Two- and three-dimensional lattice Boltzmann simulations of particle migration in microchannels

The use of two-dimensional (2D) numerical simulations with a reduced particle-based Reynolds number (Re) for studying particle migration in a microchannel with equally spaced multiple constrictions was investigated. 2D and 3D colloidal lattice Boltzmann (LB) models were used to simulate particle-fluid hydrodynamics. Experiments were conducted with inert microparticles in a creeping flow in a microflow channel with symmetric wall obstacles. Lowering Re in 2D simulations by a factor of R (the dimensionless particle radius in LB simulations) resulted in a close match between numerically computed and experimentally obtained particle velocities, indicating that Re-based dimensional scaling was needed to capture the 3D particle flow dynamics in 2D simulations of experimental data. We captured particle displacement motion in a microchannel with symmetric inline obstacles in 2D simulations, where symmetry in the flow field was broken by local disturbances in the flow field due to particle motion, indicating that asymmetry in channel geometry is not the sole cause for particle displacement motion. Particle acceleration/deceleration around each constriction followed the same pattern, but each constriction acted like a particle accelerator in 2D and 3D simulations, in which particles exhibited progressively higher velocities in each subsequent constriction. Particles migrated across multiple streamlines in converging and diverging flow zones in a creeping flow, which calls into question the use of steady streamlines for calculating transient particle flow. Monotonicity in particle acceleration toward the constriction and deceleration beyond the constriction was broken by interparticle hydrodynamic interactions leading to more pronounced particle migration across multiple streamlines.     

Dynamics of rotating paramagnetic particle chains simulated by particle dynamics,Stokesian dynamics and lattice Boltzmann methods

Paramagnetic particles, when subjected to external unidirectional rotating magnetic fields, form chains which rotate along with the magnetic field. In this paper three simulation methods, particle dynamics (PD), Stokesian dynamics (SD) and lattice Boltzmann (LB) methods, are used to study the dynamics of these rotating chains. SD simulations with two different levels of approximations—additivity of forces (AF) and additivity of velocities (AV)—for hydrodynamic interactions have been carried out. The effect of hydrodynamic interactions between paramagnetic particles under the effect of a rotating magnetic field is analyzed by comparing the LB and SD simulations, both of which include hydrodynamic interactions, with PD simulations in which hydrodynamic interactions are neglected. It was determined that for macroscopically observable properties like average chain length as a function of Mason number, reasonable agreement is found between all the three methods. For microscopic properties like the force distribution on each particle along the chain, inclusion of hydrodynamic interaction becomes important to understand the underlying physics of chain formation. Any opinion, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

Volume preserving viscoelastic fluids with large deformations using position-based velocity corrections

We propose a particle-based hybrid method for simulating volume preserving viscoelastic fluids with large deformations. Our method combines smoothed particle hydrodynamics (SPH) and position-based dynamics (PBD) to approximate the dynamics of viscoelastic fluids. While preserving their volumes using SPH, we exploit an idea of PBD and correct particle velocities for viscoelastic effects not to negatively affect volume preservation of materials. To correct particle velocities and simulate viscoelastic fluids, we use connections between particles which are adaptively generated and deleted based on the positional relations of the particles. Additionally, we weaken the effect of velocity corrections to address plastic deformations of materials. For one-way and two-way fluid-solid coupling, we incorporate solid boundary particles into our algorithm. Several examples demonstrate that our hybrid method can sufficiently preserve fluid volumes and robustly and plausibly generate a variety of viscoelastic behaviors, such as splitting and merging, large deformations, and Barus effect.     

Efficient computation of micro-particle dynamics including wall effects

This study describes an effective method for one-way coupled Eulerian-Lagrangian simulations of spherical micro-size particles, including particle-wall interactions and the quantification of near-wall stasis at possibly elevated concentrations. The focus is on particle-hemodynamics simulations where particle suspensions are composed of critical blood cells, such as monocytes, and the carrier fluid is non-Newtonian. Issues regarding adaptive time-step integration of the particle motion equation, relevant point-force model terms, and adaptation of surface-induced particle forces to arbitrary three-dimensional geometries are outlined. By comparison to available experimental trajectories, it is shown that fluid-element pathlines may be used to simulate non-interacting blood particles removed from wall boundaries under dilute transient conditions. However, when particle-wall interactions are significant, an extended form of the particle trajectory equation is required which includes terms for Stokes drag, near-wall drag modifications, or lubrication forces, pressure gradients, and near-wall particle lift. Still, additional physical and/or biochemical wall forces in the nano-meter range cannot be readily calculated; hence the near-wall residence time (NWRT) model indicating the probability of blood particle deposition is presented. The theory is applied to a virtual model of a femoral bypass end-to-side anastomosis, where profiles of the Lagrangian-based NWRT parameter are illustrated and convergence is verified. In order to effectively compute the large number of particle trajectories required to resolve regions of particle stasis, the proposed particle tracking algorithm stores all transient velocity field solution data on a shared memory architecture (SGI Origin 2400) and computes particle trajectories using an adaptive parallel approach. Compared to commercially available particle tracking packages, the algorithm presented is capable of reducing computational time by an order of magnitude for typical transient one-way coupled blood particle simulations in complex cyclical flow domains.     

Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow

Coupling the immersed boundary (IB) method and the lattice Boltzmann (LB) method might be a promising approach to simulate fluid-structure interaction (FSI) problems with flexible structures and moving boundaries. To investigate the possibility for future IB-LB coupled simulations of the heart flow dynamics, an IB-LB coupling scheme suitable for rapid boundary motion and large pressure gradient FSI is proposed, and the mitral valve jet flow considering the interaction of leaflets and fluid is simulated. After analyzing the respective concepts, formulae and advantages of the IB and LB methods, we first explain the coupling strategy and detailed implementation procedures, and then verify the effectiveness and second-order accuracy of the scheme by simulating a benchmark case, the relaxation of a stretched membrane immersed in fluid. After that, the diastolic filling jet flow between mitral leaflets in a simplified 2D left heart model is simulated. The model consists of the simplified transmitral passage of the heart and two curvilinear leaflets. In the simulation, the atrial and ventricular pressure histories of normal human are specified as boundary conditions, and the leaflets are treated as fibers that interact with the fluid to define their deformations and movements. The resulting opening and closing movements of the leaflets and the flow patterns of the filling jet are qualitatively reasonable and compare well with existing numerical and measured data. It is shown that this IB-LB coupling method is feasible for treating flexible boundary FSI problems with rapid boundary motion and large pressure gradient, the results of the mitral leaflet flow are valuable for understanding the transmitral FSI dynamics, and it is possible to simulate the more realistic 3D heart flow by the scheme in the future.     

Coupled lattice Boltzmann and discrete element modelling of fluid–particle interaction problems

Particle–fluid systems encountered in many scientific and engineering applications impose a significant modelling challenge. This paper outlines a new solution strategy that couples lattice Boltzmann (LB), large eddy simulation (LES), and discrete element (DE) methodologies for the simulation of particle–fluid systems at moderately high Reynolds numbers. The following main computational issues are considered: (1) the use of the standard LB formulation for the solution of fluid flows; (2) the incorporation of the one-parameter Smagorinski turbulence model in the LB equations for turbulent flows; (3) the utilisation of one immersed boundary scheme for computing hydrodynamic interaction forces between the fluid and moving particles; and (4) the use of DE methods accounting for the interaction between solid particles. The new contributions made in the current work include the application of the Smagorinski turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling in order to ensure an overall stable LB–DE solution. A complex transport problem involving 70 large moving particles with moderately high Reynolds number (around 56,000) is provided to demonstrate the capability of the presented coupling strategy.     

Realistic and stable simulation of turbulent details behind objects in smoothed‐particle hydrodynamics fluids

This paper presents a novel realistic and stable turbulence synthesis method to simulate the turbulent details generated behind objects in smoothed particle hydrodynamics (SPH) fluids. Firstly, by approximating the boundary layer theory on the fly in SPH fluids, we propose a vorticity production model to identify which fluid particles shed from object surfaces and which are seeded as vortex particles. Then, we employ an SPH‐like summation interpolant formulation of the Biot–Savart law to calculate the fluctuating velocities stemming from the generated vorticity field. Finally, the stable evolution of the vorticity field is achieved by combining an implicit vorticity diffusion technique and an artificial dissipation term. Moreover, in order to efficiently catch turbulent details for rendering, we propose an octree‐based adaptive surface reconstruction method for particle‐based fluids. The experiment results demonstrate that our turbulence synthesis method provides an effect way to model the obstacle‐induced turbulent details in SPH fluids and can be easily added to existing particle‐based fluid–solid coupling pipelines. Copyright © 2014 John Wiley & Sons, Ltd.     

Aggregation and clogging phenomena of rigid microparticles in microfluidics

We developed a numerical tool to investigate the phenomena of aggregation and clogging of rigid microparticles suspended in a Newtonian fluid transported through a straight microchannel. In a first step, we implement a time-dependent one-way coupling Discrete Element Method (DEM) technique to simulate the movement and effect of adhesion on rigid microparticles in two- and three-dimensional computational domains. The Johnson–Kendall–Roberts (JKR) theory of adhesion is applied to investigate the contact mechanics of particle–particle and particle–wall interactions. Using the one-way coupled solver, the agglomeration, aggregation and deposition behavior of the microparticles is studied by varying the Reynolds number and the particle adhesion. In a second step, we apply a two-way coupling CFD–DEM approach, which solves the equation of motion for each particle, and transfers the force field corresponding to particle–fluid interactions to the CFD toolbox OpenFOAM. Results for the one-way (DEM) and two-way (CFD–DEM) coupling techniques are compared in terms of aggregate size, aggregate percentages, spatial and temporal evaluation of aggregates in 2D and 3D. We conclude that two-way coupling is the more realistic approach, which can accurately capture the particle–fluid dynamics in microfluidic applications.     

Coupling of rigid body dynamics and moving particle semi-implicit method for simulating isothermal multi-phase fluid interactions

The moving particle semi-implicit (MPS) method does not require grids for simulating fluid motions. Therefore, the MPS method can easily handle a large deformation of fluid. However, the MPS method has some difficulties in simulating transfer of momentum caused by a physical collision between different fluids because fluid particles have no mass or volume and only have weights for interacting with other particles. To overcome this inherent defect of the MPS method, rigid body dynamics is explicitly coupled with the MPS method in this study. In the first step, the MPS calculation is performed with particles which are considered to have no mass or volume. In the second step, rigid body dynamics comes into the calculation and considers the particles to have a slightly lesser diameter than the initial distance between particles. Then, physical contacts between particles are simulated with the dynamic energy conserved while the incompressibility of fluids is effectively maintained. In the single fluid region, the coupled method deals with the behavior of the particles. For the interface of the different fluids, only rigid body dynamics is used to simulate the transfer of the momentum caused by physical collisions of fluids. Through this coupling of rigid body dynamics and the MPS method, the overall stability related with the incompressibility of a fluid is comparatively increased in the single-phase fluid simulation. For the calculation of the multi-phase fluids behavior, fluids interactions can be easily treated with improving stability of the MPS calculation. In this study, collapse of water column and the isothermal fuel–coolant interaction (FCI), in which a water jet is directed into a denser fluid pool, were simulated to validate the coupling method of the MPS method and rigid body dynamics.     

A lattice Boltzmann study of the effect of stirring on the migration rate of a curved interface in binary slurries

Morphological evolution of particles in semisolid slurries has been modeled as the migration of a double-peak shape solid–liquid interface. The valley between the peaks represents the solute-trapping area between the dendrite arms. Various boundary shear conditions were considered to mimic the real processing environments. A lattice Boltzmann model for isothermal miscible binary flows has been utilized to handle the hydrodynamics and chemical diffusion. Fixed solute concentration at the solid–liquid interface was introduced to simulate the steady growth of the solid particle. Numerical simulations reveal that shearing the slurries in a direction perpendicular to the growth direction of the particle tips encourages dendrite growth, which agrees with the theoretical prediction based on interface stability analysis. Shearing the boundary along a direction parallel to the growth direction of the particle tips, however, caused a larger increment in the migration rate of the interface in the valley, and is considered the major reason for dendrite–rosette morphological transformation.     

Stable and Fast Fluid–Solid Coupling for Incompressible SPH

The solid boundary handling has been a research focus in physically based fluid animation. In this paper, we propose a novel stable and fast particle method to couple predictive–corrective incompressible smoothed particle hydrodynamics and geometric lattice shape matching (LSM), which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences. By combining the boundary particles sampled from solids with a momentum‐conserving velocity‐position correction scheme, our approach can alleviate the particle deficiency issues and prevent the penetration artefacts at the fluid–solid interfaces simultaneously. We further simulate the stable deformation and melting of solid objects coupled to smoothed particle hydrodynamics fluids based on a highly extended LSM model. In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs using compute unified device architecture. The advantages of our two‐way fluid–solid coupling method in computer animation are demonstrated via several virtual scenarios.     

Multiscale simulations of primary atomization

A liquid jet upon atomization breaks up into small droplets that are orders of magnitude smaller than its diameter. Direct numerical simulations of atomization are exceedingly expensive computationally. Thus, the need to perform multiscale simulations. In the present study, we performed multiscale simulations of primary atomization using a Volume-of-Fluid (VOF) algorithm coupled with a two-way coupling Lagrangian particle-tracking model to simulate the motion and influence of the smallest droplets. Collisions between two particles are efficiently predicted using a spatial-hashing algorithm. The code is validated by comparing the numerical simulations for the motion of particles in several vortical structures with analytical solutions. We present simulations of the atomization of a liquid jet into droplets which are modeled as particles when away from the primary jet. We also present the probability density function of the droplets thus obtained and show the evolution of the PDF in space.     

Hybrid particle–grid fluid animation with enhanced details

Simulating large-scale fluid while retaining and rendering details still remains to be a difficult task in spite of rapid advancements of computer graphics during the last two decades. Grid-based methods can be easily extended to handle large-scale fluid, yet they are unable to preserve sub-grid surface details like spray and foam without multi-level grid refinement. On the other hand, the particle-based methods model details naturally, but at the expense of increasing particle densities. This paper proposes a hybrid particle–grid coupling method to simulate fluid with finer details. The interaction between particles and fluid grids occurs in the vicinity of “coupling band” where multiple particle level sets are introduced simultaneously. First, fluids free of interaction could be modeled by grids and SPH particles independently after initialization. A coupling band inside and near the interface is then identified where the grids interact with the particles. Second, the grids inside and far away from the interface are adaptively sampled for large-scale simulation. Third, the SPH particles outside the coupling band are enhanced by diffuse particles which render little computational cost to simulate spray, foam, and bubbles. A distance function is continuously updated to adaptively coarsen or refine the grids near the coupling band and provides the coupling weights for the two-way coupling between grids and particles. One characteristic of our hybrid approach is that the two-way coupling between these particles of spray and foam and the grids of fluid volume can retain details with little extra computational cost. Our rendering results realistically exhibit fluids with enhanced details like spray, foam, and bubbles. We make comprehensive comparisons with existing works to demonstrate the effectiveness of our new method.     

On the direct employment of dipolar particle interaction in microfluidic systems

This review article will summarize recent developments in the employment of dipolar coupled magnetic particle structures. We will discuss the basics of magnetic dipolar particle interaction in static and rotating magnetic fields. In dependence on the magnetic fields employed, agglomerates of different dimensionality may form within the carrier liquid. The stability and formation dynamics of these particle structures will be presented. Furthermore, we will review recent microfluidic applications based on the interaction of magnetic particles and present methods for surface patterning with micron-sized and nano-sized particles which employ dipolar particle coupling.     

Lagrangian particle model for multiphase flows

A Lagrangian particle model for multiphase multicomponent fluid flow, based on smoothed particle hydrodynamics (SPH), was developed and used to simulate the flow of an emulsion consisting of bubbles of a non-wetting liquid surrounded by a wetting liquid. In SPH simulations, fluids are represented by sets of particles that are used as discretization points to solve the Navier-Stokes fluid dynamics equations. In the multiphase multicomponent SPH model, a modified van der Waals equation of state is used to close the system of flow equations. The combination of the momentum conservation equation with the van der Waals equation of state results in a particle equation of motion in which the total force acting on each particle consists of many-body repulsive and viscous forces, two-body (particle-particle) attractive forces, and body forces such as gravitational forces. Similar to molecular dynamics, for a given fluid component the combination of repulsive and attractive forces causes phase separation. The surface tension at liquid-liquid interfaces is imposed through component dependent attractive forces. The wetting behavior of the fluids is controlled by phase dependent attractive interactions between the fluid particles and stationary particles that represent the solid phase. The dynamics of fluids away from the interface is governed by purely hydrodynamic forces. Comparison with analytical solutions for static conditions and relatively simple flows demonstrates the accuracy of the SPH model.     

A three-dimensional hydro-geochemical model to assess lake acidification risk

Biogeochemical and hydrological fluxes from riparian zones to lake environments can be significant, particularly for shallow systems experiencing large variations in water level, yet they are not considered in water quality models. To address this challenge we dynamically coupled a three-dimensional surface water model with a soil hydro-geochemical model of the riparian zone and used the coupled system to simulate the impacts of acid sulfate soils on the water quality of a morphologically complex coastal lake system in South Australia. A 3-yr simulation was undertaken to capture a period of exposure and re-flooding of pyrite-bearing sediments and acid fluxes to the lake. Model performance was assessed against data from several acidification events that occurred and the simulations reproduced the observed spatio-temporal variation in the expression of soil and water acidity. The model approach introduced here has potential for simulating systems where the terrestrial–aquatic linkage is important in shaping water quality.     

Experimental and numerical investigation on particle–particle interaction of multi-particle separation in an alternating and repetitive microchannel

Inertial focusing plays a major role in size-based cell separation or enrichment for microfluidic applications in many medical areas such as diagnostics and treatment. These applications often deal with suspensions of different particles which cause interactions between particles with different diameters such as particle–particle collision. In this study, particle–particle interaction in a laminar flow through a low aspect ratio alternating and repetitive microchannel is investigated both numerically and experimentally. It is revealed that particle–particle collision affects high quality particle focusing. computational fluid dynamics simulations are conducted for demonstrating the effect of the flow field in the transverse cross-section on the focusing quality and position. The experiments and simulations both revealed that if the flow is seeded with a mixture of particles of 3.3 and 9.9 µm diameters, the quality of focusing intensity is degenerated compared to the focusing features obtained by particles with a diameter of 9.9 µm solely. The results clearly show that particle–particle collision between the 3.3 and 9.9 µm particles has a negative effect on particle focusing behavior of the 9.9 µm particles.

     

Coupling of local visualization and numerical approach for particle microfiltration optimization

The performance of the microfiltration process is controlled by the filter fouling due to the accumulation of solid matter forming a cake layer on the membrane surface. The objective of this work is to study the cake build up and growth at the particle level and to establish correlations with microfiltration performance measured at the process scale. A theoretical model coupling Navier–Stokes equation, convective/diffusion particle transport and deposit formation is developed to simulate a sequence of microfiltration in a confined geometry (Comsol Multyphysics^®). This model is used to make predictive simulations of cake growth during the filtration of diluted particles in the range of size of microorganism (5 μm). In the same time a specific filtration micro-system including an optical chamber and a microsieve (Aquamarijn^®) filtration membrane is designed in order to perform an experimental approach allowing in situ 3D-visualization of a deposit of model particles (polystyrene fluorescent microspheres) using Confocal laser scanning microscopy (CLSM). Based on image analysis, the cake building and properties (particle arrangement, thickness) are analyzed. These experimental data will be further used to improve the filtration model in order to obtain a predictive tool for process optimization.     

Assessment of the 1-fluid method for DNS of particulate flows: Sedimentation of a single sphere at moderate to high Reynolds numbers

This paper introduces an original 1-fluid method for direct simulation of the motion of rigid particles in fluids. The model is based on the implicit treatment of a single fictitious fluid over a fixed grid, and uses an augmented Lagrangian optimization algorithm for the velocity-pressure coupling. The paper focuses on the case of a rigid sphere settling in a viscous medium. For validation purposes, simulations of the transient motion of a sedimenting sphere at Reynolds numbers ranging from 1.5 to 31.9 are compared to the PIV data published by Ten Cate et al. [Ten Cate A, Nieuwstad CH, Derksen JJ, Van den Akker HEA. Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity. Phys Fluids 2002;14(11):4012-25]. Accurate reproduction of the experimental data is obtained. Further simulations are intended to investigate higher Reynolds numbers. Predictions of transient particle sedimentation at Reynolds number 280 are performed and compared with experimental data of the sedimentation trajectory, as well as with simulation results based on the lattice-Boltzmann method.     

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position–momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.