Particle-wall Distance Research Articles

Dynamics of single cavitation bubble collapse jet under particle-wall synergy

The interaction between a particle and a cavitation bubble significantly influences the erosive effect on the wall surface of flow passage components in fluid machinery. This paper investigates the dynamics of a single bubble collapse jet under the synergetic effects of a particle and a wall, using Kelvin impulse theory and high-speed photographic experiments. A theoretical model to predict the intensity and direction of the collapse jet at arbitrary locations near the particle and the wall is constructed on the basis of the image method and Weiss's theorem. The accuracy of the model is verified by comparison with a large number of experimental results. The mechanisms underlying the relative contributions of the particle and wall to the behavior of jet intensity and direction are explored. The effects of key parameters on jet intensity and direction are also quantitatively analyzed, including the relative positions of the particle, wall, and the bubble and the dimensionless particle radius. The main conclusions are as follows: (1) the particle will cause a deflection in the direction of the collapse jet near the wall, leading to the formation of a jet attraction zone. The proposed theoretical model effectively predicts the spatial location of this zone. (2) There exists a region in which the jet is weak, and there is a jet equilibrium point with zero impulse between the particle and the wall. The position of this equilibrium point gradually approaches the wall in a nonlinear manner with increasing particle size and in a quasi-linear manner with decreasing particle–wall distance. (3) When the particle and the bubble are the same distance from the wall, the jet direction gradually changes from toward the particle to vertical to the wall in a nonlinear manner as the bubble–particle distance increases. Moreover, the effective range of the particle's influence on the jet direction decreases as the particle–wall distance decreases.

Rotational and translational drags of a Janus particle close to a wall and a lipid membrane

HypothesisMeasuring rotational and translational Brownian motion of single spherical particles reveals dissipations due to the interaction between the particle and the environment. ExperimentsIn this article, we show experiments where the in-plane translational and the two rotational drag coefficients of a single spherical Brownian particle can be measured. These particle drags are functions of the particle size and of the particle–wall distance, and of the viscous dissipations at play. We measure drag coefficients for Janus particles close to a solid wall and close to a lipid bilayer membrane. FindingsFor a particle close to a wall, we show that according to hydrodynamic models, particle–wall distance and particle size can be determined. For a particle partially wrapped by lipid membranes, in absence of strong binding interactions, translational and rotational drags are significantly larger than the ones of non-wrapped particles. Beside the effect of the membrane viscosity, we show that dissipations in the deformed membrane cap region strongly contribute to the drag coefficients.

Interface-resolved simulations of the confinement effect on the sedimentation of a sphere in yield-stress fluids

We perform three-dimensional numerical simulations to investigate the confinement effect on the sedimentation of a single sphere in an otherwise quiescent yield stress fluid, in the presence of finite elasticity and weak inertia. The carrier fluid is modeled using the elastoviscoplastic constitutive laws proposed by Saramito (2009). The additional elastic stress tensor is fully coupled with the flow equation, while the rigid particle is represented by an immersed boundary method. The simulations show the faster relaxation of the fluid velocity and the progressive translation of the location of the negative wake downstream of the sphere as the bounding walls are brought closer to the particle. Moreover, the sphere drag decreases by increasing the particle–wall distance. We show that the confinement ratio (ratio of the gap between rigid confining walls and the sphere radius) reaches a critical value beyond which the wall-effect on the particle and flow dynamics becomes negligible. The key finding here is that the critical confinement ratio and the maximum variation of the Stokes drag with confinement ratio are weakly dependent on the level of material elasticity and plasticity for a certain range of material parameters. Finally, we propose an expression for the Stokes drag coefficient, as a function of material plasticity and confinement ratio.

Particle/wall electroviscous effects at the micron scale: comparison between experiments, analytical and numerical models

We report a experimental study of the motion of 1 μm single particles interacting with functionalized walls at low and moderate ionic strengths conditions. The 3D particle’s trajectories were obtained by analyzing the diffracted particle images (point spread function). The studied particle/wall systems include negatively charged particles interacting with bare glass, glass covered with polyelectrolytes and glass covered with a lipid monolayer. In the low salt regime (pure water) we observed a retardation effect of the short-time diffusion coefficients when the particle interacts with a negatively charged wall; this effect is more severe in the perpendicular than in the lateral component. The decrease of the diffusion as a function of the particle–wall distance h was similar regardless the origin of the negative charge at the wall. When surface charge was screened or salt was added to the medium (10 mM), the diffusivity curves recover the classical hydrodynamic behavior. Electroviscous theory based on the thin electrical double layer (EDL) approximation reproduces the experimental data except for small h. On the other hand, 2D numerical solutions of the electrokinetic equations showed good qualitative agreement with experiments. The numerical model also showed that the hydrodynamic and Maxwellian part of the electroviscous total drag tend to zero as h → 0 and how this is linked with the merging of both EDL’s at close proximity.

Photophoretic asymmetry factors for an absorptive dielectric cylinder near a reflecting planar boundary

The effect of a perfectly reflecting boundary (i.e., planar wall) on the photophoretic asymmetry factors (PAFs) for an absorptive dielectric cylinder is investigated. The expression for the normalized intensity function for the electric field internal to the cylinder is used in conjunction with the multiple scattering theory of waves, the translational addition theorem in cylindrical coordinates, and the method of images to derive analytically and compute numerically the longitudinal (L) and transverse (T) PAFs for the cylinder as well as the internal dimensionless intensity function. Both TM- and TE-polarized plane progressive waves with arbitrary incidence (in the polar plane) are considered. Particular emphases are given on the dimensionless size parameter of the cylinder, the incidence angle of the illuminating field, and the dimensionless distance parameter from the flat surface. The results show that the net effect of the planar wall increases or decreases the amplitudes of the PAFs (thus, the photophoretic force and torque), depending on the particle-wall distance, incidence angle, particle size, and the polarization of the incident field. The results of this analysis are useful in applications related to electromagnetic/optical scattering, particle manipulations, optically bound matter, and photophoresis.

Contribution of Particle–Wall Distance and Rotational Motion of a Single Confined Elliptical Particle to the Effective Viscosity in Pressure-Driven Plane Poiseuille Flows

Rheological properties of the suspension flow, especially effective viscosity, partly depend on spatial arrangement and motion of suspended particles. It is important to consider effective viscosity from the microscopic point of view. For elliptical particles, the equilibrium position of inertial migration in confined state is unclear, and there are few studies on the relationship between dynamics of suspended particles and induced local effective viscosity distribution. Contribution of a single circular or elliptical particle flowing between parallel plates to the effective viscosity was studied, focusing on the particle–wall distance and particle rotational motion using the two-dimensional regularized lattice Boltzmann method and virtual flux method. As a result, confinement effects of the elliptical particle on the equilibrium position of inertial migration were summarized using three definitions of confinement. In addition, the effects of particle shape (aspect ratio and confinement) on the effective viscosity were assessed focusing on the particle–wall distance. The contribution of particle shape to the effective viscosity was found to be enhanced when the particle flowed near the wall. Focusing on the spatial and temporal variation of relative viscosity evaluated from wall shear stress, it was found that the spatial variation of the local relative viscosity was larger than temporal variation regardless of the aspect ratio and particle–wall distance.

Numerical Study of Paramagnetic Elliptical Microparticles in Curved Channels and Uniform Magnetic Fields.

We numerically investigated the dynamics of a paramagnetic elliptical particle immersed in a low Reynolds number Poiseuille flow in a curved channel and under a uniform magnetic field by direct numerical simulation. A finite element method, based on an arbitrary Lagrangian-Eulerian approach, analyzed how the channel geometry, the strength and direction of the magnetic field, and the particle shape affected the rotation and radial migration of the particle. The net radial migration of the particle was analyzed after executing a rotation and at the exit of the curved channel with and without a magnetic field. In the absence of a magnetic field, the rotation is symmetric, but the particle-wall distance remains the same. When a magnetic field is applied, the rotation of symmetry is broken, and the particle-wall distance increases as the magnetic field strength increases. The causation of the radial migration is due to the magnetic angular velocity caused by the magnetic torque that constantly changes directions during particle transportation. This research provides a method of magnetically manipulating non-spherical particles on lab-on-a-chip devices for industrial and biological applications.

Acoustic radiation force on a cylindrical particle near a planar rigid boundary

The aim of this investigation is to provide improved mathematical series expansions of the longitudinal and transverse acoustic radiation forces for a rigid cylindrical particle in 2D of arbitrary cross-section located near a planar rigid wall. Incident plane progressive waves with variable angle of incidence are considered in a non-viscous fluid. The multiple scattering effects occurring between the particle and the rigid boundary are described using the partial-wave decomposition in cylindrical coordinates, the method of images and the translational addition theorem. Initially, an effective acoustic field incident on the particle is defined, which includes the primary incident field, the reflected waves from the flat wall and the scattered field from the image object. Subsequently, the incident effective field along with the scattered field from the object are utilized to obtain closed-form mathematical expressions for the longitudinal and transverse radiation force functions, based on a scattering approach in the far-field. The radiation force vector components are formulated in partial-wave series in cylindrical coordinates, which involve the incidence angle, the expansion coefficients of the scatterer and its image, and the distance from the center of mass of the particle to the boundary. Numerical examples for a rigid circular cylinder are considered. Computations for the longitudinal and transverse non-dimensional radiation force functions are performed. Emphasis is given on varying the size of the particle, the incidence angle of the source field and the particle-wall distance. Depending on the particle-wall distance and incidence angle, zero-longitudinal and transverse force components arise, thus, the particle becomes unaffected by the linear momentum transfer. Moreover, pushing or pulling forces between the particle and wall are predicted depending on the particle-wall distance, the incidence angle and size parameter. The results may find possible applications in the development of acousto-fluidic devices, acoustic levitation of particles nearby a boundary, cloaking/invisibility, and underwater acoustics to name a few areas, where most investigations resort initially to numerical simulations to guide the experimental design processes.

Extrinsic and intrinsic acoustical cross-sections for a viscous fluid particle near a planar rigid boundary: circular cylinder example

The objective of this investigation is to derive closed-form partial-wave series expansions for the extrinsic and intrinsic acoustical scattering, extinction and absorption cross-sections of a fluid viscous cylindrical particle of arbitrary geometrical cross-section, located nearby a flat rigid boundary. Plane progressive waves with arbitrary incidence angle are considered in a non-viscous fluid. The multiple scattering between the particle and the boundary is described using the multipole expansion in cylindrical coordinates, the method of images and the translational addition theorem. The extrinsic cross-sections are determined by integrating the associated power flow densities over a virtual surface of large radius enclosing the object and its image, stemming from far-field expressions of the incident and scattered pressure fields. The expressions for the intrinsic cross-sections are established after defining an effective acoustic field incident on the particle, which includes the primary incident field, the reflected waves from the boundary and the scattered field from the image object. Subsequently, the incident effective field is used with the scattered field from the object to derive closed-form analytical expressions for the intrinsic cross-sections, based on a far-field scattering approach, which does not introduce any approximation in the evaluation of the expressions. The obtained expressions involve the angle of incidence, the expansion coefficients of the scatterer and its image, and the distance from the center of mass of the particle to the boundary. Numerical examples for a viscous fluid circular cylindrical cross-section are considered, and computations illustrate the analysis with particular emphasis on varying the size of the particle, the angle of incidence and the particle-wall distance. The results find potential applications in the quantitative predictions of the acoustical cross-sections from fluid/soft/compressible objects nearby a boundary, such as contrast agents in biomedicine, oceanography, sonochemistry, marine science, and (borehole) geophysical applications to name a few examples.

Modelling and Simulation of Drag Forces of Non-spherical Particles Moving Towards a Surface in Polymer Melt Flows

This work deals with the drag forces acting on non-spherical particles translating normal to a surface in a polymer melt in which the particle–surface distance is small compared with particle dimension in the flow direction. Hence, drag forces will be modified as a function of distance. A finite element model was used in order to calculate the drag forces for the motion of particles. Several non-spherical particles geometries were simulated towards a plane surface wall.The fitting of the numerical results with empirical expressions presented two very well defined tendencies. Up to a given value of particle-wall distance the influence of the wall was strong, hence it was necessary to apply a correction to the analytical calculations. In addition, the relevance of the shape of the channel between the particle and the sink was demonstrated. The computational results provided a clear benefit to validate empirical approaches using analytical approximations.

Numerical simulations of the competition between the effects of inertia and viscoelasticity on particle migration in Poiseuille flow

In this work, we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow at finite Reynolds numbers, in order to clarify the simultaneous effects of viscoelasticity and inertia on the lateral particle motion.The governing equations are solved through the finite element method by adopting an Arbitrary Lagrangian–Eulerian (ALE) formulation to handle the particle motion. The high accuracy provided by such a method even for very small particle–wall distances, combined with proper stabilization techniques for viscoelastic fluids, allows obtaining convergent solutions at relatively large flow rates, as compared to previous works. As a result, the detailed non-linear dynamics of the migration phenomenon in a significant range of Reynolds and Deborah numbers is presented.The simulations show that, in agreement with the previous literature, a mastercurve relating the migration velocity of the particle to its ‘vertical’ position completely describes the phenomenon. Remarkably, we found that, for comparable values of the Deborah and Reynolds numbers, inertial effects are negligible: migration is in practice driven by fluid viscoelasticity only. At moderate Reynolds numbers (20<Re<200) and by lowering De, the transition from viscoelasticity-driven to inertia-driven regimes occurs through two intermediate regimes characterized by multiple stable solutions, i.e. attractors of particle trajectories at different vertical positions across the gap. At low but non-zero Reynolds numbers, only two stable solutions are found for any non-zero Deborah number in the investigated range. In particular, the wall is always an attractor for the migrating particle.

Effect of direct current dielectrophoresis on the trajectory of a non‐conducting colloidal sphere in a bent pore

Dielectrophoresis has shown a wide range of applications in microfluidic devices. Force approximations utilizing the point-dipole method in dielectrophoresis have provided convenient predictions for particle motion by neglecting interactions between the particle and its surrounding electric and flow fields. The validity of this approach, however, is unclear when the particle size is comparable to the characteristic length of the channel and when the particle is in close proximity to the channel wall. To address this issue, we apply an accurate numerical approach based on the boundary-element method (BEM) to solve the coupled electric field, flow, and particle motion. This method can handle much closer particle-wall distances than the other numerical approaches such as the finite-element method. Using the BEM and integrating the Maxwell stress tensor, we simulate an electrokinetic, spherical particle moving within a bent cylindrical pore to investigate how the dielectrophoretic force affects the particle's trajectory. In the simulation, both the particle and the channel wall are non-conducting, and the electric double layers adjacent to the solid surfaces are assumed to be thin with respect to the particle radius and particle-wall gap. The results show that as the particle comes close to the wall, its finite size has an increasingly important effect on its own transient motion and the point-dipole approximation may lead to significant error.

Motion of a sphero-cylindrical particle in a viscous fluid in confined geometry

The motion of a millimeter size spherocylinder particle settling in a very viscous oil in a closed container is measured by laser interferometry, with the goal to model the motion of a particle of this shape in a fluid at microscales. The container is a cylinder with vertical axis and closed at both ends by horizontal plates. The displacement of the particle along the container axis is recorded with a resolution of the order of 100 nm, that is much smaller than the particle–wall separation when in the lubrication regime. The particle friction coefficient, measured as a function of the particle–wall distance, is then used to test the theoretical predictions of an accurate hydrodynamic analysis. The Stokes flow problem is solved by using the hydromultipole method, that is in general appropriate for spheres but is extended here to a non-spherical particle by using a compound of overlapping spheres. The lateral wall effect is negligible but the two parallel horizontal end plane walls are accurately taken into account. The result of the theoretical model is in good quantitative agreement with experiment for the whole settling motion of the spherocylinder, that is for any position between the walls.

On discretization in time in simulations of particulate flows

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows.The scheme is intended to work robustly in the lubrication regime when the distance between two particles immersed in the fluid or between a particle and the walltends to zero. The idea consists in introducing a small threshold for the particle-wall distance below which the real trajectory of the particleis replaced by an approximated one where the distance is kept equal to the threshold value. The error of this approximation is estimated both theoretically and by numerical experiments.Our time marching scheme can be easily incorporated into a full simulation method where the velocity of the fluid is obtained by a numerical solution to Stokes or Navier-Stokes equations.We also provide a derivation of the asymptotic expansion for the lubrication force (used in our numerical experiments) acting on a disk immersed in a Newtonian fluid and approaching the wall.The method of this derivation is new and can be easily adapted to other cases.

The approach of a sphere to a wall at finite Reynolds number

The approach to a wall of a non-Brownian rigid spherical particle, settling in a viscous fluid with a Reynolds number of the order of unity, is studied experimentally. Far from the wall, the fluid motion around the particle is driven by inertia and viscosity forces. The particle Stokes number is also of the order of unity, so that the particle motion far from the wall is driven by inertia. In the close vicinity of the wall, however, the particle–wall hydrodynamic interaction decelerates the particle significantly. An interferometric device is used to measure the vertical displacement of a millimetric size spherical bead at distances from the wall smaller than 0.1 sphere radius, with a spatial resolution of 100 nm. For the range of impact Stokes number (St*, based on the limit velocity of the sphere in an unbounded fluid) explored here (up toSt* ≅ 5), the measurements reveal that a small region of negligible particle inertia still exists just prior to contact of the sphere with the wall. In this lubrication-like region, the particle velocity decreases linearly with decreasing particle–wall distance and vanishes at contact, ruling out the possibility of a rebound. The vertical extent of this region decreases with increasing Stokes number and is e.g. only 10 μm large at impact Stokes numberSt* ≅ 5.

Tangential electroviscous drag on a sphere surrounded by a thin double layer near a wall for arbitrary particle–wall separations

When a charged particle moves along a charged wall in a polar fluid, it experiences an electroviscous lift force normal to the surface and an electroviscous drag, superimposed on the viscous drag, parallel to the surface. Here a theoretical analysis is presented to determine the electroviscous drag on a charged spherical particle surrounded by a thin electrical double layer near a charged plane wall, when the particle translates parallel to the wall without rotation, in a symmetric electrolyte solution at rest. The electroviscous (electro-hydrodynamic) forces, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, for electroviscous ion concentration (perturbed ion clouds), electroviscous potential (perturbed electric potential) and electroviscous or electro-hydrodynamic flow field (perturbed flow field). The problem was previously solved for small gap widths and low Peclet numbers in the inner region around the gap between the sphere and the wall, using lubrication theory. Here the restriction on the particle–wall distances is removed, and an analytical and numerical solution is obtained valid for the whole domain of interest. For large sphere–wall separations the solution approaches that for the electroviscous drag on an isolated sphere in an unbounded fluid. For small particle–wall distances it differs from that obtained by the use of lubrication theory, showing that lubrication theory is inadequate for electroviscous problems. The analytical results are in complete agreement with the full numerical calculations. For small particle–wall distances a model is given which provides both physical insight and an easy way to calculate the force with high precision.

Viscoelasticity-induced migration of a rigid sphere in confined shear flow

Suspensions of solid particles in liquids are often made to flow in devices with characteristic dimensions comparable to that of the suspended particles, the so-called confined situation, as in the case of several microfluidic applications. Combination of confinement with viscoelasticity of the suspending liquid can lead to peculiar effects. In this paper we present the first 3D simulation of the dynamics of a particle suspended in a viscoelastic liquid under imposed confined shear flow. The full system of equations is solved through the finite element method. A DEVSS/SUPG formulation with a log-representation of the conformation tensor is implemented, assuring stable and convergent results up to high flow rates. Particle motion is handled through an ALE formulation. To optimize the computational effort and to reduce the remeshing and projection steps required when the mesh becomes too distorted, a rigid motion of the grid in the flow direction is performed, so that, in fact, the particle moves along the cross-streamline direction only. Confinement and viscoelasticity are found to induce particle migration, i.e., transverse motion across the main flow direction, towards the closest wall. Under continuous shearing, three different dynamical regimes are recognized, related to the particle-wall distance. A simple heuristic argument is given to link the cross-flow migration to normal stresses in the suspending liquid. The analysis is then extended to a time-dependent shear flow imposed by periodically inverting the direction of wall motion. A slower migration is found for higher forcing frequency. A peculiar effect arises if the inversion period is chosen close to the fluid relaxation time: the migration velocity oscillates around zero, and the overall migration is suppressed. Such novel prediction of a dynamic instability scenario, with the particle escaping the center plane of the channel, and many features of the computed results, are in nice agreement with recent experiments reported in the literature [14].

Numerical simulations of particle migration in a viscoelastic fluid subjected to shear flow

Particle migration is a relevant transport mechanism whenever suspensions flow in channels with gap size comparable to particle dimensions (e.g. microfluidic devices). Several theoretical as well as experimental studies have been performed on this topic, showing that the occurring of this phenomenon and the migration direction are related to particle size, flow rate, and the nature of the suspending liquid. In this work we perform a systematic analysis on the migration of a single particle in a sheared viscoelastic fluid through 2D finite element simulations in a Couette planar geometry. To focus on the effects of viscoelasticity alone, inertia is neglected. The suspending medium is modeled as a Giesekus fluid. An ALE particle mover is combined with a DEVSS/SUPG formulation with a log-representation of the conformation tensor giving stable and convergent results up to high flow rates. To optimize the computational effort and reduce the remeshing and projection steps, needed as soon as the mesh becomes too distorted, a ‘backprojection’ of the flow fields is performed, through which the particle in fact moves along the cross-streamline direction only, and the mesh distortion is hence drastically reduced. Our results, in agreement with recent experimental data, show a migration towards the closest walls, regardless of the fluid and geometrical parameters. The phenomenon is enhanced by the fluid elasticity, the shear thinning and strong confinements. The migration velocity trends show the existence of a master curve governing the particle dynamics in the whole channel. Three different regimes experienced by the particle are recognized, related to the particle-wall distance. The existence of a unique migration behavior and its qualitative aspects do not change by varying the fluid parameters or the particle size.

History force on an asymmetrically rotating body in Poiseuille flow inducing particle migration across a slit pore

Experimental evidence shows that suspended particles preferentially migrate away from confining boundaries due to the effect of a shear flow. In this paper, we consider an asymmetric particle in Poiseuille flow and determine an inertial lift force which can contribute to the particle migration. Under the influence of Poiseuille flow in a slit pore, an arbitrary particle undergoes periodic rotation which is described by Jeffery’s orbit [G. Jeffery, Proc. R. Soc. London, Ser. A 102, 161 (1922)]. In the absence of rotational symmetry, a rotating particle produces an unsteady scattered field. The fluid inertia due to the unsteadiness causes an inertial force on the rotating body if the Reynolds number Re and the temporal variation in viscous force on the particle are nonzero. The resulting effect of this force on the particle migration can be significant especially for microfluidic systems, where gravitational contribution is negligible. In this paper, we consider two systems where the Reynolds number is assumed to be small but finite. In the first problem, we analyze the inertial force on a body asymmetrically rotating around its fixed center. In the second case, we focus on a freely suspended heavy particle which is considerably denser than the solvent so that the product of Re and the particle-solvent density ratio is greater than unity. For both systems, the Reynolds number and the temporal variation in viscous force are significant enough to produce a considerable inertial force on the particle. Our results indicate that the mean of this inertial component perpendicular to the boundaries is nonzero and acts in the direction away from the wall. The magnitude of this force is relatively larger near the wall and gradually decays as the particle-wall distance increases. Hence, we conclude that the discussed effect influences the preferential particle migration in conjunction with other factors.

Experimental Verification of an Exact Evanescent Light Scattering Model for TIRM

Total internal reflection microscopy (TIRM) is a method for the precise measurement of interaction potentials between a spherical colloidal particle and a wall. The method is based on single-particle evanescent wave light scattering. The well-established model used to interpret TIRM data is based on an exponential relation between scattering intensity and particle wall distance. However, applying this model for a certain range of experimental parameters leads to significant distortions of the measured potentials. Using a TIRM setup based on a two-wavelength illumination technique, we were able to directly measure the intensity distance relation revealing deviations from an exponential decay. The intensity-distance relations could be compared to scattering simulations taking into account exact experimental parameters and multiple reflections between a particle and the wall. Converging simulation results were independently obtained by the T-matrix method and the discrete sources method (DSM) and show excellent agreement with experiments. Using the new scattering model for data evaluation, we could reconstruct the correct potential shape for distorted interaction potentials as we demonstrate. The comparison of simulations to experiment intrinsically yields a new method to determine absolute particle-wall distances, a highly desired quantity in TIRM experiments.