Axisymmetric Particles Research Articles

Rotational Taylor dispersion in linear flows

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.

Numerical investigation of punch-through mitigation in stiff-over-soft clays using skirted spudcan

Punch-through failure, a critical issue in offshore engineering, occurs when a foundation penetrates through strong-over-weak soil layers. This paper presents a study on the effectiveness of skirt addition to spudcans in addressing punch-through failure through numerical simulations using the axisymmetric Particle Finite Element Method (PFEM). The validity of the PFEM is verified by simulating a spudcan penetration centrifuge test. Subsequently, PFEM simulations are conducted to analyse the penetration behaviour of both generic and skirted spudcans in stiff-over-soft clays. Results from the simulations reveal the bearing responses of spudcans as they penetrate into clays, elucidate associated failure mechanisms, and underscore the significant of considering the spudcan-driving process in estimating punch-through failure mitigation. Findings indicate that, the skirt effectively mitigates punch-through failure by increasing plug height in the lower soft layer, thus reducing the rate of bearing capacity reduction. Furthermore, critical factors such as skirt length, upper layer thickness, lower layer strength gradient, and the strength ratio between lower and upper layers are assessed through comprehensive parametric studies to evaluate the efficacy of skirted spudcans in mitigating punch-through failure, with eventual goal to provide essential guidance for practical design considerations in offshore foundation systems.

Drag, lift, and torque correlations for axi-symmetric rod-like non-spherical particles in linear wall-bounded shear flow

This paper presents novel correlations to predict the drag, lift, and torque coefficients of axi-symmetric non-spherical rod-like particles in a wall-bounded linear shear flow. The particle position and orientation relative to the wall are varied to systematically investigate the influence of the wall on the hydrodynamic forces. The newly derived correlations for drag, lift, and torque on the particle depend on various parameters, including the particle Reynolds number, the orientation angle between the major axis of the particle and the main local flow direction, the aspect ratio of the particle, and the dimensionless distance from the particle centre to the wall. The impact of the wall on the hydrodynamic forces is accounted for as a function of a multiplication factor on the drag force in case of locally uniform flow, and an additional force contribution for the lift and the torque, modifying the resultant forces experienced by a particle in a locally uniform flow. The changes in the hydrodynamic forces prove to be substantial, emphasizing the necessity of accounting for wall effects across all particle types and flow conditions investigated in this study. The coefficients of the correlations are determined through a fitting process utilizing the data generated from our previous study on the interaction forces between a locally uniform flow and an axi-symmetric non-spherical rod-like particles, as well as from data of novel direct numerical simulations (DNS) performed in this work of flow past axi-symmetric rod-like particles near a wall. The proposed correlations exhibit a good agreement compared to the DNS results, with median errors of 2.89%, 5.37%, and 11.00%, and correlation coefficients of 0.99, 0.99, and 0.96 for the correlations accounting for the drag, lift, and torque coefficients of a non-spherical particle in wall-bounded linear shear flow profile, respectively. These correlations can be used in large-scale simulations using an Eulerian–Lagrangian or a CFD/DEM framework to predict the behaviour of axi-symmetric rod-like non-spherical particles in wall-bounded shear flow to locally uniform flow conditions.

An advanced light scattering imaging model for total internal reflection microscopy considering a stratified medium

An advanced light scattering model for Total Internal Reflection Microscopy (TIRM) is presented. The model considers the specific TIRM geometry and deals with the scattering by an axisymmetric particle of arbitrary orientation placed in a stratified medium and the imaging of the scattered field. The scattered field is computed by truncating the scattered and internal field expansions and by using spherical and plane wave expansions for the free-space dyadic Green’s function. While the first expansion is valid outside a sphere enclosing the particle, the second one is valid outside the tangent planes bounding the particle from above and below. We demonstrate that in both cases, the results are the same, and thus, that the restrictive condition according to which the interface should not intersect the particle’s circumscribed sphere is not relevant. The image of the scattered field is computed by using the Debye diffraction integral and fast Fourier transform, while for a better reconstruction of the particle orientation, an image processing step consisting in a contour extraction and ellipse fitting is considered. The numerical simulations dealing with scattering by a prolate spheroid provide evidence of the remarkably sensitivity of the geometric parameters of the image ellipse to the particle orientation angles, as well as, of the integral response of the detector to the distance between the particle and the interface.

Influence of small inertia on Jeffery orbits

We experimentally investigate the rotational dynamics of neutrally buoyant axisymmetric particles in a simple shear flow. A custom-built shearing cell and a multi-view shape-reconstruction method are used to obtain direct measurements of the orientation and period of rotation of particles having oblate and prolate shapes (such as spheroids and cylinders) of varying aspect ratios. By systematically changing the viscosity of the fluid, we examine the effect of inertia (which may be originated from either phase) on the dynamical behaviour of these suspended particles up to a particle Reynolds number of approximately one. While no significant effect on the period of rotation is found in this small-inertia regime, a systematic drift among several rotations toward limiting stable orbits is observed. Prolate particles are seen to drift towards the tumbling orbit in the plane of shear, whereas oblate particles are driven either to the tumbling or to the vorticity-aligned spinning orbits, depending on their initial orientation. These results are compared with recent small-inertia asymptotic theories, assessing their range of validity, as well as to numerical simulations in the small-inertia regime for both prolate and oblate particles.

Drag, lift and torque correlations for axi-symmetric rod-like non-spherical particles in locally linear shear flows

This paper derives new correlations to predict the drag, lift and torque coefficients of axi-symmetric non-spherical rod-like particles for several fluid flow regimes and velocity profiles. The fluid velocity profiles considered are locally uniform flow and locally linear shear flow. The novel correlations for the drag, lift and torque coefficients depend on the particle Reynolds number Rep, the orientation of the particle with respect to the main fluid direction θ, the aspect ratio of the rod-like particle α, and the dimensionless local shear rate G̃. The effect of the linear shear flow on the hydrodynamic forces is modeled as an additional component for the resultant of forces acting on a particle in a locally uniform flow, hence the independent expressions for the drag, lift and torque coefficients of axi-symmetric particles in a locally uniform flow are also provided in this work. The data provided to fit the coefficient in the new correlation are generated using available analytical expressions in the viscous regime, and performing direct numerical simulations (DNS) of the flow past the axi-symmetric particles at finite particle Reynolds number. The DNS are performed using the direct-forcing immersed boundary method. The coefficients in the proposed drag, lift and torque correlations are determined with a high degree of accuracy, where the mean error in the prediction lies below 2% for the locally uniform flow correlations, and bwlow 1.67%, 5.35%, 6.78% for the correlation accounting for the change in the drag, lift, and torque coefficients in case of a linear shear flow, respectively. The proposed correlations for the drag, lift and torque coefficients can be used in large-scale simulations performed in the Eulerian-Lagrangian framework with locally uniform and non-uniform flows.

Phoresis kernel theory for passive and active spheres with nonuniform phoretic mobility.

By introducing geometry-based phoresis kernels, we establish a direct connection between the translational and rotational velocities of a phoretic sphere and the distributions of the driving fields or fluxes. The kernels quantify the local contribution of the field or flux to the particle dynamics. The field kernels for both passive and active particles share the same functional form, depending on the position-dependent surface phoretic mobility. For uniform phoretic mobility, the translational field kernel is proportional to the surface normal vector, while the rotational field kernel is zero; thus, a phoretic sphere with uniform phoretic mobility does not rotate. As case studies, we discuss examples of a self-phoretic axisymmetric particle influenced by a globally-driven field gradient, a general scenario for axisymmetric self-phoretic particle and two of its special cases, and a non-axisymmetric active particle.

Modeling the Anisotropic Transport Behavior for Axisymmetric 2D Electrode Particles Using a Modified Pseudo-2D Model Framework

This presentation extends widely used pseudo-2D (P2D) Li-ion battery models to include electrode particles that have strong crystal-scale anisotropies and possibly non-spherical shapes. Typical P2D models predict Li transport with representative spherical electrode particles by solving a one-dimensional diffusion equation in spherical coordinates. However, battery electrodes (graphite, NMC, etc.) may have strong crystalline anisotropies, leading to transport and mechanical properties that vary by orders of magnitude depending on crystallographic orientations. The anisotropic transport can cause large concentration gradients, possibly leading to particle fracture associated with concentration-induced stress. The remainder of the P2D model, such as Li-ion transport within the electrolyte solvent, remains essentially unchanged. The charge-transfer boundary conditions at the particle surfaces do need to accommodate the crystallographic anisotropy.The present model discretizes representative electrode particles in a two-dimensional finite-volume axisymmetric geometry, accounting for the anisotropic behaviors. The computational burden is greater than it is for the one-dimensional spherical solution. However, the P2D model with two-dimensional axisymmetric particle discretization still runs in only a few minutes on a typical personal computer.The model shows how electrode-particle anisotropy affects the battery performance, such as charge-discharge characteristics and electrochemical impedance spectroscopy. The model also predicts the concentration gradients and correlated stress for various axisymmetric, non-spherical particles.

DEM study of the stress fields around the closed-ended displacement pile driven in sand

Three-dimensional discrete element method (DEM) is employed to model the published calibration chamber test of a closed-ended displacement pile driven in sand. To achieve large chamber-to-pile and pile-to-particle size ratios for unbiased predictions, a high-performance graphics processing unit-powered DEM code is utilised in conjunction with the axisymmetric assumption and particle refinement method. The DEM parameters are first calibrated against the drained triaxial compression test data on Fontainebleau sand. Then, the DEM modelling of pile driving demonstrates quantitative agreement with the experimental counterpart in terms of cone resistance, stress contours, and distributions.

Viscosity and dynamics of rigid axisymmetric particles in power-law fluids

Viscosity and dynamics of rigid axisymmetric particles in power-law fluids

High resolution characterization of a sheathed axisymmetric variable supersaturation condensation particle sizer

Diffusive condensation particle counters (CPCs) injecting the aerosol near the symmetry axis within a larger flow of a vapor-containing sheath gas have previously exhibited a size resolving power considerably lower than theoretically expected. We hypothesize that reexamining these instruments with particles of improved uniformity in composition, size and shape should reveal a much better performance, well suited for high resolution particle sizing and basic heterogeneous nucleation studies. Accordingly, we investigate the performance of the Variable Supersaturation Condensation Particle Sizer (VSCPS) of Gallar et al. (2006) with an aerosol of uniform singly charged polyethylene glycol particles (3–9 nm diameter), produced by a bipolar electrospray, and size-selected by a differential mobility analyzer of high resolution. The condensation size resolution obtained with n-butanol vapor almost triples that previously demonstrated for this instrument, exceeds that established for any other CPC, and can apparently be further increased. Flow and temperature field calculations of the maximal supersaturation in the VSCPS would enable basic heterogeneous nucleation studies, as well as high resolution sizing of neutral or charged particles.

Soundiation: A software in evaluation of acoustophoresis driven by radiation force and torque on axisymmetric objects.

Acoustic radiation force and torque arising from wave scattering are commonly used to manipulate micro-objects without contact. We applied the partial wave expansion series and the conformal transformation approach to estimate the acoustic radiation force and torque exerted on the axisymmetric particles. Meanwhile, the translational and rotational transformations are employed to perform the prediction of the acoustophoresis. Although these theoretical derivations are well-developed [Tang and Huang, J. Sound Vibr. 532, 117012 (2022), Tang and Huang, Phys. Rev. E 105, 055110 (2022)], coding the required systems, including generation of the wave function, implementation of the transformations, calculations between modules, etc., is non-trivial and time-consuming. Here, we present a new open-source, matlab-based software, called Soundiation [GitHub Repository: https://github.com/Tountain/SoundiationAcoustophoresis, GPL-3.0 license], to address the acoustic radiation force and torque while supporting the dynamic prediction of non-spherical particles. The implementation is basically generic, and its applicability is demonstrated through the validation of numerical methods. A graphical user interface is provided so that it can be used and extended easily.

MPS-based axisymmetric particle method for bubble rising with density and pressure discontinuity

Numerical simulation of gas bubble rising in liquid is challenging due to high density and viscosity ratios. This study proposes to model the liquid and gas phases separately by the incompressible and Weakly Compressible Moving Particle Semi-implicit (MPS) methods with the aim of preserving the interfacial discontinuity. The liquid-gas interface is explicitly represented by a series of discrete nodes. By adequately enforcing the stress conditions on these moving interface nodes, the MPS and WC-MPS methods are coupled. The surface tension is considered as a pressure jump rather than the volume force. Without applying any smoothing or averaging scheme, the density, viscosity and pressure are discontinuous across the interface. The axisymmetric formulation is directly introduced based on the least squares method to save computational cost. In addition, a multi-time step algorithm is proposed so that independent time increments can be adopted for different phases. Furthermore, the particle shifting technique is extended to control the multi-spatial resolution dynamically. Several numerical tests, including hydrostatic pressure problems, droplet deformation and bubble rising benchmark are conducted to show the accuracy, efficiency and stability. Finally, validations are performed using experimental results with wide ranges of Reynolds number and Bond number, which dominate the bubble shape.

Theoretical framework to predict the acoustophoresis of axisymmetric irregular objects above an ultrasound transducer array.

Acoustic radiation force and torque arising from wave scattering are able to translate and rotate matter without contact. However, the existing research mainly focused on manipulating simple symmetrical geometries, neglecting the significance of geometric features. For the nonspherical geometries, the shape of the object strongly affects its scattering properties, and thus the radiation force and torque as well as the acoustophoretic process. Here, we develop an analytical framework to calculate the radiation force and torque exerted on the sound-hard or the sound-soft, axisymmetric particles excited by a user-customized transducer array based on a conformal transformation approach, capturing the significance of the geometric features. The derivation framework is established under the computation coordinate system (CCS), whereas the particle is assumed to be static. For the dynamic processes, the rotation of particle is converted as the opposite rotation of transducer array, achieved by employing a rotation transformation to tune the incident driving field in the CCS. Later, the obtained radiation force and torque in the CCS should be transformed back to the observation coordinate system for force and torque analysis. The radiation force and torque exerted on particles with different orientations are validated by comparing the full three-dimensional numerical solution in different phase distributions. It is found that the proposed method presents superior computational accuracy, high geometric adaptivity, and good robustness to various geometric features, while the computational efficiency is more than 100 times higher than that of the full numerical method. Furthermore, it is found that the dynamic trajectories of particles with different geometric features are completely different, indicating that the geometric features can be a potential degree of freedom to tune acoustophoretic process. The ability to predict the acoustophoretic process of nonspherical particles above a user-customized transducer array has improved our understanding of the effect of shape asymmetry, which can also be used to verify the effectiveness of acoustic tweezers in manipulating nonspherical objects.

Motion of asymmetric bodies in two-dimensional shear flow

At low Reynolds numbers, axisymmetric ellipsoidal particles immersed in a shear flow undergo periodic tumbling motions known as Jeffery orbits, with the orbit determined by the initial orientation. Understanding this motion is important for predicting the overall dynamics of a suspension. While slender fibres may follow Jeffery orbits, many such particles in nature are neither straight nor rigid. Recent work exploring the dynamics of curved or elastic fibres have found Jeffery-like behaviour along with chaotic orbits, decaying orbital constants and cross-streamline drift. Most work focuses on particles with reflectional symmetry; we instead consider the behaviour of a composite asymmetric slender body made of two straight rods, suspended in a two-dimensional shear flow, to understand the effects of the shape on the dynamics. We find that for certain geometries the particle does not rotate and undergoes persistent drift across streamlines, the magnitude of which is consistent with other previously identified forms of cross-streamline drift. For this class of particles, such geometry-driven cross-streamline motion may be important in giving rise to dispersion in channel flows, thereby potentially enhancing mixing.

FEM ANALYSIS OF ENERGY LOSS DUE TO WAVE PROPAGATION FOR MICRO-PARTICLE IMPACTING SUBSTRATE WITH HIGH VELOCITIES

The impact between particles and material surface is a micro-scaled physical phenomenon found in various technological processes and in the study of the mechanical properties of materials. Design of materials with desired properties is a challenging issue for most industries. And especially in aviation one of the most important factors is mass. Recently with the innovations in 3D printing technologies, the importance of this phenomenon has increased. Numerical simulation of multi-particle systems is based on considering binary interactions; therefore, a simplified but as much accurate as possible particle interaction model is required for simulations. Particular cases of axisymmetric particle to substrate contact is modelled at select impact velocities and using different layer thicknesses. When modelling the particle impact at high contact velocity, a substrate thickness dependent change in the restitution coefficient was observed. This change happens is due to elastic waves and is important both to coating and 3D printing technologies when building layers of different properties materials.

Mean acoustic fields exerted on a subwavelength axisymmetric particle.

The acoustic radiation force produced by ultrasonic waves is the "workhorse" of particle manipulation in acoustofluidics. Nonspherical particles are also subjected to a mean torque known as the acoustic radiation torque. Together they constitute the mean acoustic fields exerted on the particle. Analytical methods alone cannot calculate these fields on arbitrarily shaped particles in actual fluids and are no longer fit for purpose. Here, a semi-analytical approach is introduced for handling subwavelength axisymmetric particles immersed in an isotropic Newtonian fluid. The obtained mean acoustic fields depend on the scattering coefficients that reflect the monopole and dipole modes. These coefficients are determined by numerically solving the scattering problem. Our method is benchmarked by comparison with the exact result for a subwavelength rigid sphere in water. Besides, a more realistic case of a red blood cell immersed in blood plasma under a standing ultrasonic wave is investigated with our methodology.

Drag and heat transfer coefficients for axisymmetric nonspherical particles: A LBM study

In this work, the thermal lattice Boltzmann method with immersed moving boundary conditions has been employed to calculate the drag coefficients and Nusselt numbers for isolated axisymmetric nonspherical particles in uniform flow for a wide range of Reynolds numbers (Re) and aspect ratios (Ar). The simulation results demonstrate that the drag coefficient for ellipsoids and a spherocylinder evolves as sin2θ, viz. θ being the incident angle of the particle. However, the Nusselt number for prolate ellipsoids evolves as sinmθ, viz. m being a function of particle aspect ratio. A correlation for m has been developed for 1<Ar≤4 based on the simulation data. The Nusselt number for a spherocylinder of aspect ratio 4 evolves as sin1.278θ. Moreover, we observe that the drag coefficients and Nusselt numbers for a prolate ellipsoid of aspect ratio 4 and a spherocylinder of aspect ratio 4 are comparable with a maximal relative deviation 5%. Based on the simulation data and the data from literature, a drag correlation for oblate (0.2≤Ar<1 and 1≤Re≤100) and prolate (1≤Ar≤5 and 1≤Re≤2000) ellipsoids has been developed to broaden the range of applicability of existing drag correlations. The average relative deviation between the drag correlation and the fitting data is 9.4%. The Nusselt number correlation for prolate ellipsoids is valid for 1≤Ar≤4 and Re≤500. On the other hand, the Nusselt number correlation proposed for a spherocylinder is valid for Ar=4 and Re≤500. The new drag and Nusselt number correlations are expected to improve the accuracy of Euler-Lagrangian simulations of non-isothermal particulate flows comprising ellipsoids or spherocylinders.

Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations

We successfully perform the three-dimensional tracking in a turbulent fluid flow of small axisymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier–Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravitational torque stability number and by the particle aspect ratio. We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential orientation and tumbling rate of the particles. We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.

Drop squeezing between arbitrary smooth obstacles

Abstract