Coupled RapidCell and lattice Boltzmann models to simulate hydrodynamics of bacterial transport in response to chemoattractant gradients in confined domains

The RapidCell (RC) model was originally developed to simulate flagellar bacterial chemotaxis in environments with spatiotemporally varying chemoattractant gradients. RC is best suited for motility simulations in unbounded nonfluid environments; this limits its use in biomedical applications hinging on bacteria-fluid dynamics in microchannels. In this study, we eliminated this constraint by coupling the RC model with the colloidal lattice Boltzmann (LB) model. RC–LB coupling was accomplished by tracking positions of chemoreceptors on particle surfaces that vary with particles’ angular and translational velocities, and by including forces and torques due to particles’ tumbling and running motions in particle force- and torque-balance equations. The coupled model successfully simulated trajectories of particles in initially stagnant fluids in bounded domains, involving a chemoattractant contained in a confined zone with a narrow inlet or concentric multiringed inline obstacles, mimicking tumor vasculature geometry. Chemotactically successful particles exhibited higher attractant concentrations near the receptor clusters, transient increases in the motor bias, and transient fluctuations in methylated proteins at the cell scale, while exhibiting more frequent higher particle translation velocities and smaller angular velocities than chemotactically unsuccessful particles at the particle scale. In these simulations, the chemotactic particles reached the chemoattractant with the success rates of 20–72 %, whereas nonchemotactic particles would be unsuccessful. The coupled RC–LB model is the first step toward development of a multiscale simulation tool that bridges cell-scale signal and adaptation dynamics with particle-scale fluid-particle dynamics to simulate chemotaxis-driven bacterial motility in microchannel networks, typically observed in tumor vasculatures, in the context of targeted drug delivery.     

Three-dimensional and analytical modeling of microfluidic particle transport in magnetic fluids

We present an analytical model that can predict the three-dimensional (3D) transport of non-magnetic particles in magnetic fluids inside a microfluidic channel coupled with permanent magnets. The magnets produce a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on the particles. Resulting 3D trajectories of the particles are obtained by (1) calculating the 3D magnetic buoyancy force exerted on the particles via an analytical distribution of magnetic fields as well as their gradients, together with a nonlinear magnetization model of the magnetic fluids, (2) deriving the 3D hydrodynamic viscous drag force on the particles with an analytical velocity profile of a low Reynolds number ferrohydrodynamic flow in the channel including “wall effect” and magnetoviscous effect of the magnetic fluids, and (3) constituting and solving the governing equations of motion for the particles using the analytical expressions of magnetic buoyancy force and hydrodynamic viscous drag force. We use such a model to study the particles’ trajectories in the channel and investigate the magnitude of their deflections at different flow rates, with different properties of magnetic fluids and different geometrical parameters of the system.     

Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to simulations of the deformation and breakup of a particle-cluster aggregate in shear flows. In the simulations, the solid particle is modeled by a droplet with strong interfacial tension and large viscosity. The van der Waals attraction force is taken into account for the interaction between the particles. The ratio of the hydrodynamic drag force to cohesive force, I, is introduced, and the effect of I on the aggregate deformation and breakup in shear flows is investigated. It is found that the aggregate is easier to deform and to be dispersed when I is over 100.     

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.     

Improved drag force model and its application in simulating nanofluid flow

The circumferential distribution of the surrounding particles contribution to the drag force for the reference particle is firstly proposed and analyzed. A new formula for the drag exerted on a given particle under the interaction between particle clouds and fluid is derived. Analysis shows that even for spherical particles with symmetric shape, as the particle dispersion is nonsymmetric and the direction of the particle velocity differs from the reference particle, the direction of the drag and the particle velocity is not parallel; therefore, it increased the complexity of evolution process for the particle concentration. Due to special feature of nanoparticle surface adsorption, this study presents analysis of the radial viscosity distribution in the vicinity of liquid layer for the first time. The increasing in the viscosity of the nanolayer is considered a contributing factor to the viscosity of nanofluids as the experimental result is larger than the theoretical prediction. Considering the effect of multi-particles interaction and the characteristics of liquid layer, the new drag force model is constructed and applied to simulate the nanofluid flow. Comparison is made for computed drag force on particle between the traditional and present models. The trajectory and distribution of the nanoparticles, as well as the velocity contours of the fluid, are presented. The physical meanings of these results have been discussed.     

气固两相流模拟的随机离散模型

§1.引言 气固两相流动形式是最复杂的两相流动实例,其系统中的颗粒浓度较高,颗粒间的碰撞经常发生,从而导致细观层次上的颗粒运动具有复杂性,对于两相流动系统,拟流体模型以其大规模模拟的可行性在数值模拟领域中居重要地位。但是,拟流体模型的连续性假设     

颗粒动力学与湍动能耦合的稠密两相流动数学模型

在气相湍流流动的k-ε模型基础上,建立了颗粒动力学与湍动能耦合的稠密两相流动数学模型。颗粒相的有效粘性系数取决于颗粒之间相互碰撞而引起的层流粘性以及颗粒微团的湍流脉动而形成的湍流粘性,其中颗粒的碰撞行为以及所形成的颗粒的层流特性用颗粒动力学模型来描述,颗粒的湍流特性采用颗粒湍动能输运方程模型来描述。利用所建立的模型对提升管内气固两相流动过程进行了数值模拟,可以合理地预报出提升管内气固两相的环核流动结构。     

Simulating Gaseous Fluids with Low and High Speeds

Gaseous fluids may move slowly, as smoke does, or at high speed, such as occurs with explosions. High‐speed gas flow is always accompanied by low‐speed gas flow, which produces rich visual details in the fluid motion. Realistic visualization involves a complex dynamic flow field with both low and high speed fluid behavior. In computer graphics, algorithms to simulate gaseous fluids address either the low speed case or the high speed case, but no algorithm handles both efficiently. With the aim of providing visually pleasing results, we present a hybrid algorithm that efficiently captures the essential physics of both low‐ and high‐speed gaseous fluids. We model the low speed gaseous fluids by a grid approach and use a particle approach for the high speed gaseous fluids. In addition, we propose a physically sound method to connect the particle model to the grid model. By exploiting complementary strengths and avoiding weaknesses of the grid and particle approaches, we produce some animation examples and analyze their computational performance to demonstrate the effectiveness of the new hybrid method.     

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 dual-scale lattice gas automata model for gas–solid two-phase flow in bubbling fluidized beds

Modelling the hydrodynamics of gas/solid flow is important for the design and scale-up of fluidized bed reactors. A novel gas/solid dual-scale model based on lattice gas cellular automata (LGCA) is proposed to describe the macroscopic behaviour through microscopic gas–solid interactions. Solid particles and gas pseudo-particles are aligned in lattices with different scales for solid and gas. In addition to basic LGCA rules, additional rules for collision and propagation are specifically designed for gas–solid systems. The solid’s evolution is then motivated by the temporal and spatial average momentum gained through solid–solid and gas–solid interactions. A statistical method, based on the similarity principle, is derived for the conversion between model parameters and hydrodynamic properties. Simulations for bubbles generated from a vertical jet in a bubbling fluidized bed based on this model agree well with experimental results, as well as with the results of two-fluid approaches and discrete particle simulations.     

Simulation of floating bodies with the lattice Boltzmann method

This paper is devoted to the simulation of floating rigid bodies in free surface flows. For that, a lattice Boltzmann based model for liquid–gas–solid flows is presented. The approach is built upon previous work for the simulation of liquid–solid particle suspensions on the one hand, and on an interface-capturing technique for liquid–gas free surface flows on the other. The incompressible liquid flow is approximated by a lattice Boltzmann scheme, while the dynamics of the compressible gas are neglected. We show how the particle model and the interface capturing technique can be combined by a novel set of dynamic cell conversion rules. We also evaluate the behaviour of the free surface–particle interaction in simulations. One test case is the rotational stability of non-spherical rigid bodies floating on a plane water surface–a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the heeling stability of a floating box.     

A lattice-Boltzmann simulation study of the drag coefficient of clusters of spheres

Drag coefficients of irregularly shaped particles, constructed from spheres, were measured in lattice-Boltzmann simulations and compared to literature data. The agreement is very well. The distance between the spheres was increased to study the influence of inter-particle distance on the drag force in clusters. The drag coefficient of the clusters was found to increase with inter-particle distance. The drag force on an individual particle in a cluster is lower when that particle is shielded from the flow by other particles.     

Realistic Animation of Fluid with Splash and Foam

In this paper we describe a method for modeling and rendering dynamic behavior of fluids withsplashes and foam. A particle system is built into a fluid simulation system to represent an ocean wavecresting and spraying over another object. We use the Cubic Interpolated Propagation (CIP) method asthe fluid solver. The CIP method can solve liquid and gas together in the framework of fluid dynamicsand has high accuracy in the case of relatively coarse grids. This enables us to simulate the fluids in ashort time and describe the motion of splashes in the air that is associated with the liquid motion well.The foam floating on the water also can be described using the particle system. We integrate the rigidbody simulation with the fluid and particle system to create sophisticated scenes including splashes andfoam. We construct state change rules that are used with the particle system. This controls the generation,vanishing and transition rule of splashes and foam. The transition rule makes the seamless connection betweena splash and foam. We employed a fast volume rendering method with scattering effect for particles.One of the important features of our method is the combination of fast simulation and rendering techniques,which provides dynamic and realistic scenes in a short time.     

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied ??wall effect?? on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.     

Slow viscous flow around two particles in a cylinder

This article describes the motion of two arbitrarily located free moving particles in a cylindrical tube with background Poiseuille flow at low Reynolds number. We employ the Lamb’s general solution based on spherical harmonics and construct a framework based on cylindrical harmonics to solve the flow field around the particles and the flow within the tube, respectively. The two solutions are performed in an iterated framework using the method of reflections. We compute the drag force and torque coefficients of the particles which are dependent on the distances among the cylinder wall and the two particles. In addition, we provide detailed flow field in the vicinity of the two particles including streamlines and velocity contour. Our analysis reveals that the particle–particle interaction can be neglected when the separation distance is three times larger than the sum of particles radii when the two particles are identical. Furthermore, the direction of Poiseuille flow, the particle position relative to the axis and the particle size can make the two particles attract or repel. Unlike the single particle case, the two particles can move laterally due to the hydrodynamic interaction. Such analysis can give insights to understand the mechanisms of collision and aggregation of particles in microchannels.     

Fast SPH simulation for gaseous fluids

This paper presents a fast smoothed particle hydro-dynamics (SPH) simulation approach for gaseous fluids. Unlike previous SPH gas simulators, which solve the transparent air flow in a fixed simulation domain, the proposed approach directly solves the visible gas without involving the transparent air. By compensating the density and force calculation for the visible gas particles, we completely avoid the need of computational cost on ambient air particles in previous approaches. This allows the computational resources to be exclusively focused on the visible gas, leading to significant performance improvement of SPH gas simulation. The proposed approach is at least ten times faster than the standard SPH gas simulation strategy and is able to reduce the total particle number by 25–400 times in large open scenes. The proposed approach also enables fast SPH simulation of complex scenes involving liquid–gas transition, such as boiling and evaporation. A particle splitting and merging scheme is proposed to handle the degraded resolution in liquid–gas phase transition. Various examples are provided to demonstrate the effectiveness and efficiency of the proposed approach.     

Finite element analysis of particle motion in steady inspiratory airflow

To accurately model the inhaled particle motion, equations governing particle trajectories in carrier flow are solved together with the Navier–Stokes equations. Under the relatively dilute particle condition in the mixture, equations for two phases are coupled through the interface drag shown in the solid-phase momentum equations. The present study investigates bifurcation flow in the human central airway using the finite element method. In the gas phase, we employ the biquadratic streamline upwind Petrov–Galerkin finite element model to simulate the incompressible air flow. To solve the equations of motion for the inhaled particles, we apply another biquadratic streamline upwind finite element model. A feature common to two models applied to each phase of equations is that both of them provide nodally exact solutions to the convection–diffusion and the convection–reaction equations, which are prototype equations for the gas-phase and the solid-phase equations, respectively. In two dimensions, both models have ability to introduce physically meaningful artificial damping terms solely in the streamline direction. With these terms added to the formulation, the discrete system is enhanced without compromising the numerical diffusion error. Tests on inspiratory problem were conducted, and the results are presented, with an emphasis on the discussion of particle motion.     

Lift and multiple equilibrium positions of a single particle in Newtonian and Oldroyd-B fluids

A heavy particle is lifted from the bottom of a channel in a plane Poiseuille flow when the Reynolds number is larger than a critical value. In this paper we obtain correlations for lift-off of particles in Oldroyd-B fluids. The fluid elasticity reduces the critical shear Reynolds number for lift-off. The effect of the gap size between the particle and the wall, on the lift force, is also studied. A particle lifted from the channel wall attains an equilibrium height at which its buoyant weight is balanced by the hydrodynamic lift force. Choi and Joseph [Choi HG, Joseph DD. Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation. J Fluid Mech 2001;438:101-128] first observed multiple equilibrium positions for a particle in Newtonian fluids. We report several new results for the Newtonian fluid case based on a detailed study of the multiple equilibrium solutions, e.g. we find that at a given Reynolds number there are regions inside the channel where no particle, irrespective of its weight, can attain a stable equilibrium position. This would result in particle-depleted zones in channels with Poiseuille flows of a dilute suspension of particles of varying densities. Multiple equilibrium positions of particles are also found in Oldroyd-B fluids. All the results in this paper are based on 2D direct numerical simulations.     

Dissipative particle dynamics simulation of circular and elliptical particles motion in 2D laminar shear flow

The dissipative particle dynamics (DPD) method is a relatively new computational method for modeling the dynamics of particles in laminar flows at the mesoscale. In this study, we use the DPD approach to model the motion of circular and elliptical particles in a 2D shear laminar flow. Three examples are considered: (i) evaluation of the drag force exerted on a circular particle moving in a stagnant fluid, (ii) rotation of an elliptical particle around its center in a shear flow, and (iii) motion of an ellipsoidal particle in a linear shear flow. For all cases, we found a good agreement with theoretical and finite element solutions available. These results show that the DPD method can effectively be applied to model motion of micro/nano-particles at the mesoscale. The method proposed can be used to predict the performances of intravascularly administered particles for drug delivery and biomedical imaging.     

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.