Multiparticle Suspension Research Articles

Transient electrophoresis of spherical colloidal particles in a multi-particle suspension

Transient electrophoresis of spherical colloidal particles in a multi-particle suspension

Immersed-finite-element method for deformable particle suspensions in viscous and viscoelastic media

Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid and fluid domains. An immersed boundary algorithm is exploited known as the immersed finite element method (IFEM) which accurately determines the internal forces in the solid domain. The scheme utilized has the advantages of requiring no costly re-meshing, handling finite Reynold's number, as well as incorporating non-linear viscoelasticity in the fluid domain. Our algorithm is designed for computationally efficient simulation of multi-particle suspensions with mixed structure types. The internal force calculation in the solid domain in the IFEM is coupled with a finite volume based incompressible fluid solver, both of which are massively parallelized for distributed memory architectures. We performed extensive case studies to ensure the fidelity of our algorithm. Namely, a series of single particle simulations for capsules, red blood cells, and elastic solid deformable particles were conducted in viscous and viscoelastic media. All of our results are in excellent quantitative agreement with the corresponding reported data in the literature which are based on different simulation platforms. Furthermore, we assess the accuracy of multi-particle simulation of blood suspensions (red blood cells in plasma) with and without platelets. Finally, we present the results of a novel simulation of multiple solid deformable objects in a viscoelastic medium.

Multi-particle suspension in a laminar flow agitated by a Rushton turbine

Multi-particle suspension in a laminar stirred tank flow agitated by a standard Rushton turbine was investigated experimentally and numerically. In the experiments, the motion of the particles was measured by two high-speed cameras and was quantitatively analyzed. Two very stable particle patterns were observed. Strong flow is required to break these patterns because their formation hinders the particle lift-off process. The experimental trajectories and vertical velocities of the particles were measured, and highly reproducible results were found. Direct numerical simulations based on the lattice-Boltzmann method and the resolved particle model were performed to fully resolve the motion of the particles and the flow field. The influence of the friction coefficient and the subgrid lubrication force model on particle suspension was evaluated. Except for the random characteristics of particles interaction at the initial lift-off stage, the predicted trajectories and velocities of the particles are in good agreement with the experimental results. The pressure gradient around the particles is a key mechanism for the lift-off process.

A numerical study on dynamic inertial focusing of microparticles in a confined flow

Inertial microfluidics is regarded as a promising approach to facilitate precise, robust and continuous manipulation of particles through inertial focusing of particles in microchannels. Although there is a need to gain rich insights into the focusing dynamics of particles, it has been hardly studied numerically. In this study, the complex focusing dynamics of particles is simulated numerically for multi-particle suspensions in confined microchannels. To this end, we develop a new method that couples the discrete element method (DEM) with the direct numerical simulation (DNS). This method is referred to as the DEM–DNS method. In order to validate the DEM–DNS method, we then investigate complex dependence of particle behaviour on Reynolds number and channel geometries. With good agreement between the numerical results and existing observations, it is shown for the first time that the DEM–DNS method can simulate the counterintuitive focusing dynamics of particles. This study thus establishes that the DEM–DNS method is a powerful tool to examine the focusing dynamics of particles in inertial microfluidics.

Fluid-particle Drag Force in Binary-solid Suspensions

The drag force on a particle in a multiparticle suspension is a function of the particle-fluid relative velocity and of the particle volume concentration. Its determination heavily relies on experimental observations, as theoretical support is still limited to viscous flow regime and dilute solid concentrations. When uniform particle suspensions are considered, there is a certain abundance of experimental data available which has permitted the proposition of simple and reliable relationships for the determination of the drag force: these relationships are normally expressed through the use of the so-called “voidage function”, i.e. a function by which the drag force on an isolated particle has to be multiplied in order to obtain the drag force on a particle in a multiparticle suspension. The extension of the approach mentioned above to suspensions made up of particles differing in size and density has been attempted here and new simple relationships are presented for the case of binary-solid systems. The basic idea draws an analogy between binary-solid suspension and single-particle suspensions thereby making possible the use of well established results. The simple relationships obtained for the estimation of the drag force on a particle in a binary-solid suspension have been tested, with satisfactory success, against experimental data available in literature.

Simulation of multi-particle suspensions in a quasi-two-dimensional symmetric stenotic artery with Lattice Boltzmann method

The three-dimensional Lattice Boltzmann model has been applied to the study of rigid particle suspensions through a quasi-two-dimensional modelled arterial stenosis. Only when two particles are positioned symmetrically to the centerline to an extremely high accuracy, the particles can be blocked completely at the stenosis throat. Particles incline to gather near the centerline for a stenosis throat width b < 2d, consistent with the observation that red blood cells tend to concentrate near the center of the vessel. The present study shows that the quasi-two-dimensional system is an effective model to study the behaviour of three-dimensional multi-particle suspension in stenotic arteries.

Lattice Boltzmann simulation of a single charged particle in a Newtonian fluid.

The lattice Boltzmann method is used to study the sedimentaion of a single charged circular cylinder in a two-dimensional channel in a Newtonian fluid. When the dielectric constant of the liquid is smaller than that of the walls, there are attractive forces between the particle and the walls. The hydrodynamic force pushes the particle towards the centerline at low Reynolds numbers. Due to the competition between the Coulomb force and the hydrodynamic force in opposite directions, there is a critical linear charge density q(c) at which the particle will fall vertically off centerline, which is a metastable state in addition to the stable state on centerline, for any initial position of the particle sufficiently far from the proximal wall. It is found that the rotation of the particle plays an important role in the stability of such metastable states. The particle hits on the wall or falls on the centerline when the linear charge density on the particle is greater or less than q(c). The simulation method and the new phenomena are also helpful in the study of charged multiparticle suspensions.

The particle-in-a-tube analogy for a multiparticle suspension

A simple analogy between a multiparticle suspension and a single particle in a tube has been obtained by using the concept of “hydraulic diameter”. Fully theoretical derivations for the effect of the wall on the single particle enable the solid-fluid interaction force to be estimated with no empirical input for the viscous and the inertial flow regimes. The analogy is successfully tested in the intermediate flow regime and finally the expansion characteristics of homogeneous fluidised beds is obtained, in good agreement with the Richardson & Zaki (1954) equation, by using experimental data on the terminal settling velocity of a lone particle in a tube.

A relationship for the wall effect on the settling velocity of a sphere at any flow regime

By using a fluid dynamic analogy between a single particle in a tube and a multiparticle suspension previously derived, a relationship for the wall effect on the terminal settling velocity of a single particle in a cylindrical tube is obtained. Unlike previous relationships, this one is valid for any flow regime, from viscous to fully inertial, and it is in good agreement with experimental evidence.

Wall effects on the sedimentation velocity of suspensions in viscous flow

AbstractThe sedimentation velocity of multiparticle suspensions was investigated experimentally for cases where the column wall is likely to have a nonnegligible effect. The experiments demonstrate that the container wall diameter influeces the falling velocity only for dilute systems, which is in contrast with a widely used, established empirical relationship.

Determination of crystal growth kinetics from desupersaturation measurements

The growth kinetics of oxalic acid dihydrate have been determined in a multiparticle suspension by measuring (a) the solution concentration during growth and (b) the final crystal size distribution. The method of calculation involves the use of the number mean size together with the second and third moments of the product size distribution. It is necessary to assume that the number of crystals remains constant and that crystal growth rate is independent of size.

空間率関数とレイノルズ数

The sedimentation rate of multiparticle suspension in a stationary fluid, um, decreases with increasing particle concentrations. The voidage function F(e) is defined as F(e)=v∞/um, where v∞ is the terminal velocity of single particle in the infinite stationary fluid.In order to generalize the voidage function to cover the entire ranges of flow, namely, laminar (St), intermediate (Al), and turbulent (N) flow regions, the following equation is given.FSt(e)=[FAl(e)]m=[FN(e)]2where m varies from 1 to 1.63 continuously with Reynolds number in the intermediate flow region, when calculated from the drag coefficient correlation of a single sphere motion according to Schiller. Previously, Richardson-Zaki has pointed out that m varies from 1 to 2 in the same intermediate flow region and some other investigators reported m to be 1.4 or constant.The voidage function in each flow region, obtained from the correlations of Kozeny-Carman or Ergun, has been found in good agreement with the voidage function of Richardson-Zaki in a certain range of voidage.

Power‐law fluids flow through multiparticle system

AbstractA study on the flow of power‐law fluids through a multi‐particle system including both fixed bed and fluidized bed is presented. Equations for the pressure drop, the minimum fluidization velocity, and the bed expansion are obtained by extending the Blake‐Kozeny's equation for the pressure drop through packed beds to power‐law fluids. Bed expansion equations are also obtained by extending the Richard‐son‐Zaki's theory for the drag force in a multiparticle suspension to power‐law fluids. These equations are compared with experimental data.