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.     

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.     

Inertial focusing of microparticles in curvilinear microchannels with different curvature angles

Inertial microfluidics has become one of the emerging topics due to potential applications such as particle separation, particle enrichment, rapid detection and diagnosis of circulating tumor cells. To realize its integration to such applications, underlying physics should be well understood. This study focuses on particle dynamics in curvilinear channels with different curvature angles (280°, 230°, and 180°) and different channel heights (90, 75, and 60 µm) where the advantages of hydrodynamic forces were exploited. We presented the cruciality of the three-dimensional particle position with respect to inertial lift forces and Dean drag force by examining the focusing behavior of 20 µm (large), 15 µm (medium) and 10 µm (small) fluorescent polystyrene microparticles for a wide range of flow rates (400–2700 µL/min) and corresponding channel Reynolds numbers. Migration of the particles in lateral direction and their equilibrium positions were investigated in detail. In addition, in the light of our findings, we described two different regions: transition region, where the inner wall becomes the outer wall and vice versa, and the outlet region. The maximum distance between the tight particle stream of 20 and 15 µm particles was obtained in the 90 high channel with curvature angle of 280° at Reynolds number of 144 in the transition region (intersection of the turns), which was the optimum condition/configuration for focusing.     

Particle focusing in microfluidic devices

Focusing particles (both biological and synthetic) into a tight stream is usually a necessary step prior to counting, detecting, and sorting them. The various particle focusing approaches in microfluidic devices may be conveniently classified as sheath flow focusing and sheathless focusing. Sheath flow focusers use one or more sheath fluids to pinch the particle suspension and thus focus the suspended particles. Sheathless focusers typically rely on a force to manipulate particles laterally to their equilibrium positions. This force can be either externally applied or internally induced by channel topology. Therefore, the sheathless particle focusing methods may be further classified as active or passive by the nature of the forces involved. The aim of this article is to introduce and discuss the recent developments in both sheath flow and sheathless particle focusing approaches in microfluidic devices.     

Enhanced size-dependent trapping of particles using microvortices

Inertial microfluidics has been attracting considerable interest for size-based separation of particles and cells. The inertial forces can be manipulated by expanding the microchannel geometry, leading to formation of microvortices for selective isolation and trapping of particles or cells from a mixture. In this work, we aim to enhance our understanding of particle trapping in such microvortices by developing a model of selective particle entrapment. Design and operational parameters including flow conditions, size of the trapping region, and target particle concentration are explored to elucidate their influence on trapping behavior. Our results show that the size dependence of trapping is characterized by a threshold Reynolds number, which governs the selective entry of particles into microvortices from the main flow. We show that concentration enhancement on the order of 100,000× and isolation of targets at concentrations as low as 1/mL is possible. Ultimately, the insights gained from our systematic investigation suggest optimization solutions that enhance device performance (efficiency, size selectivity, and yield) and are applicable to selective isolation and trapping of large rare cells as well as other applications.     

Flow rate-insensitive microparticle separation and filtration using a microchannel with arc-shaped groove arrays

Inertial microfluidics can separate microparticles in a continuous and high-throughput manner, and is very promising for a wide range of industrial, biomedical and clinical applications. However, most of the proposed inertial microfluidic devices only work effectively at a limited and narrow flow rate range because the performance of inertial particle focusing and separation is normally very sensitive to the flow rate (Reynolds number). In this work, an innovative particle separation method is proposed and developed by taking advantage of the secondary flow and particle inertial lift force in a straight channel (AR = 0.2) with arc-shaped groove arrays patterned on the channel top surface. Through the simulation results achieved, it can be found that a secondary flow is induced within the cross section of the microchannel and guides different-size particles to the corresponding equilibrium positions. On the other hand, the effects of the particle size, flow rate and particle concentration on particle focusing and separation quality were experimentally investigated. In the experiments, the performance of particle focusing, however, was found relatively insensitive to the variation of flow rate. According to this, a separation of 4.8 and 13 µm particle suspensions was designed and successfully achieved in the proposed microchannel, and the results show that a qualified particle separation can be achieved at a wide range of flow rate. This flow rate-insensitive microfluidic separation (filtration) method is able to potentially serve as a reliable biosample preparation processing step for downstream bioassays.     

列车底部结构对交会高速列车气动性能的影响

用CFD法对具有复杂底部结构(带有转向架或带有转向架和裙板)的高速列车以200 km/h等速交会的情况进行数值模拟和分析,研究其压力波、气动力和气动力矩以及车体周围的流场结构的变化.结果表明:与简化模型相比,带有复杂底部结构的列车交会时的压力波的头波和尾波都有所减小且尾波减小的程度更高,带有转向架的车体的横向力、横摆力矩和侧翻力矩的峰值明显减小,但变化更复杂;带有复杂底部结构的列车在车体底部会形成涡结构,有明显的能量耗散.     

Vortex structure of steady flow in a rectangular cavity

The vortex structure of the two-dimensional steady flow in a lid-driven rectangular cavity at different depth-to-width ratios and Reynolds numbers is investigated using a lattice Boltzmann method. The aspect ratio varies from 0.1 to 7 and the Reynolds number ranges from 0.01 to 5000. The effects of the aspect ratio and Reynolds number on the size, center position and number of vortices are determined together with the flow pattern in the cavity. The present results not only confirm the vortex structure of Stokes flow reported by previous researchers, but also reveal some new evolution features of the vortices and their structure with the Reynolds number. When the Reynolds number approaches 0, the flow shows a characteristic feature of symmetric vortex structure. On the other hand, as the Reynolds number increases, the sizes and center positions of the vortices in the near-lid region appear to be strongly affected by the inertia force, resulting in an asymmetric vortex structure in this region. The influence of the inertia force decreases along the depth for the deep cavity flow. It is found that there is a critical value of the aspect ratio, which depends on the Reynolds number. When the critical value is exceeded, flow pattern in a certain region of cavity becomes symmetric again. These large symmetric vortices are similar in shape, and their sizes approach a constant.     

Lattice Boltzmann simulation of turbulent flow laden with finite-size particles

The paper describes a particle-resolved simulation method for turbulent flow laden with finite size particles. The method is based on the multiple-relaxation-time lattice Boltzmann equation. The no-slip boundary condition on the moving particle boundaries is handled by a second-order interpolated bounce-back scheme. The populations at a newly converted fluid lattice node are constructed by the equilibrium distribution with non-equilibrium corrections. MPI implementation details are described and the resulting code is found to be computationally efficient with a good scalability. The method is first validated using unsteady sedimentation of a single particle and sedimentation of a random suspension. It is then applied to a decaying isotropic turbulence laden with particles of Kolmogorov to Taylor microscale sizes. At a given particle volume fraction, the dynamics of the particle-laden flow is found to depend mainly on the effective particle surface area and particle Stokes number. The presence of finite-size inertial particles enhances dissipation at small scales while reducing kinetic energy at large scales. This is in accordance with related studies. The normalized pivot wavenumber is found to not only depend on the particle size, but also on the ratio of particle size to flow scales and particle-to-fluid density ratio.     

Parameters affecting the shape of a hydrodynamically focused stream

Even at low Reynolds numbers, momentum can impact the shape of hydrodynamically focused flow. Both theoretical and experimental characterization of hydrodynamic focusing in microchannels at Reynolds numbers ≤25 revealed the important parameters that affect the shape of the focused layer. A series of symmetric and asymmetric microfluidic channels with two converging streams were fabricated with different angles of confluence at the junction. The channels were used to study the characteristics of Y-type microchannels for flow-focusing. Computational analysis and experimental results gathered using confocal microscopy and particle image velocimetry indicated that the orientation of the sheath and the sample stream inlets, as well as the absolute flow velocities, determine the curvature in the concentration distribution of the focused stream. Decreasing the angle of confluence between sheath and sample, as well as reducing the overall Reynolds number, resulted in a flat interface between sheath and focused fluids. Alignment of the faster flowing sheath fluid channel with the main channel also reduced the inertial effects and produced a focused stream with a flat concentration profile. Control over the shape of the focused stream is important in many biosensors and lab-on-a-chip devices that rely on hydrodynamic focusing for increased detection sensitivity.     

基于换乘导向的大型客运枢纽高铁列车接续优化

针对高速铁路成网条件下的客运枢纽高铁列车接续优化问题,分析了枢纽内的旅客换乘过程,提出了中长途客流的换乘满意度概念;以平均换乘满意度和枢纽车站列车到发均衡性为优化目标,以大站合理发车时间、合理终到时间、车站作业间隔时间、旅客换乘时间、车站到发线能力等为约束条件,建立了基于换乘协同的大型客运枢纽高速列车接续优化模型。设计了改进染色体编码方式和选择策略的遗传算法对算例进行了求解。改进后的遗传算法同基本遗传算法、基本模拟退火算法相比,目标函数中所求的平均换乘满意度分别增加了5.10%、2.93%,枢纽车站列车到发均衡性分别提高了0.27%、2.31%,算例结果验证了改进遗传算法的有效性和稳定性,表明所提方法可以有效地提高大型枢纽高铁列车的接续质量。     

Electrophoresis of a spherical particle in a spherical cavity

The electrophoretic motion of a charged spherical particle situated at an arbitrary position within a charged spherical cavity along the line connecting their centers is studied theoretically for the case of thin electric double layers. To solve the electrostatic and hydrodynamic governing equations, the general solutions are constructed using the two spherical coordinate systems based on the particle and cavity, and the boundary conditions are satisfied by a collocation technique. Numerical results for the electrophoretic velocity of the particle are presented for various values of the zeta potential ratio, radius ratio, and relative center-to-center distance between the particle and cavity. In the particular case of a concentric cavity, these results agree excellently with the available exact solution. The contributions from the electroosmotic flow occurring along the cavity wall and from the wall-corrected electrophoretic driving force to the particle velocity are equivalently important and can be superimposed due to the linearity of the problem. The normalized migration velocity of the particle decreases with increases in the particle-to-cavity radius ratio and its relative distance from the cavity center and increases with an increase in the cavity-to-particle zeta potential ratio. The boundary effects on the electrokinetic migration of the particle are significant and interesting.     

SPH中一种层流入口、出口边界的处理方法

提出一种替代周期边界条件的对入口、出口边界的处理方法,这种方法使用跟随虚粒子处理入口、出口边界。跟随虚粒子设置于入口、出口的外侧,这些虚粒子的速度、位置根据对应的内部粒子的速度、位置进行更新。该方法建立在对层流特性的分析的基础上,适用于具有层流入口或出口的低雷诺数流场中。利用该入、出口边界处理新方法,分别对Poiseuille流和渐扩管平面流进行数值摸拟,数值结果与理论解吻合良好。     

Formation of vortices in long microcavities at low Reynolds number

Microcavities are a central feature of many microflow systems ranging from sprouting capillaries during angiogenesis to various microfluidic devices. Recently, the flow and transport phenomena in microcavities have been subject of a number of studies, yet a physical picture of the flow properties at low Reynolds number, which is the relevant regime in many biological applications, has not been fully brought out. We have therefore systematically investigated, experimentally and by modeling, the flow in a long microcavity and found that the flow properties depend decisively on the depth/width ratio of the cavity. Notably, if this cavity aspect ratio is higher than approximately 0.51, counter-flow vortices emerge in the cavity even at vanishing Reynolds number. The distance of the first vortex from the cavity entrance decreases with an increasing aspect ratio as an inverse power law. In the vortex-free regime below the threshold aspect ratio, the flow velocity decays exponentially away from the cavity entrance, with a decay length that scales with the width of the cavity and depends also on the aspect ratio of its cross section. The results of our numerical simulations are supported by a theoretical analysis and are in good agreement with experimental data, acquired by optical velocimetry with optical tweezers.     

改进的元胞自动机列车交通流仿真模型研究

在既有元胞自动机模型的基础上,针对移动闭塞系统下列车追踪运行的特点提出一种改进的元胞自动机模型,该模型有效解决了既有模型中列车速度变化的不合理问题,提高了模型的准确性和可靠性。应用该模型获得了移动闭塞系统下列车流的相位图,并分析了移动闭塞系统中线路上快慢车开行比例及开行速差等因素对线路通过能力及列车平均速度的影响。研究结果表明,车站对列车流具有调和的作用,能够使列车流得到一定程度的同化。此外,减小快慢车速差可以有效增大线路的通过能力,而增加快车开行比例,则能够显著提高所有列车的运行效率,从而保证整个系统的高效运营。     

Inertial particle focusing and spacing control in microfluidic devices

Focusing particles into a tight stream is usually a necessary step prior to counting, detecting and sorting them. Meanwhile, particle spacing control in microfluidic devices could also be applied in the field of accurate cell detection, material synthesis and chemical reaction. To achieve simultaneous particle focusing and spacing control, a novel microchannel composed by Dean and sheath flow section was proposed and fabricated according to the elaborated design principle with its manipulating performance in situ visualized. Using microspheres with a few microns as a template, the trajectory of the particles was discovered to follow lateral migration and reach certain equilibrium positions at the end of the designed Dean section. After being focused, the streamline was further concentrated and centralized with a controllable interparticle distance in sheath flow section. For sheath flow section, the angle between symmetrical tributaries and the mainstream channel and abrupt constriction/expansion structure of mainstream channel as important channel geometric features were investigated to minimize the focusing streamline width and optimize spacing control. An modified analytical model for sheath flow with different tributary angles was derived and proved to well describe the microsphere spacing control process.     

Eccentric electrophoretic motion of a sphere in circular cylindrical microchannels

The eccentric electrophoretic motion of a spherical particle in an aqueous electrolyte solution in circular cylindrical microchannels is studied in this paper. The objective is to investigate the influences of separation distance and channel size on particle motion. A theoretical model is developed to describe the electric field, the flow field and the particle motion. A finite element based direct numerical simulation method is employed to solve the model. Numerical results show that, when the particle is eccentrically positioned in the channel, the electric field and the flow field are not symmetric, and the strongest electric field and the highest flow velocity occur in the small gap region. It is shown that the rotational velocity of the particle increases with the decrease of the separation distance. With the decrease of the separation distance, the translational velocity increases in a smaller channel; while it decreases first and then increases in a relatively large channel. When a particle moves eccentrically at a smaller separation distance from the channel wall, both the translational velocity and the rotational velocity increase with the decrease of the channel size.     

Effect of particle migration on heat transfer in suspensions of nanoparticles flowing through minichannels

Recent work has shown that suspensions of highly thermally conducting nanoparticles with a size considerably smaller than 100 nm have great potential as a high-energy carrier for small channel systems. However, it is also known that particles in a suspension under certain conditions may migrate. This indicates that the efficiency of heat transfer in the small channels may not be as superior as expected, which bears significance to the system design and operation. This work aims at addressing this issue by examining the effect of particle migration on heat transfer under a fully developed laminar flow regime in small channels. This involves the development of both flow and heat transfer models, and a numerical solution to the models. The flow model takes into account the effects of the shear-induced and viscosity-gradient-induced particle migration, as well as self-diffusion due to Brownian motion, which is coupled with an energy equation. The results suggest a significant non-uniformity in particle concentration and, hence, thermal conductivity over the tube cross-section due to particle migration, particularly for large particles at high concentrations. Compared with the constant thermal conductivity assumption, the non-uniform distribution due to particle migration leads to a higher Nusselt number, which depends on the Peclet number and the mean particle concentration. Further improvement of the model is needed to take into account other factors such as entrance effects, as well as the dynamics of particles and particle–wall interactions.     

Improved particle concentration by cascade AC electroosmotic flow

The importance of electrokinetics in microfluidic technology has been growing owing to its versatility and simplicity in fabrication, implementation, and handling. Alternating-current electroosmosis (ACEO), which is the motion of fluid due to the ion movement by an interaction between AC electric field and an electrical double layer on the electrode surface, has a potential for a particle concentration method to detecti rare samples flowing in a microchannel. This study investigates an improved ACEO-based particle concentration by cascade electrokinetic approach. Flow field induced by ACEO and accumulation behavior of particles were parametrically measured to discuss the concentrating mechanism. The accumulation of particles by ACEO can be explained by a balance between the attenuating electroosmotic flow to transport particles and the inherent diffusive motion of the particles, which is hindered due to the near-wall location. Although a parallel double-gap electrode geometry enables particles to be collected at the center of electrode very sharply, it has scattering zones with accumulated particles at sidewalls of the channel. This drawback can be overcome by applying sheath flow or introducing cascade electrode pattern upstream of the focusing zone. As a result, total concentration efficiency was 98.4 % for all the particles flowing in the cascade device. The resultant concentrated particles exist on the electrode surface within 5 μm, and three-dimensional concentration of particle with the concentration factor as large as 700 is possible using a monolithic channel, co-planar electrode, and sheathless solution feeding. This cascade electrokinetic method provides a new and effective preconcentrator for ultra-sensitive detection of rare samples.     

限速区段列车流特性及运行延误研究

通过分析列车在限速区段的运行特征,提出了四显示固定闭塞系统下限速区段列车流的元胞自动机模型,重点研究了混合列车流在限速区段的运行特性以及列车在限速区段的延误规律,并分析了造成列车延误的原因。结果表明：当客货车在具有限速区段的线路混行时,造成列车延误的原因分为限速区段限速和货车对客车的抑制作用,且列车延误时间随着限速区段长度的增加而增加;货车对客车的抑制作用随着发车间隔的增大而减弱,当发车间隔超过临界值时,造成列车延误的主要原因是限速区段的限速。当发车间隔固定时,列车的平均延误时间会随着客货车比例的增大呈现出“拱形”,客货车比例在0.55~0.65之间时,列车的平均延误达到了峰值。