Motion Of Spherical Particle Research Articles

Global solutions to coupled (Navier-)Stokes Newton systems in R 3

We consider the motion of spherical particles in the whole space R 3 filled with a viscous fluid. We show that, when modelling the fluid behavior with an incompressible Stokes system, solutions are global and no collision occurs between the spheres in finite time.

Study of fibre movement in a bifurcation

The nature of fibre motion is much more complex than the motion of spherical particles. A complex model must be used for tracking of the fibre carried by the flow. The model must take into account the orientation of the fibre against the flow and solve the consequent rotation of the fibre. Description of such model can be found in this article. It is then used for simulation and analysis of fibre movement in a single planar bifurcation.

Sim-to-Real for High-Resolution Optical Tactile Sensing: From Images to Three-Dimensional Contact Force Distributions.

The images captured by vision-based tactile sensors carry information about high-resolution tactile fields, such as the distribution of the contact forces applied to their soft sensing surface. However, extracting the information encoded in the images is challenging and often addressed with learning-based approaches, which generally require a large amount of training data. This article proposes a strategy to generate tactile images in simulation for a vision-based tactile sensor based on an internal camera that tracks the motion of spherical particles within a soft material. The deformation of the material is simulated in a finite element environment under a diverse set of contact conditions, and spherical particles are projected to a simulated image. Features extracted from the images are mapped to the three-dimensional contact force distribution, with the ground truth also obtained using finite-element simulations, with an artificial neural network that is therefore entirely trained on synthetic data avoiding the need for real-world data collection. The resulting model exhibits high accuracy when evaluated on real-world tactile images, is transferable across multiple tactile sensors without further training, and is suitable for efficient real-time inference.

Axisymmetric motion of a slip spherical particle in the presence of a Brinkman interface with stress jump

The axisymmetric motion of a spherical particle in the presence of a porous interface is considered in the limit of small Reynolds and capillary numbers where the interface is of negligible deformation. We consider the translation along and the rotation about an axis perpendicular to the interface. The flow through the porous medium is modeled by Brinkman equation with a tangential stress jump condition applied at the interface and a slip boundary condition is used at the surface of the particle. A semi-analytical approach based on a collocation technique is used. Due to the linearity of the present problem, the flow variables for the two flow regions are constructed by superposing basic solutions in both cylindrical and spherical coordinate systems. The collocation solutions for the normalized hydrodynamic drag force and torque acted on the particle are calculated with good convergence for various values of the separation parameter, the stress jump coefficient, viscosity ratio and the permeability parameter. The results for the normalized drag and torque coefficients are in good agreement with the available solutions in the literature for the limiting cases.

Dimensionless critical shear stress for sediment particles under varying slope conditions

One of the most fundamental and practical issues in sedimentology is making predictions on initial sediment motion. Many widely used bedload sediment-transport models are based on the concept that sediment transport either begins at or can be scaled by, a constant value of the dimensionless critical shear stress. Flume experiments were conducted for three different diameters of spherical particles under varying channel slope. A model is presented to determine the dimensionless critical shear stress for the incipient motion of spherical particles on nonhorizontal slopes. The findings of the study have been illustrated with mathematical relationships and graphical representations for various combinations of input variables.

Particle approach to a stagnation point at a wall: Viscous damping and collision dynamics

Highly resolved numerical simulations by the immersed boundary method are used to study neutrally buoyant spherical particle motion when carried by fluid approaching a wall. The carrying flow studied is the Hiemenz-Homann (HH) axisymmetric straining flow into a stagnation point at a flat rigid wall, with a boundary layer of thickness 3δ = 3√ν/B, with B the strain rate of the flow and ν the kinematic viscosity of the fluid. The pressure in the carrying flow increases on approach to the stagnation point, as a result of the deceleration of the fluid.

Cross-stream migration of non-spherical particles in a second-order fluid – theories of particle dynamics in arbitrary quadratic flows

Particle migration in viscoelastic suspensions is vital in many applications in the biomedical community and the chemical/oil industries. Previous studies have provided insight into the motion of spherical particles in simple viscoelastic flows, yet the combined effect of more complex flow profiles and particle shapes is under-explored. Here, we develop approximate analytical expressions for the polymeric force and torque on an arbitrarily shaped particle in a second-order fluid, subject to a general quadratic flow field. This model is exact for the case when the first and second normal stress coefficients satisfy . Under this assumption, we examine how particle shape alters cross-stream particle migration (i.e. lift) and particle orientation in both shear- and pressure-driven flows. In shear-driven flows, we observe that spheroidal particles adjust their orientation to align their longer axis along the vorticity direction, although significant deviations from slender-body theories occur for finite aspect ratios. In a slit-like pressure-driven flow, we identify scaling theories to quantify how the particle lift depends on shape for a wide variety of shapes. We find that prolate particles slowly transition to a log-rolling state as they approach the flow centre, with the lift initially being larger than that of an equal-volume sphere, but then becoming smaller as log-rolling emerges. The net effect is a smaller average migration speed for particles with larger aspect ratio. Lastly, we discuss future directions for experimental studies on particle dynamics as well as directions to extend the current work towards more complicated systems.

Spherical probes for simultaneous measurement of rotational and translational diffusion in 3 dimensions

Real time visualization and tracking of colloidal particles with 3D resolution is essential for probing the local structure and dynamics in complex fluids. Although tracking translational motion of spherical particles is well-known, accessing rotational dynamics of such particles remains a great challenge. Here, we report a novel approach of using fluorescently labeled raspberry-like colloids with an optical anisotropy to concurrently track translational and rotational dynamics in 3 dimensions. The raspberry-like particles are coated by a silica layer of adjustable thickness, which allows tuning the surface roughness. The synthesis and applicability of the proposed method is demonstrated by two types of probes: rough and smoothened. The accuracies of measuring Mean Squared (Angular) Displacements are also demonstrated by using these 2 probes dispersed in 2 different solvents. The presented 3D trackable colloids offer a high potential for wide range of applications and studies, such as probing the dynamics of crystallization, phase transitions, biological interactions and the effect of surface roughness on diffusion.

Discrete Element Method of the Dynamic Behavior of Flaky Particles Using the Rigid Plate Model

The discrete element method (DEM) can be used to simulate the behavior of spherical particles. The spherical particles are regarded as rigid bodies in the calculation of DEM. However, the properties of these spherical particles are not applicable to powders consisting of plate-shaped or flaky particles because of the lack of geometrical consideration. Inevitably, the lack of geometrical consideration brings the misunderstanding of the powder flow with plate-shaped particles. In this research study, we suggest a new model, called flaky particles, consisting of a series of spherical particles to simulate the behavior of powder with spherical particles. To mimic the dynamic behavior of the hard particles, the relative motion of spherical particles, constituting a plate, is restricted. Afterwards, the suggested model is validated by the drop-and-bounce test and by theoretical results. The magnitude of the errors in the computation of the translational and the rotational velocities after collision are compared and the results show that the generated error is negligible (below 2%).

Effect of Eccentric Mass Distribution on the Motion of Spherical Particles in Shear Flows

Abstract A particle-resolved direct numerical simulation is performed on the motion of spherical particles with an eccentric internal mass distribution in lateral linear shear flow, which is oriented in the vertical direction and sheared in a horizontal direction. We examine the effect of mass eccentricity on the two-way interactions of particles with both laminar and turbulent shear flows. A spherical shell/hollow particle with an inner spherical core is focused on as a typical example of mass eccentric particles. The Navier–Stokes equations and the Newton–Euler equations are solved for the fluid phase and the particles, respectively. An immersed boundary method is adopted to represent the shell particle. The Newton–Euler equations are solved using the body-fixed coordinate system and four quaternion parameters, considering the deviation of the center of mass from the center of the spherical shell particle. Simulations are performed at a relatively low particle volume fraction of 0.4%. In turbulent flows, the Taylor-microscale Reynolds number reached about 49 at the end of the simulations. Numerical results show that shear-induced particle rotation is suppressed by the torque due to gravity. It is found that the lateral migration of mass eccentric particles becomes less vigorous in both laminar and turbulent flows since the effect of the Magnus lift force is also weakened for mass eccentric particles. It is also found that the evolution of fluid kinetic energy is significantly affected by the mass eccentricity of particles in laminar flows.

Motion of a spherical particle in a microbubble plume and the behavior of microbubbles around the particle

This study aims to investigate the motion of a solid spherical particle in a microbubble plume and the behavior of bubbles around the particle. Microbubbles (mean diameter 0.037 mm) released into a rectangular conduit by the electrolysis of water rise via buoyancy and form a bubble plume in the conduit. A solid spherical particle with a diameter of 10 mm and density of 1022 kg/m3 is placed on a mesh stretched across the cross-section near the bottom of the conduit, and microbubbles are then released from the cathode. Experiments are conducted with the bubble volumetric flux in the conduit j G at 0.05 and 0.09 mm/s. The particle repeatedly rises and falls when j G = 0.05 mm/s, and it rises almost vertically when j G = 0.09 mm/s. The absolute value of the vertical velocity of the particle is lower than that of the bubble. There is a belt-like region where the bubble velocity is extremely lower behind the particle. Such wake behind the particle clearly appears when the particle is falling, because the bubble velocity relative to the particle is higher.

Semiempirical Method for Determining the Rate of Slow Hindered Motion

Semiempirical equations have been derived for determining the rate of slow hindered motion of spherical particles in a liquid, which agree with empirical data with a high degree of accuracy. It has been shown that the variational principle of the minimum intensity of energy dissipation can be used in determining the rate of hindered motion.

Wireless detector for translational and rotational motion of spherical-particle flow

To measure the translational and rotational motion of spherical particles in a three-dimensional granular flow, a wireless spherical detector with a built-in wireless module and a three-axis gyroscope and three-axis accelerometer was developed. The three-axis acceleration and three-axis angular velocity can be measured and stored by the detector in real time. The attitude angle, the spatial rotation of the detector coordinate system relative to the laboratory coordinate system, described via the Euler angle is obtained with a Quaternion algorithm and Kalman filter. The gravity acceleration component in the acceleration data can be removed with the attitude angle. The test results show that the acceleration error is ±0.02G, and the average cumulative angle error is 0.02°/s. Finally, the detector was tested as a tracer particle in hopper flow. According to the results, the variation value of the rotation angles of the spherical detector obeys an exponential distribution.

Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method

The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time.

Rotational diffusion of partially wetted colloids at fluid interfaces

HypothesisRotational Brownian diffusions of colloidal particles at a fluid interface play important roles in particle self-assembly and in surface microrheology. Recent experiments on translational Brownian motion of spherical particles at the air-water interface show a significant slowing down of the translational diffusion with respect to the hydrodynamic predictions (Boniello et al., 2015). For the rotational diffusions of partially wetted colloids, slowing down of the particle dynamics can be also expected. ExperimentsHere, the rotational dynamics of Janus colloids at the air-water interface have been experimentally investigated using optical microscopy. Bright field and fluorescent microscopies have been used to measure the in-plane and out-of-plane particle rotational diffusions exploiting the Janus geometry of the colloids we fabricated. FindingsOur results show a severe slowing down of the rotational diffusion Dr,⊥ connected to the contact line motion and wetting-dewetting dynamics occurring on particle regions located at opposite liquid wedges. A slowing down of the particle rotational diffusion about an axis parallel to the interfacial normal Dr,|| was also observed. Contact line fluctuations due to partial wetting dynamics lead to a rotational line friction that we have modelled in order to describe our results.

Effects of convex rib height on spherical particle milling in a lab-scale horizontal rice mill

Improvement of critical components for rice mill is one of the issues constraining the development of rice milling industry. Unfortunately, the effect of configuration of rotating shaft on the flow behaviors, collision characteristics and even milling mechanisms of rice particles in a rice mill still remains poorly understood. In this work, motion of spherical particles in a lab-scale horizontal rice mill with different heights of convex ribs fixed on rotating shaft was simulated using the platform based on the discrete element method (DEM). Validity of the numerical model was confirmed by comparing individual resident time and power draw obtained from experiments with those from simulations. Effects of height of convex ribs on flow properties including the dispersion in the axial direction and the velocity gradient along the radial direction, and further on collision characteristics which are closely related to the rice milling mechanisms, were investigated from the quantitative and qualitative points of view. The results showed that the migration index characterizing dispersion degree and the mean effective collision number, increases to a maximum and then decreases with the increase in the height, while the difference index representing velocity gradient and the mean collision energy increases at first and then decreases with the increase in the height. This implies that the mean effective collision number describing uniformity of milling mainly depends on the degree of dispersion, whereas the mean collision energy representing intensity of milling primarily relies on the velocity gradient. Furthermore, an increase in the height within the accepted range leads to the larger total collision energy, which accelerates wear of rice grains. The results are useful for providing the theoretic guidelines to select appropriate parameters of rotating shaft for the design of stirrer mills.

The Movement of an Ion-exchange Microparticle in a Weak External Electric Field

The electrokinetic motion of spherical particle suspended in the electrolyte solution under influence of external electric field is studied. Due to impermeability of particle’s surface for one kind of ion species the particle exhibit behavior different to well investigated dielectric particles. Under an assumption of a weak external electric field, we derive the analytical estimation of the particle’s velocity by means of a method of matched asymptotic expansions. The analytical analysis is complemented by numerical solution, which gives the distribution of ion’s concentrations, electric potential profiles and flows streamlines. The analytical results are successfully compared with the results of numerical simulation.

Asymptotics for spherical particle motion in a spherically expanding flow

In the context of an increasing number of complex multiparametric dust coma models it was found convenient to construct an elementary model with a minimum number of parameters selected to represent the key processes acting on the dust. The models outputs can be used as a reference evaluation of these processes with rough estimates of the resulting dust properties e.g. velocity.The present work introduces three, universal, dimensionless parameters which characterize the dust motion in an expanding flow, and computes as a function of these parameters the dust terminal velocity, the time it takes to acquire it, and the distance at which it is acquired.The motion of dust grains is presented as a system of dimensionless ordinary differential equations the solution of which depends upon the above mentioned three parameters. The numerical integration of this system was performed over a wide range of parameter space covering the whole range of physically possible conditions.Precomputed results of dust terminal velocity, time and distance where it is reached are presented in dimensionless form. To obtain dimensional values for a particular case it is sufficient to perform algebraic operations.

The effects of friction characteristic of particle on milling process in a horizontal rice mill

The physical and mechanical properties of rice are of significant change during milling from brown rice to white rice, especially the friction characteristics. In order to clarify the effects of roughness of rice surface on the milling process and mechanism, in this work, motion of spherical particle in a horizontal rice mill under different static friction coefficients (i.e., between particle and cylinder sieve wall μs,pt and between particles μs,pp) was simulated using the discrete element method. The uniformity of axial motion and circular motion were qualitatively and quantitatively analyzed, which are characterized by introducing the axial dispersion coefficient and uniformity index, respectively. Then, the effects of static fiction coefficients on residence time and collision energy among particles were discussed. The results indicated that the μs,pt mainly affects the axial motion while the μs,pp primarily influences on the circular motion. The residence time is strongly affected by the uniformity of axial motion while the collision energy is significantly influenced by the uniformity of circular motion. Finally, the relationship between friction characteristics and milling performance can be described based on the method of polynomial fitting. This work is useful for providing essential references to control the quality of milled rice.

Tomographic active optical trapping of arbitrarily shaped objects by exploiting 3D refractive index maps

Optical trapping can manipulate the three-dimensional (3D) motion of spherical particles based on the simple prediction of optical forces and the responding motion of samples. However, controlling the 3D behaviour of non-spherical particles with arbitrary orientations is extremely challenging, due to experimental difficulties and extensive computations. Here, we achieve the real-time optical control of arbitrarily shaped particles by combining the wavefront shaping of a trapping beam and measurements of the 3D refractive index distribution of samples. Engineering the 3D light field distribution of a trapping beam based on the measured 3D refractive index map of samples generates a light mould, which can manipulate colloidal and biological samples with arbitrary orientations and/or shapes. The present method provides stable control of the orientation and assembly of arbitrarily shaped particles without knowing a priori information about the sample geometry. The proposed method can be directly applied in biophotonics and soft matter physics.