A device for measuring the concentration and dispersion quality ofmagnetic particle suspensions

A technique, called rheomagnetic measurement, for studying the concentration and orientation of magnetic particles through inductance measurement is presented. The particles are oriented in a predominantly extensional flow field, and, because they are magnetic, their orientation can be detected with a weak magnetic sensing field. Because flocs of magnetic particles orient differently in a flow field than primary particles do, this method can be useful in obtaining information about the particle flocculation aspect of dispersion quality. A magnetic sensing field can also be used to detect the particle concentration in a quiescent flow. Experimental data on the effects of particle concentration and milling for rod-like γ-Fe₂O₃ and plate-like Ba-ferrite suspensions are discussed. The results for Ba-ferrite magnetic markedly contrast with those for the rod-like magnetic particles but showed similarity with those for rod-like γ-Fe₂O₃     

Numerical investigations of strong hydrodynamic interaction between neighboring particles inertially driven in microfluidic flows

Dispersed particles traveling at a high throughput in microchannels laterally migrate and focus into a streamline at each channel face. The focusing attractors within the cross-section are determined by the balance between the lift forces. However, particles in close proximity (e.g. due to high concentration and abrupt particle contact) suffer a breakdown of distinct focusing due to excessive hydrodynamic interaction. Here, I present numerical investigations into the effects of the strong hydrodynamic interaction on the inertial focusing. The direct numerical simulation is used to calculate the focusing/defocusing of particles, specifically since the particle-induced disturbance flows vary at the particle scale and hence affect the individual particle motion. The simulated defocusing of many-body systems prefer finite inter-particle separation, in contrast with sedimentation of two mobile particles, whereby the trailing particle catches up with the leading particle due to reduced drag in its wake. I numerically demonstrate that the finite separation between nearest neighbors is a consequence of hydrodynamic repulsive motion unique to wall-bound shear flows. The author further presents direct demonstrations of the effects of the strong hydrodynamic interaction on the inertial focusing in an experimentally unachievable manner. The excessive hydrodynamic interaction drastically dissipates the near-wall focusing attractors and thus causes irreversible defocusing by breaking the balance between the lift forces. Unexpectedly, I also find that moderate hydrodynamic interaction can alter focusing speed on specific conditions, suggesting that an optimum concentration may significantly boost the inertial focusing in microfluidic-based applications.     

Motion of a solid sphere in a general flow near a plane boundary at zero Reynolds number

It is demonstrated how the hydrodynamic force and moment of force acting on a solid sphere may be calculated when it is placed at rest at an arbitrary position in a two dimensional flow at zero Reynolds number in which the region of flow is bounded by either an undeformable planar free surface or by a plane solid wall. The results so obtained are used to calculate the motion of a freely moving solid sphere in an asymmetric vortex in the presence of an underformable free surface. It is seen that the sphere, depending on the direction of the undisturbed flow, will either spiral into or out of the vortex. This implies that when a dilute suspension of such spherical particles undergoes such a vortex motion in the presence of the free surface, the vortex will either fill up with particles from the surrounding flow or become devoid of particles.Deceased, July 31, 1995     

An improved immersed moving boundary for hydrodynamic force calculation in lattice Boltzmann method

Particles suspension is considerably prevalent in petroleum industry and chemical engineering. The efficient and accurate simulation of such a process is always a challenge for both the traditional computational fluid dynamics and lattice Boltzmann method. Immersed moving boundary (IMB) method is promising to resolve this issue by introducing a particle-fluid interaction term in the standard lattice Boltzmann equation, which allows for the smooth hydrodynamic force calculation even for a large grid size relative to the solid particle. Although the IMB method was proved good for stationary particles, the deviation of hydrodynamic force on moving particles exists. In this work, we reveal the physical origin of this problem first and figure out that the internal fluid effect on the hydrodynamic force calculation is not counted in the previous IMB. An improved immersed moving boundary method is therefore proposed by considering the internal fluid correction, which is easy to implement with the little extra computation cost. A 2D single elliptical particle and a 3D sphere sedimentation in Newtonian fluid is simulated directly for the validation of the corrected model by excellent agreements with the standard data.     

Investigating the flow of rod-like particles in a horizontal rotating drum using DEM simulation

Understanding the flow and mixing of rod-like particles is fundamental because of the widespread use of rods in the process industry. In this paper, discrete element method is used to investigate the flow and mixing of rod-like particles in a horizontal rotating drum, with rod-like particles being modeled by super-ellipsoids. The influence of the aspect ratio of the rod and the rotation speed of the drum on the flow of rod-like particles is studied. The investigation of spherical particles is also included in this paper to reveal the differences between rod-like and spherical particles. The simulation results show that the flow of rods is more intermittent than that of spheres and that there is more intermittent flow for rod-like particles with larger aspect ratios. Both the aspect ratio of the rod and the rotation speed of the drum considerably influence particle mixing. The mixing rate, as quantified by the slope of the variation in the mixing index with respect to drum revolution, increases as rotation speed and aspect ratio decrease. The study of particle orientation indicates that rod-like particles have a preferred orientation during rotation of the drum: the major axis of the rod inclines to be parallel to the end plate of the drum.     

Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

Capillary attraction of floating rods

The capillary attraction of two parallel cylinders with circular cross-section representing slender particles floating at the interface between two immiscible fluids is considered. Given the particle separation, the elevation of the particle centers in hydrostatics is computed to satisfy the vertical force balance involving the buoyancy force, the capillary force, and the particle weight. A numerical procedure is developed for calculating the horizontal force exerted on a pair of cylinders in solitary or periodic arrangement. The results confirm that the particles attract each other under the conditions considered. The particle motion and transient flow due to the particle attraction are computed using a boundary-integral method for Stokes flow. In the algorithm, the particle center velocity of translation and angular velocity of rotation are calculated to satisfy force and torque balances. Numerical simulations using a boundary-element method subject to an initial state provided by hydrostatics illustrate the nature of the motion and furnish estimates for the particle velocity induced by capillarity.     

DEM-aided direct shear testing of granular sands incorporating realistic particle shape

Discrete element method (DEM) of granular sands incorporating the effect of the realistic particle shape has been an important issue for many years. In this context, this study proposed a novel framework for the generation of realistic-shaped particles of natural sands in 3D DEM simulations. The generation framework mainly included micro-CT (μCT) scanning of sand particles, image processing of μCT images, spherical harmonic reconstruction of the particle surface, and clump generation by the overlapping multisphere clump method (OMCM) in DEM simulations. To validate the accuracy of OMCM, the volume and inertia moment of the clump were carefully investigated, and a set of optimized generation parameters was then determined to ensure the accuracy of the clump and the limit number of the filling spheres. Based on the generation framework, a clump sample with realistic particle shapes and a corresponding sphere sample were generated to conduct a series of direct shear testing. The simulation results demonstrated that the realistic particle shape highly increases the particle interlocking rather than the anisotropic intensity of strong contact force chains, and in turn enhances the shear resistance and the shear-induced dilation of the sands. It was also found that the inter-particle contacts of the clump sample have higher friction mobilization than that of the sphere sample, which identified the micromechanism of the shape effect on the particle interlocking.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

Interception of two spherical particles with arbitrary radii in simple shear flow

Summary The interception of two force-free and torque-free spherical particles with arbitrary radii freely suspended in simple shear flow is investigated in the limit of vanishing Reynolds number. At any instant, the flow is computed in a frame of reference with origin at the center of one particle using a cylindrical polar coordinate system whose axis of revolution passes through the center of the second particle. The problem is formulated as a decoupled system of integral equations for the zeroth, first, and second Fourier coefficients of the boundary traction with respect to the meridional angle. The derived integral equations are solved with high accuracy using a boundary element method that features adaptive discretization and automatic time-step adjustment according to the inter-particle gap. The results illustrate particle trajectories and describe the particle rotation and evolution of the stress tensor during the interception. The particle interaction is found to always cause a positive shift in the rotational phase angle due to the rolling motion at close contact. As the gap between two particles tends to zero, the shear stress diverges even though the net force and torque exerted on each particle remain zero, independent of the particle relative radius. A frictional force for rough surfaces and small gaps eliminates the slip velocity and promotes the rolling motion.     

Brownian dynamics simulations of rigid rod-like macromolecular particles flowing in bounded channels

Brownian dynamics simulations have been carried out of the joint probability distribution functions (PDF), P(ξ,θ), for macromolecular rod-like particles in the limit of infinite dilution in a solution under hydrodynamic linear flow. These PDF are calculated as a function of the orientations of the rod-like particles, θ and of the positions, ξ, of their centres of mass measured from a solid surface boundary. These simulations are developed in the neighbourhood of a solid surface boundary and in a confined space bounded by two such boundaries. They are constructed for a wide range of key quantities depicting the ratio of the hydrodynamic shear rate to the rotational Brownian diffusion coefficient. The notion of restitution is introduced to develop an algorithm for the consequences of the Brownian and hydrodynamic collisions of these macromolecules with impenetrable solid surface boundaries, which approach applies to a wide range of surfaces and macromolecules. The simulation results for the PDF distributions are given for typically low and high hydrodynamic flow conditions, and their properties are discussed. We show, for example, for low shear rates that a phenomenon which we call Brownian restitution enables the macromolecular rods to pass through a channel that is narrower than the rod length.     

氧化铝悬浮液剪切流变特性的研究

分析了柠檬酸铵(TAC,分散剂)稳定的氧化铝悬浮液的剪切流变行为,研究了TAC加入比例及颗粒大小对流变特性的影响.认为静态时悬浮液中存在由于颗粒布朗运动而形成的热力学颗粒簇,剪切变稀是在剪切作用下热力学颗粒簇分解的结果,而剪切稠化源于剪切作用下水力学颗粒簇的形成.通过悬浮液中颗粒成簇势垒概念的引入,提出悬浮液的低剪粘度和高剪粘度分别取决于氧化铝颗粒表面的ζ电位和Stern电位,通过加入过量的柠檬酸铵可以抑制悬浮液的剪切稠化,推导出了剪切稠化临界剪切速率与颗粒粒径关系的数学表达式.     

Drag,lift and torque acting on a two-dimensional non-spherical particle near a wall

Gas-solid granular flows with non-spherical particles occur in many engineering applications such as fluidized beds. Such flows are usually contained by solid walls and always some particles move close to a wall. The proximity of a wall considerably affects the flow fields and changes the hydrodynamic forces and torque acting on particles moving near the wall. In this paper, we numerically investigate the drag, lift and torque acting on a non-spherical particle in the vicinity of a planar wall by means of lattice Boltzmann simulations. To gain an exhaustive understanding of the complex hydrodynamics and study the influence of various geometrical and flow parameters, a single 2D elliptical particle is selected as our case study. In the simulations, the effect of particle Reynolds number, distance to the wall, orientation angle and aspect ratio on drag, lift and torque is studied. Our study shows that the presence of a wall causes significant changes in hydrodynamic forces, with increasing or decreasing drag and lift forces, depending on the distance from the wall. Even the direction of lift and torque may change, depending on both the distance from the wall and particle orientation angle. Also, an ellipse with higher AR experiences larger hydrodynamic forces and torque whatever the gap size and orientation angle.     

Dynamic simulation of the flow of suspensions of two-dimensional particles with arbitrary shapes

A boundary-element method is implemented for simulating the motion of two-dimensional rigid particles with arbitrary shapes suspended in a viscous fluid in Stokes flow. The numerical implementation results in a system of linear equations for the components of the hydrodynamic traction over boundary elements distributed over the particle surfaces, and for the velocity of translation and angular velocity of rotation of the particles about designated centers. The linear system is solved by the method successive substitutions based on a physically motivated iterative procedure that involves decomposing the influence matrix into diagonal blocks consisting of physical particle clusters, and performing updates by matrix-vector multiplication using the inverses of the diagonal blocks. The iterations are found to converge as long as the particles are separated by a sufficiently large distance that depends on the particle shape and level of discretization. The stiffness of the governing equations due to lubrication forces developing between intercepting particles is removed by preventing the particles from approaching one another by less than a specified distance. Simulations are carried out for doubly-periodic suspensions of circular and elliptical particles in simple shear flow. The simulation algorithm is found to be successful for particles with moderate aspect ratios, and for small and moderate areal fractions up to 0.25. Higher areal fractions require long simulation times due to the large size of spontaneously forming particle clusters. The results illustrate the performance of various aspects of the boundary-element method and provide insights into the effect of the particle areal fraction and aspect ratio on the rheological properties of the suspension and on the geometrical properties of the evolving microstructure.     

Influence of particle shape on sheared dense granular media

We study by means of molecular dynamics simulations of periodic shear cells, the influence of particle shape on the global mechanical behavior of dense granular media. At large shear deformation samples with elongated particles, independent of their initial orientation, reach the same stationary value for both shear force and void ratio. At the micro-mechanical level the stress, the fabric and the inertia tensors of the particles are used to study the evolution of the media. In the case of isotropic particles the direction of the principal axis of the fabric tensor is aligned with the one of the principal stress, while for elongated particles the fabric orientation is strongly dependent on the orientation of the particles. The shear band width is shown to depend on the particle shape due to the tendency of elongated particles to preferential orientations and less rotation.     

Assessment of shear modulus of tissue using ultrasound radiation force acting on a spherical acoustic inhomogeneity

An ultrasound-based method to locally assess the shear modulus of a medium is reported. The proposed approach is based on the application of an impulse acoustic radiation force to an inhomogeneity in the medium and subsequent monitoring of the spatio-temporal response. In our experimental studies, a short pulse produced by a 1.5-MHz highly focused ultrasound transducer was used to initiate the motion of a rigid sphere embedded into an elastic medium. Another 25 MHz focused ultrasound transducer operating in pulse-echo mode was used to track the displacement of the sphere. The experiments were performed in gel phantoms with varying shear modulus to demonstrate the relationship between the displacement of the sphere and shear modulus of the surrounding medium. Because the magnitude of acoustic force applied to sphere depends on the acoustic material properties and, therefore, cannot be used to assess the absolute value of shear modulus, the temporal behavior of the displacement of the sphere was analyzed. The results of this study indicate that there is a strong correlation between the shear modulus of a medium and spatio-temporal characteristics of the motion of the rigid sphere embedded in this medium.     

Study on a large-scale discrete element model for fine particles in a fluidized bed

The discrete element method (DEM) is widely used to comprehend complicated phenomena such as gas–solid flows. This is because the DEM enables us to investigate the characteristics of the granular flow at the particle level. The DEM is a Lagrangian approach where each individual particle is calculated based on Newton’s second law of motion. However, it is difficult to use the DEM to model industrial powder processes, where over a billion particles are dealt with, because the calculation cost becomes too expensive when the number of particles is huge. To solve this issue, we have developed a coarse grain model to simulate the non-cohesive particle behavior in large-scale powder systems. The coarse grain particle represents a group of original particles. Accordingly, the coarse grain model makes it possible to perform the simulations by using a smaller number of calculated particles than are physically present. As might be expected, handling of fine particles involving cohesive force is often required in industry. In the present study, we evolved the coarse grain model to simulate these fine particles. Numerical simulations were performed to show the adequacy of this model in a fluidized bed, which is a typical gas–solid flow situation. The results obtained from our model and for the original particle systems were compared in terms of the transient change of the bed height and pressure drop. The new model can simulate the original particle behavior accurately.     

求解平面固体几何大变形问题的有限质点法

有限质点法是基于向量式力学提出的一种新兴的数值计算方法。它采用物理计算模式,将分析域定义成一组质点的集合,并根据牛顿第二定律描述质点的运动,从而取代了传统数值方法中数学连续体的概念。该方法通过虚拟逆向运动分离刚体位移和变形位移,并采用变形坐标的形式来计算内力,再利用显式时间积分逐步求解质点运动方程。分析中可以通过描述各质点的轨迹来追踪整体的运动行为。该文阐述了有限质点法的基本概念和原理,推导了平面固体的内力求解公式,并将其应用于平面固体几何大变形问题的数值计算,通过自编程序对实例计算的结果表明,该方法有良好的精度和收敛性,对于求解平面固体的大位移、大转动问题是有效的、可行的。     

注塑充模聚合物流动形态与力学行为分子机制研究

以聚甲基丙烯酸甲酯(Polymeric methyl methaerylate,PMMA)为实验材料,基于分子动力学模拟实验研究了注塑成型聚合物充模流动与力学行为的分子机制.构建包含10条聚合度为20的无规PMMA分子链所构成的链团模型,基于能量最小化与SA算法实现了体系能量初始化;基于周期性边界,引入COMPASS从头算分子力场及Velocity-Verlet算法,实现了PMMA胞元在恒温平面流场中的流态与力学行为模拟实验.结果表明,PMMA充模与形变过程首先需要克服包含体系内能、分子链松弛与解缠在内的“活化能”,且存在时间和应力阈值,前者体现了瞬时加载内能协调效应,后者对应于高剪切力作用下分子松弛与解缠现象.体系C原子回转半径分布表明剪切力的作用使得高分子沿流场方向取向排布,剪切力越大则取向越明显,剪切力过大则分子链将断裂而弹性恢复.MSD结果揭示了熔态聚合物充模流动的实质是大分子链定向迁移和取向排布协调运动的结果,且进一步验证了“活化能”的存在,克服这一制约之后大分子链的迁移效应才变得明显,且迁移速率随剪切应力的增大呈非线性增大变化.