Viscosity of concentrated noncolloidal bidisperse suspensions

At the same solid volume fraction (Φ) the relative viscosity (η _r ) of a concentrated noncolloidal bidisperse suspension of hard spherical particles is lower than that of a monodisperse suspension. In this paper a semi-analytical viscosity model of noncolloidal bidisperse suspensions is derived using an integration method. In this model the random loose packing density obtained by computer simulation is taken as the limit of solid volume fraction Φ _m which depends upon both the diameter ratio (λ) of large to small particles and the volume fraction of large particles (ξ=Φ _l /Φ). This model shows that at high solid volume fraction, Φ > 0.40, both λ and ξ significantly influence η _r . For example, at Φ=0.5, it predicts that for monodisperse suspensions η _r =70, while for bidisperse suspensions (λ=2 and ξ=0.7) η _r =40. Comparison shows that, at high solid volume fraction (0.4–0.5), the relative viscosity predicted by this model is in good agreement with that predicted by the work of Shapiro and Probstein (1992) and of Patlazhan (1993), but is higher than that predicted by the work of others. Received: 27 February 2001 Accepted: 25 April 2001     

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.     

Physical based numerical schemes for the discretization of the sediment settling term

In this paper, the discretization of the sediment settling term is investigated. Two potential problems induced by the incorrect discretization of this term are analyzed. It shows that even the first-order upwind algorithm, the most stable and conservative scheme, cannot always ensure stability and mass conservation. To tackle these issues, three rules are proposed. Based on these rules, two schemes are designed. The performances of different schemes are tested in a study of sediment motions under a wave-breaking situation. The results show that the unphysical problems are relieved or totally avoided by the new schemes.     

Prediction of multiple overshoots in shear stress during fast flows of bidisperse polymer melts

We present a differential constitutive model of stress relaxation in polydisperse linear polymer melts and solutions that contains contributions from reptation, contour-length fluctuations, and chain stretching. The predictions of the model during fast start-up and steady shear flows of polymer melts are in accord with experimental observations. Moreover, in accordance with reported experimental literature (Osaki et al. in J Polym Sci B Polym Phys 38:2043–2050, 2000), the model predicts, for a range of shear rates, two overshoots in shear stress during start-up of steady shear flows of bidisperse polymer melts having components with widely separated molar masses. Two overshoots result only when the stretch or Rouse relaxation time of the higher molar mass component is longer than the terminal relaxation time of the lower molar mass component. The “first overshoot” is the first to appear with increasing shear rate and occurs as a result of the stretching of longer chains. Transient stretching of the short chains is responsible for the early time second overshoot. The model predictions in steady and transitional extensional flows are also remarkable for both monodisperse and bidisperse polymer solutions. The computationally efficient differential model can be used to predict rheology of commercial polydisperse polymer melts and solutions.     

A conservative and shape-preserving semi-Lagrangian method for the solution of the shallow water equations

Semi-Lagrangian methods are now perhaps the most widely researched algorithms in connection with atmospheric flow simulation codes. In order to investigate their applicability to hydraulic problems, cubic Hermite polynomials are used as the interpolant technique. The main advantage of such an approach is the use of information from only two points. The derivatives are calculated and limited so as to produce a shape-preserving solution. The lack of conservation of semi-Lagrangian methods, however, is widely regarded as a serious disadvantage for hydraulic studies, where non-linear problems in which shocks may develop are often encountered. In this work we describe how to make the scheme conservative using an FCT approach. The method proposed does not guarantee an unconditional shock-capturing ability but is able to correctly reproduce the discontinuous flows common in open channel simulation without any shock-fitting algorithm. It is a cheap way to improve existing 1D semi-Lagrangian codes and allows stable calculations beyond the usual CFL limits. A basic semi-Lagrangian method is presented that provides excellent results for a linear problem: the new techniques allow us to tackle non-linear cases without unduly degrading the accuracy for the simpler problems. Two one-dimensional hydraulic problems are used as test cases, water hammer and dam break. In the latter case, because of the non-linearity, special care is needed with the low-order solution and we show the advantages of using Leveque's large-time step version of Roe's scheme for this purpose.     

Liquid suspensions of single and binary component solid particles—An overview

In this paper theoretical approaches and experimental findings relative to the hydrodynamics of liquid suspensions of solid particles by liquids are reported and discussed. For the single particle specie systems, advantages and possible faults of well known empirical correlations are discussed. For binary-solid mixture suspensions, experimental evidence are reviewed and approaches capable of successfully describing observed behaviour are reported.     

Statistical model of collisions of bidisperse particles in an anisotropic turbulent flow

A statistical model for describing the motion and collisions of a bidisperse mixture of particles in anisotropic turbulent flows is presented. The model is based on a kinetic equation for the particle velocity probability density function (PDF). The results are compared with the data of a direct numerical simulation of the sedimentation of a bidisperse mixture of particles under the action of the gravity force.     

Numerical simulation of nanoparticle pattern fabricated by electrostatic spray deposition

Electrospray deposition(ESD) as a patterning method of nanoparticles deposited on a substrate has attracted much attention due to several advantages over other methods.However,obtaining an optimum ESD processing condition for nanoparticle pattern relies much on trial experiments because of the lack of reliable numerical simulation.In this study,the deposition characteristics of nanoparticle generated by electrospray were investigated by using a three-dimensional Lagrangian model.Three important process parameters,including solution dielectric constant,applied voltage and surface charge density on mask were considered by fixing the geometrical parameters of the ESD device.Simulation result showed that under the condition of without a mask,the spray diameter increases with increasing solvent dielectric constant,and higher applied voltage makes the spray area wider.Controllability of focusing by changing surface charge density on the mask was confirmed:higher surface charge density on the mask results in more focused deposition.Validity of the numerical simulation developed in this study was verified by comparison with experimental data.     

三峡库区侏罗系易滑地层沉积特征及其对岩石物理力学性质的影响

三峡库区崩滑地质灾害频发 ,其中以侏罗系易滑地层为甚。侏罗系易滑地层特殊的地层结构和岩石物理力学性质是控制崩滑灾害发生的主要因素。本文通过岩相古地理和沉积环境演变两个方面来研究三峡库区侏罗系易滑地层的沉积特征 ,并研究了三峡库区地层的沉积环境和沉积结构对岩层物理力学性质的影响 ,对三峡库区以滑坡为代表的地质灾害频发的原因给出沉积学和物理力学解释     

Reconciling different formulations of viscous water waves and their mass conservation

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been proposed. Our analysis compares three common sets of model equations. The first set has a rotational kinematic boundary condition at the surface. In the second set, a gauge choice for the velocity vector is made that cancels the rotational contribution in the kinematic boundary condition, at the cost of rotational velocity in the bulk and a rotational pressure. The third set circumvents the problem by introducing two domains: the irrotational bulk and the vortical boundary layer. This comparison puts forward the link between rotational pressure on the surface and vorticity in the boundary layer, addresses the existence of nonlinear vorticity terms, and shows where approximations have been used in the models. Furthermore, we examine the conservation of mass for the three systems, and how this can be compared to the irrotational case.     

Efficient higher-order backward characteristics schemes for transient advection

The use of the highest-order ((N – 1)th-order) Lagrangian interpolation Polynomial for the approximation of the exact solution in the backward characteristics scheme with N nodes is inefficient owing to the excessive number of terms in the polynomial. New schemes based on a combination of lower-order polynomials to approximate the exact solution are developed, with the relative weighting of the polynomials determined by Fourier mode analysis. With the addition of a flux limiter and a modified discriminator, the resulting schemes are oscillation-free, highly accurate, efficient and more cost-effective as compared with those schemes using the highest-order Lagrangian polynomial.     

Dispersion and clustering of bidisperse particles in isotropic turbulence

A statistical kinetic model describing the dispersion and clustering of particles with different inertia in homogeneous turbulence is presented. The model developed is used for calculating the relative velocity, the radial distribution function, and the particle collision kernel in a stationary bidisperse suspension. The results obtained are compared with the data of a direct numerical simulation.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 94–107. Original Russian Text Copyright © 2005 by Alipchenkov and Zaichik.     

Gas-solid interaction force from direct numerical simulation (DNS) of binary systems with extreme diameter ratios

nding the large particles becomes less in case ofa bidisperse mixture, as compared to a monodisperse system with the same volume fraction. We further investigated this discrepancy by calculating the volume per particle by means of Voronoi tessellation.     

Stability of some shear flows for concentrated suspensions

In this paper we investigate the stability of some viscometric flows for a concentrated suspension model which allows for the effects of shear-induced migration, including plane and circular Couette and Poiseulle flows, and unbounded and bounded torsional flows. In the bounded torsional flow, where its radial outer boundary is assumed frictionless, an exact closeform solution is given. With the exception of torsional flows, we find that a limit point for all the steady-state solutions can exist for certain range in the parameter values. In all cases, disturbances can persist for a long time, O (H ²/a ²), where H is a dimension of the flow field, and a is the particles' radius.     

A numerical methodology for investigating the formation of adiabatic shear bands

In this paper, we present a numerical approach for analyzing thermo-visco-plastic deformation in one dimension. The method, which is accurate to second order, is based on integration along the characteristic lines. It is able to simulate fully localized plastic flow with high resolution and good efficiency. We apply this numerical scheme to the analysis of shear localization, emphasizing the interactions between a single shear band and its surroundings and among the members of a periodic array of shear bands. It is found that a shear band may grow intermittently due to interactions with other bands. The developed method is specifically adequate for analyzing the self-organized multiple adiabatic formation process, which will be discussed in the follow-up paper.     

A split operator scheme for ocean wave simulation

A coupled discrete spectral model was developed for the prediction of ocean waves by solving the energy conservation equation of the two-dimensional wave spectrum. The model includes the dispersion correction terms in the governing equation to account for the dispersive effect due to the frequency-dependent velocities of waves. A split operator scheme is used to deal with the numerical problems arising from different terms of the governing equation. The advection terms are solved by the proven accurate minimax characteristics method to avoid excessive numerical damping or oscillations. The dispersion correction terms are solved by central differencing. The source and sink terms are solved by a quasi-second-order explicit scheme with limitation on energy growth per time step to allow the use of a large time step. The model was verified by ideal test cases and wave-hindcasting studies under typhoon conditions in the South China Sea near Hong Kong.     

Modelling of the dyeing process of packed cotton threads using reactive dyes

The Method of Volume Averaging is used to model the process of dyeing textile threads on bobbins. This analysis allows one to upscale the relevant information at the micro-scale, composed of the textile fibres of the thread in contact with the dyeing bath fluid, to the macro-scale, consisting of the bobbins of threads inside the equipment. The final mathematical model consists of two equations, one for the fluid phase external to the thread and the other for the fluid phase internal to the thread. In order to solve the partial differential equations obtained in the mathematical model, the authors developed a computation code using the Method of Finite Volumes. This code utilized a system of generalized coordinates to facilitate application of the boundary conditions to different bobbin geometries. The numerical results for the kinetics of dyeing packed cotton threads with reactive dyes are compared to the experimental results obtained in Brazilian textile industries, leading to good agreement between theory and experiment. This demonstrates that the model developed in this paper is able to predict the operational conditions to be used in the textile industries, minimizing the consumption of dyes and other auxiliaries necessary for the dyeing process.     

CFD–DEM simulation of particle deposition characteristics of pleated air filter media based on porous media model

In this study, the three-dimensional physical model of pleated air filtration media was simplified to porous media model, and the calculation parameters of porous media were obtained based on experimental data. The model of V-shaped pleated air filter media is constructed, the height of the media pleat is 50 mm and the pleat thickness is 4 mm, the pleat angle is 3.7°. The Hertz-Mindlin contact model was modified by Johnson Kendall Roberts (JKR) adhesion contact model. The deposition process of particles in media was simulated based on computational fluid dynamics (CFD) theory and discrete element method (DEM). Results show that the CFD–DEM coupling method can be effectively applied to the macro research of pleated air filter media. The particles will form dust layer and dendrite structure on the fiber surface, and the dust layer will affect the subsequent air flow organization, and the dendrite structure will eventually form a “particle wall”. The formation of the “particle wall” will prevent the particles from moving further in the fluid domain, which makes area of pleated angle become the “low efficiency” part about the particle deposition. Compared with area of pleated angle, the particles are concentrated in the opening area and the middle area of the pleated to agglomerate and deposit.     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.