Particle Migration Model Research Articles

Shear-induced migration in concentrated suspensions: Particle mass conservation, contact pressure and jamming

A two-velocity fluid model is presented to describe particle migration in mono-disperse suspensions of neutrally buoyant particles. In contrast to previous migration models, the proposed formulation allows us to impose explicit boundary conditions on particle velocity, and thereby to satisfy strict mass conservation for the particle phase. In addition, the upper bound on particle volume fraction (jamming limit) is strictly enforced through a non-smooth complementarity condition and the introduction of a particle jamming pressure. The model is applied to an axisymmetric Poiseuille flow and solved using a finite-element method. For that purpose, a specific, fully implicit algorithm based on non-smooth optimisation tools is developed and validated. Preliminary comparisons with experimental data from the literature show promising agreement. In particular, the model properly captures the formation of an inner plug region, in which the suspension is saturated and jammed. • New particle migration model for suspension. • Strict mass conservation for each phase. • Two-velocity description. • Jamming via non-smooth complementarity condition.

Evaluation of Formation Blockage Risk in Geothermal Water Reinjection Using a Novel Particle Migration Model Based on the Bridging Principle

Evaluation of Formation Blockage Risk in Geothermal Water Reinjection Using a Novel Particle Migration Model Based on the Bridging Principle

A Coupled Nonlinear Flow Model for Particle Migration and Seepage Properties of Water Inrush through Broken Rock Mass

A large number of statistics indicate that broken rock mass always transforms into a flowing channel and leads to water inrush disasters in mining engineering, such as fault, karst, and strongly weathered rock mass. During the process of water inrush, the structure of the broken rock mass is constantly changing due to seepage erosion under high-velocity flow. Therefore, it is of vital importance to quantitatively evaluate the flow behavior of the water inrush related to the seepage erosion in order to prevent or reduce the risks. This study described a coupled nonlinear flow model, which couples the high-velocity seepage, the small particle migration, and the evolution of the broken rock mass structure. The model was verified firstly for simulation of nonlinear flow behavior by comparing with the traditional one. Then, the proposed model was used to simulate the evolution of particle migration and seepage properties of the water inrush through broken rock mass by a numerical case. The simulation results generally agree well with the existing experimental results. The simulations indicate that small particle migration causes the unstable characteristics of the seepage and the heterogeneity properties of the broken rock mass, which lead to the nonlinear flow behavior of the water inrush in both time and space. From a different perspective, it also indicates that the proposed model is capable of simulating the interaction of high-velocity seepage, small particle migration, and evolution of broken rock mass structure in the process of water inrush.

Numerical Simulation of Sulfur Deposit with Particle Release

Sulfur deposition commonly occurs during the development of a high-sulfur gas reservoirs. Due to the high gas flow velocity near the wellbore, some of the deposited sulfur particles re-enter the pores and continue to migrate driven by the high-speed gas flow. The current mathematical model for sulfur deposition ignores the viscosity between particles, rising flow caused by turbulence, and the corresponding research on the release ratio of particles. In order to solve the above problems, firstly, the viscous force and rising force caused by turbulence disturbance are introduced, and the critical release velocity of sulfur particles is derived. Then, a release model of sulfur particles that consider the critical release velocity and release ratio is proposed by combining the probability theory with the hydrodynamics theory. Notably, based on the experimental data, the deposition ratio of sulfur particles and the damage coefficient in the sulfur damage model are determined. Finally, a comprehensive particle migration model considering the deposition and release of sulfur particles is established. The model is then applied to the actual gas wells with visible sulfur deposition that target the Da-wan gas reservoir, and the results show that the model correctly reflects flow transport during the process of sulfur deposition in porous media. In addition, through the numerical simulation experiments, it was found that considering the release of sulfur particles reduces the saturation of sulfur particles within a specific range around the well and improve the reservoir permeability in this range. From the perspective of gas production rate, the release of sulfur particles has a limited effect on the gas production rate, which is mainly due to the sulfur particle release being limited, having only a 5 m range near the wellbore area, and thus the amount of gas flow from the unaffected area is basically unchanged.

Time-accurate calculation of two-phase granular flows exhibiting compaction, dilatancy and nonlinear rheology

In this paper we propose a time-accurate algorithm for the calculation of two-phase granular flows via two-velocity, two-pressure Eulerian models. Such flows exhibit a number of important characteristics that make their computation particularly challenging. For example, even at constant-density flows the suspended granular phase can compact or expand so that the velocity fields of the two phases are not solenoidal. Also, the granular material typically exhibits a complex and highly nonlinear rheological behaviour. Moreover, the governing equation for the granular volume fraction (often referred to in the literature as “compaction equation” or “particle migration model”) involves stresses as source terms and, therefore it is strongly coupled to the momentum balance laws. Herein we show that this coupling can be a strong destabilising factor in the computations if it is not treated properly. Our algorithm is based on a predictor–corrector time-integration scheme. Further, it employs a generalized double projection method for non-solenoidal velocity fields that results in second-order elliptic equations for the phasial pressures. The efficiency of the proposed algorithm is illustrated via a series of simulations of transient flows with strong concentration gradients, namely, sedimentation of a granular suspension, compaction of a dense sediment bed, and collapse of a submerged granular column. Numerical grid-convergence studies further show that the algorithm exhibits satisfactory convergence rates. Overall, these numerical results indicate that the proposed algorithm is well suited for the simulation of flows of dense suspensions, flows with high volume-fraction variations or material interfaces, as well as for unsteady fluid–solid interaction problems.

Improved understanding of the acoustophoretic focusing of dense suspensions in a microchannel.

We provide improved understanding of acoustophoretic focusing of a dense suspension (volume fraction φ>10%) in a microchannel subjected to an acoustic standing wave using a proposed theoretical model and experiments. The model is based on the theory of interacting continua and utilizes a momentum transport equation for the mixture, continuity equation, and transport equation for the solid phase. The model demonstrates the interplay between acoustic radiation and shear-induced diffusion (SID) forces that is critical in the focusing of dense suspensions. The shear-induced particle migration model of Leighton and Acrivos, coupled with the acoustic radiation force, is employed to simulate the continuum behavior of particles. In the literature, various closures for the diffusion coefficient D_{φ}^{*} are available for rigid spheres at high concentrations and nonspherical deformable particles [e.g., red blood cells (RBCs)] at low concentrations. Here we propose a closure for D_{φ}^{*} for dense suspension of RBCs and validate the proposed model with experimental data. While the available closures for D_{φ}^{*} fail to predict the acoustic focusing of a dense suspension of nonspherical deformable particles like RBCs, the predictions of the proposed model match experimental data within 15%. Both the model and experiments reveal a competition between acoustic radiation and SID forces that gives rise to an equilibrium width w^{*} of a focused stream of particles at some distance L_{eq}^{*} along the flow direction. Using different shear rates, acoustic energy densities, and particle concentrations, we show that the equilibrium width is governed by Péclet number Pe and Strouhal number Stasw^{*}=1.4(PeSt)^{-0.5} while the length required to obtain the equilibrium-focused width depends on St as L_{eq}^{*}=3.8/(St)^{0.6}. The proposed model and correlations would find significance in the design of microchannels for acoustic focusing of dense suspensions such as undiluted blood.

Synergy between shear-induced migration and secondary flows on red blood cells transport in arteries: considerations on oxygen transport.

Shear-induced migration of red blood cells (RBCs) is a well-known phenomenon characterizing blood flow in the small vessels (micrometre to millimetre size) of the cardiovascular system. In large vessels, like the abdominal aorta and the carotid artery (millimetre to centimetre size), the extent of this migration and its interaction with secondary flows has not been fully elucidated. RBC migration exerts its influence primarily on platelet concentration, oxygen transport and oxygen availability at the luminal surface, which could influence vessel wall disease processes in and adjacent to the intima. Phillips' shear-induced particle migration model, coupled to the Quemada viscosity model, was employed to simulate the macroscopic behaviour of RBCs in four patient-specific geometries: a normal abdominal aorta, an abdominal aortic aneurysm (AAA), a normal carotid bifurcation and a stenotic carotid bifurcation. Simulations show a migration of RBCs from the near-wall region with a lowering of wall haematocrit (volume fraction of RBCs) on the posterior side of the normal aorta and on the lateral-external side of the iliac arteries. A marked migration is observed on the outer wall of the carotid sinus, along the common carotid artery and in the carotid stenosis. No significant migration is observed in the AAA. The spatial and temporal patterns of wall haematocrit are correlated with the near-wall shear layer and with the secondary flows induced by the vessel curvature. In particular, secondary flows accentuate the initial lowering in RBC near-wall concentration by convecting RBCs from the inner curvature side to the outer curvature side. The results reinforce data in literature showing a decrease in oxygen partial pressure on the inner curvature wall of the carotid sinus induced by the presence of secondary flows. The lowering of wall haematocrit is postulated to induce a decrease in oxygen availability at the luminal surface through a diminished concentration of oxyhaemoglobin, hence contributing, with the reported lowered oxygen partial pressure, to local hypoxia.

Model for particle migration in bidisperse suspensions by use of effective temperature

A model for the particle migration in a bidisperse flowing suspension is proposed and compared to experimental data. A mixture formulation, describing the suspension velocity and pressure and the concentrations of two solid fractions is derived from a multi-fluid model. In the multi-fluid model the liquid phase and both dispersed phases are interpenetrating phases. The closure relations are based on a mean field approach extending closure relations of a monodisperse suspension. The model is used to predict segregation based on particle size in channel flow where the particles are subjected to Brownian motion and shear-induced migration. The comparison of the model results with experimental data shows that particle migration is predicted well by the given formulation.

Numerical simulation of natural convection of a water-based nanofluid

We simulated steady and unsteady natural convection flows of a nanofluid in a square cavity. If the particle distribution is perfectly uniform there is a reduction of the heat transfer rates of about 1% in comparison with those corresponding to the pure liquid. The Lagrangian tracking of the particles shows that there is no preferential concentration of particles. However the local instantaneous fluctuations of the particle concentration induced by the tracking of a finite number of particles produce reductions of the heat transfer rates of about 2-3%. The particle migration model used predicts negligible non-uniformities in the particle distribution.

Red blood cell migration in microvessels

Red blood cell (RBC) migration effects and RBC-plasma interactions occurring in microvessel blood flow have been investigated numerically using a shear-induced particle migration model. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced RBC migration in concentrated suspensions. The model couples a non-Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the viscosity is dependent on the haematocrit and the shear rate (Quemada model). The focus of this paper is on the determination of the two phenomenological parameters, Kc and Kmu, in a diffusive flux model when using the non-Newtonian Quemada model and assuming deformable particles. Previous use of the diffusive flux model has assumed constant values for the diffusion coefficients which serve as tuning parameters in the phenomenological equation. Here, previous data [Biophys. J. 92 (2007), 1858-1877; J. Fluid Mech. 557 (2006), 297-306] is used to develop a new model in which the diffusion coefficients depend upon the tube haematocrit and the dimensionless vessel radius for initially uniform suspensions. This model is validated through previous publications and close agreement is obtained.

Three‐dimensional free surface flow simulation of segregating dense suspensions

AbstractThis paper presents a 3D numerical solution algorithm for the simulation of free surface flows of dense suspensions including particle migration phenomena. Segregation of the solid phase in processes such as powder injection molding and molding of semi‐solid materials affects the rheology of the mixture and therefore the filling pattern. Segregation affects also the final properties and characteristics of such molded parts as a non‐uniform particles distribution leads to non‐uniform shrinkage, warpage and non‐uniform mechanical properties. In this paper, particle migration is modeled using the diffusion flux model of Phillips et al. (Phys. Fluids A 1992; 4:30–40) and is extended to address 3D mold filling problems. The solution algorithm is validated against flow problems for which experimental and numerical data are available: circular Couette flow, piston‐driven flow and sudden contraction–expansion flow. The particle migration model is then used to simulate mold filling problems in which the piston movement in the sleeve is known to induce particle migration before the material enters the cavity. An arbitrary Lagrangian–Eulerian (ALE) formulation is developed and combined to a level‐set front capturing method to simulate the piston movement and the evolution of the free surface in molding simulations. The ALE formulation is first compared with an Eulerian solution for the case of the piston‐driven flow problem. The approach is then applied to injection molding problems to study the evolution of particle distributions during molding and in the final molded parts. Copyright © 2008 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.

Determination of phenomenological constants of shear-induced particle migration model

Particles in initially well-mixed suspensions subject to inhomogeneous shear flows will migrate and establish a particle concentration gradient and a non-Newtonian velocity profile. In this study, a phenomenological diffusive flux model coupled with flow equations was employed to describe the shear-induced particle migration in a concentrated suspension. The focus of the paper is on the determination of the two phenomenological constants in the diffusive flux model k c and k η . They were determined inversely by employing a least square analysis on the experimental pressure data with different capillary die ratios of length to diameter of the die. The pressures and the flow patterns of the non-Newtonian concentrated suspension were predicted in terms of these two phenomenological constants. The results indicated that particle migration should be accounted for to properly characterize the rheological behaviour of concentrated suspensions.

Mathematical model of migration of spherical particles in tube flow under the influence of inertia and particle-particle interaction

In this paper, a mathematical model is considered of the migration of non-colloidal, spherical particles suspended in Newtonian fluid under Poiseuille flows by combining the inertial migration theory by Ho and Leal (JFM, 1974) and particle migration model in concentrated suspension by Phillips et al. (Phys. Fluids, 1992). The numerical solutions of the model equations reveal that the model set up here explains the experimental observation reported in the literature when Re p<1, at least qualitatively. It was concluded that both the inertia and particle-particle interaction should be taken into account properly to understand the particle migration in tube flow of suspension regardless of particle loading.

Shear-induced diffusion model for microfiltration of polydisperse suspensions

A detailed study on concentration polarisation during microfiltration (MF) was carried out in order to improve control on cake layer formation. Concentration polarisation is reduced by several back-transport mechanisms, however, for particles in the size range 0.5–30 μm shear-induced diffusion is the predominant one. Shear-induced diffusion is caused by the hydrodynamic interactions between particles in shear flow, which are strongly dependent on the particle size. Because of this, the polydispersity of suspensions is expected to have a large effect on cake layer formation. Although this aspect will be of considerable practical relevance, it has only received minor attention in literature. In this work, the effect of particle size distribution on MF was investigated by studying the steady-state flux of bidisperse suspensions with a ratio of particle radii of 3. The flux appeared to be completely determined by the smaller particles; it remained almost constant between a volume fraction of 0.2 and 1 of small particles. This trend in the steady-state flux was in good agreement with calculations based on a shear-induced particle migration model for polydisperse suspensions. Since polydispersity is a common property of suspensions, the present work may contribute to optimisation of flux and selectivity in MF processes, which depend largely on adequate control of cake layer formation. This can be achieved by implementation of the developed model in process control routines.

Shear-induced particle migration in a short-dwell coater

This paper aims at simulating the flow of a pigment suspension in a short-dwell coater (SDTA), a common device used for the production of value-added paper. The process consists of depositing onto a paper web a thin coating layer, the uniformity and the quality of which depend on the short-dwell coater geometry and the coating color rheology. In order to understand the possible interactions between the hydrodynamics in the pond and the rheological behavior of the suspension, this study focuses on a phenomenon known as shear-induced particle migration, which may result in an non-homogeneous suspension. For this purpose, a numerical methodology based on a shear-induced particle migration model (Sim) and the finite element method is presented and validated against analytical results and experimental data. This numerical approach constitutes the first step towards a better understanding of the hydrodynamic mechanisms that govern particle migration in a short-dwell paper coater. In this work, a parametric study of the suspension flow behavior is carried out via the introduction of a new dimensionless number that characterizes the importance of the shear-induced migration with respect to particle convection. The proposed model is used to generate particle distribution templates. It is shown that the particle size and Reynolds number are preponderant factors that affect the extent at which migration occurs in the short-dwell coater. In particular, it is shown that increasing the Reynolds number amplifies the migration phenomena and the formation of high concentration zones within a ring located in a vortex just before the nip. Such a concentration overshoot may then be dragged into the nip, resulting in runnability problems such as web breaks or coating color spitting.

Drift Velocity Concept for Sediment-Laden Flows

The vertical distribution of suspended sediment concentration in open channel flows is usually described by the advection-diffusion equation. Hence, only the mechanisms of advection and diffusion affect the movement of sediment particles. However, recent publications show that the equation could not describe fully the sediment concentration distribution in open channels. A new model for particle migration in sediment-laden turbulent flow is presented. The model assumes there is an additional mechanism influencing the particle movement in sediment-laden flows. A new mechanism, which is called the drift, acts independently of advection and turbulent diffusion. Based on all three mechanisms, a new equation for the concentration distribution is derived. The equation describes the vertical distribution of sediment concentration more accurately than the advection-diffusion equation.

Discussions and Closure: Analytical Model for Particle Migration within Base Soil-Filter System

Discussions and Closure: Analytical Model for Particle Migration within Base Soil-Filter System

Discussion of “Analytical Model for Particle Migration within Base Soil-Filter System” by Lakshmi N. Reddi

Discussion of “Analytical Model for Particle Migration within Base Soil-Filter System” by Lakshmi N. Reddi

Closure to “Analytical Model for Particle Migration within Base Soil-Filter System” by B. Indraratna

Closure to “Analytical Model for Particle Migration within Base Soil-Filter System” by B. Indraratna

Finite size particle diffusion to the surface of a rotating disk

Levich's convective diffusion model for particle migration towards the surface of a rotating disk is extended to account for the particle size. The solution of the convective diffusion integral equation shows that the diffusional boundary layer thickness, δ c, is independent of the disk radius but is inversely dependent on the particle size. The surface flux is shown to be higher for larger particles than Levich's prediction, but the two models approach as the particles become smaller.