport and topics that fall outside that purview and thus offer transformative insights into the physics governing transport behavior. First, we discuss the unique colloid characteristics relative to molecules and larger particles. Then, the classical advection–dispersion–filtration models (both conceptual and mathematical) of colloid transport are introduced as well as anomalous transport behaviors. Next, the forces of interaction between colloids and porous media surfaces are discussed. Fourth, applications that are interested in maximizing the transport of colloids through porous media are considered. Then the concept of motile, active biocolloids is introduced, and finally, colloid swarming as a newly recognized mode of transport is summarized.

     

Fundamentals of migrating multi-block lattice Boltzmann model for immiscible mixtures in 2D geometries

This paper proposes an extension scheme for the application of the single phase multi-block lattice Boltzmann method (LBM) to the multiphase Gunstensen model, in which the grid is refined in a specific part of the domain where a fluid–fluid interface evolves, and the refined grid is free to migrate with the suspended phase in the flow direction. The method is applicable to single and multiphase flows, and it was demonstrated by simulating a benchmark single phase flow around a 2D asymmetrically placed cylinder in a channel and for investigating the shear lift of 2D neutrally buoyant drop in a parabolic flow.     

Fluid Permeability in Stratified Unconsolidated Particulate Bed

Fluid permeability of polydisperse particulate bed with finite thickness has been examined. On the assumption of creeping flow, the permeability of monodisperse particles with arbitrary arrangement is calculated by means of Stokesian dynamics approach in which the interaction between individual particles and interstitial fluid is described by multipole expansion of the Oseen tensor. We have extended such calculation method to polydisperse particulate systems which have not so dense structures (up to particle volume fraction ${\phi \sim}$ 0.2). The particles are located infinitely in space and their interaction has been taken into account by Ewald summation technique. For the spatial distribution of polydisperse particles, we consider locally stratified particulate beds and define stratification degree as a parameter which apparently and mathematically represents the thickness of the mixing region of different-sized particles. The permeability profiles in the particulate beds with different stratification degree show the dependence of local permeability on the spatial and size distribution of particles. Consequently, the calculation results indicate that the permeability of non-uniform polydisperse particulate bed can be predicted by integrating the local permeation resistance which is determined by the local specific surface area.     

Evolution of shock waves in polydisperse gas suspensions with a nonuniform particle concentration distribution

The results of a numerical investigation of the laws of shock wave propagation in polydisperse (two-fraction) gas suspensions with a non-uniform initial particle concentration distribution are presented. Examples of shock wave propagation in extended layers of a gas suspension with linearly increasing, linearly decreasing and sinusoidal laws of variation of the particle concentration are considered. It is shown that when shock waves pass through layers of a gas suspension with increasing and decreasing laws of variation of the particle concentration, respectively, amplification and attenuation of the waves are observed; when shock waves travel through gas suspensions with a periodic law of variation of the particle concentration the pressure distribution behind the wave fronts is nonmonotonic. The solutions corresponding to polydisperse and monodisperse gas suspensions with an effective particle size are examined. The nonequilibrium and thermodynamic-equilibrium solutions are compared.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 183–190, September–October, 1991.