Particles In Poiseuille Flow Research Articles

Motion of a solid particle in an ore-lifting riser with transverse vibrations

Deep-sea mining lifting risers experience vibrations induced by the action of ocean waves and currents, and these vibrations have an impact on the lifting efficiency of ores transported inside the risers. Here, to investigate the effect of riser vibration on ore transport, the motion of a single solid particle in a riser oscillating in the lateral direction is simulated taking account of collisions between the particle and the riser using the governing equation for motion of a spherical particle in Poiseuille flow and the Hertz–Mindlin soft sphere collision model. Validations are conducted based on comparisons between numerical and experimental results. Then, the motion of the particle in the vibrating riser is explored, considering the effects of the initial position of release of the particle, the frequency and amplitude of the riser vibrations, and collisions between the particle and the riser. It is found that the initial position of release affects only the initial motion of the particle, but not its overall motion. With increasing vibrational frequency and amplitude of the riser, the relative lateral velocity of the particle shows an increasing trend, while its vertical velocity and lifting distance are clearly decreased. The frequency with which the vertical particle velocity varies is twice as the vibrational frequency of the riser. Moreover, collisions have significant effects on the particle motion, especially on the velocities of the particle, the phase difference between the displacements of the particle and the vibrating riser, and the particle trajectory. Finally, the behavioral regime map of the particle under different vibrational frequencies and amplitudes of the riser is established preliminarily.

Migration and heat transfer modeling of a neutrally buoyant melting particle in Poiseuille flow

A computational model is developed to simulate the hydrodynamic and heat transfer behavior of a melting cylindrical solid particle in plane Poiseuille flow between horizontal parallel plates. The two-dimensional transient conservation equations for mass, momentum, and energy are solved using a finite-volume scheme implemented on a deforming mesh, accounting for the rotation and non-uniform melting of the particle. An arbitrary Lagrangian–Eulerian (ALE) method is employed to directly track the moving and deforming solid–liquid interface during the particle migration and phase change. The developed model was validated by comparison with the previously reported numerical results for migration of a non-melting neutrally buoyant cylindrical particle in plane Poiseuille flow with heat transfer. The effects of flow Reynolds (Re), Grashof (Gr), and Stefan (Ste) numbers, as well as the initial position of the melting particle across the channel on the particle trajectory, melting rate, and average Nusselt (Nu) number were investigated. It was found that the melting rate increased by increasing Gr and Ste and decreased by increasing Re. The Nu did not change more than 20% with increasing Re number from 100 to 1000, but increased significantly by increasing Gr. It was also observed that by increasing Re, the particle migrates toward the channel center because of the stronger Magnus effect. Increasing Gr, on the other hand, pushes the particle to the bottom wall due to the stronger downward flow adjacent to the particle induced by buoyancy-driven convection (natural convection).

Inertial migration of rigid red blood cell particles in Poiseuille flow

Inertial migration of single and multiple red blood cell (RBC) particles in a tube Poiseuille flow is studied using the lattice Boltzmann method coupled with the Galilean invariant momentum exchange method. Different blockage ratios, Reynolds numbers, and solid volume fractions are considered. In the single particle case, the RBC particle migrating in tumbling and rolling modes is called the tumbling particle and rolling particle, respectively. Simulation results show that the tumbling particle has a higher equilibrium position and longer rotation period than the rolling particle. For both the tumbling and rolling particles, when the blockage ratio increases, the equilibrium position moves closer to the tube centerline, and the rotation period becomes longer. The higher Reynolds number strongly affects the angular velocity of the RBC particle, leading the RBC particle to rotate faster; however, the equilibrium position is insensitive to the Reynolds number based on the limited observation. In the multiparticle case, the second and third inner particle annuluses unexpectedly form inside the Segré–Silberberg annulus as the solid volume fraction increases. Furthermore, smaller particles form the perfect Segré–Silberberg annulus at a lower solid volume fraction than larger particles. The third inner annulus of smaller particles is located further from the tube centerline than that of larger particles. This work is beneficial for understanding the motion of RBC particles in Poiseuille flow. It can positively contribute to the design of microfluidic devices for focusing, separating, and transporting red blood cells.

Swirling of vesicles: Shapes and dynamics in Poiseuille flow as a model of RBC microcirculation

Soft particles display a rich zoology of dynamics with bifurcation dynamics depending on the interfacial mechanical response. One intriguing issue is the origin of motions along helices, a dynamic only observed with active particles. Numerical simulations of a vesicle, a passive particle in Poiseuille flow, show that this dynamic called swirling is in fact more ubiquitous and emerges spontaneously. Swirling is the ultimate state of the symmetry loss sequence parachute \ensuremath{\rightarrow} croissant \ensuremath{\rightarrow} slipper \ensuremath{\rightarrow} swirling, where the last symmetry lost is the mirror plane of the slipper.

Steady State of Motion of Two Particles in Poiseuille Flow of Power-Law Fluid.

The steady state of motion of two particles in Poiseuille flow of power-law fluid is numerically studied using the lattice Boltzmann method in the range of Reynolds number 20 ≤ Re ≤ 60, diameter ratio of two particles 0.125 ≤ β ≤ 2.4, and power-law index of the fluid 0.4 ≤ n ≤ 1.2. Some results are validated by comparing with other available results. The effects of Re, β, and n on the steady state of motion of two particles are discussed. The results show that, for two particles of the same diameter, the particle spacing l in the steady state is independent of n. In shear-thinning fluid, l increases rapidly at first and then slowly, finally approaching a constant for different Re. In shear-thickening fluid, although l tends to be stable in the end, the values of l after stabilization are different. For two particles of different sizes, l does not always reach a stable state, and whether it reaches a stable state depends on n. When the small particle is downstream, l increases rapidly at first and then slowly in shear-thickening fluid, but increases rapidly at first and then decreases slowly, finally approaching a constant in a shear-thinning fluid. In shear-thinning fluid, the larger n is, the smaller l is. In shear-thickening fluid, β has no effect on l in steady-state. When the large particle is downstream, l increases rapidly at first and then slowly in shear-thinning fluid but increases rapidly at first and then decreases in a shear-thickening fluid. The effect of n on l in the steady state is obvious. In shear-thinning fluid, l increases rapidly at first and then slowly, the larger Re is, the smaller l is. In shear- thickening fluid, l will reach a stable state.

Migration and Heat Transfer Modeling of a Melting Particle in Poiseuille Flow

Migration and Heat Transfer Modeling of a Melting Particle in Poiseuille Flow

Research on the Inertial Migration Characteristics of Bi-Disperse Particles in Channel Flow

The inertial focusing effect of particles in microchannels shows application potential in engineering practice. In order to study the mechanism of inertial migration of particles with different scales, the motion and distribution of two particles in Poiseuille flow are studied by the lattice Boltzmann method. The effects of particle size ratio, Reynolds number, and blocking rate on particle inertial migration are analyzed. The results show that, at a high blocking rate, after the same scale particles are released at the same height of the channel, the spacing between the two particles increases monotonically, and the change in the initial spacing has little effect on the final spacing of inertial migration. For two different size particles, when the smaller particle is downstream, the particle spacing will always increase and cannot remain stable. When the larger particle is downstream, the particle spacing increases firstly and then decreases, and finally tends to be stable.

Tracking particles in Poiseuille flow for several pipe diameters in three dimensions

A setup is devised to track suspended particles in a pipe in three-dimensional space using the ShadowgraphyPTV technique. This system consists of a single camera and a mirror, and is used to track particles for over 20 pipe diameters at three downstream locations. Pipe to particle diameter ratios (D/d) of 18, 9, and 6 are investigated. The bulk Reynolds number is varied between Reb = 300-1250. As expected, particles are observed to migrate radially to a location corresponding to the Segre-Silberberg annulus. In addition, ´we observe particles also moving in the azimuthal direction (clockwise or counter-clockwise), with some particles moving as much as 180◦ during their passage through the field of view. This helical motion persists throughout the pipe (600D long) and the azimuthal velocity increases with the Reynolds number (Reb). The effect of particle size and the Reynolds number on this previously undocumented, three-dimensional motion is studied.

Migration and Alignment of Three Interacting Particles in Poiseuille Flow of Giesekus Fluids

Effect of rheological property on the migration and alignment of three interacting particles in Poiseuille flow of Giesekus fluids is studied with the direct-forcing fictitious domain method for the Weissenberg number (Wi) ranging from 0.1 to 1.5, the mobility parameter ranging from 0.1 to 0.7, the ratio of particle diameter to channel height ranging from 0.2 to 0.4, the ratio of the solvent viscosity to the total viscosity being 0.3 and the initial distance (y0) of particles from the centerline ranging from 0 to 0.2. The results showed that the effect of y0 on the migration and alignment of particles is significant. The variation of off-centerline (y0 ≠ 0) particle spacing is completely different from that of on-centerline (y0 = 0) particle spacing. As the initial vertical distance y0 increased, the various types of particle spacing are more diversified. For the off-centerline particle, the change of particle spacing is mainly concentrated in the process of cross-flow migration. Additionally, the polymer extension is proportional to both the Weissenberg number and confinement ratio. The bigger the Wi and confinement ratio is, the bigger the increment of spacing is. The memory of shear-thinning is responsible for the reduction of d1. Furthermore, the particles migrate abnormally due to the interparticle interaction.

Numerical simulations of a stick-slip spherical particle in Poiseuille flow

The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions sufficiently far from or near the centerline, respectively. The basin of attraction of the tube axis grows with particle confinement and slip coefficient although the dynamics is qualitatively unaffected.

Inertial migration of circular particles in Poiseuille flow of a power-law fluid

The immersed boundary-lattice Boltzmann method is used to study the inertial migration of particles in Poiseuille flow of a power-law fluid. The effects of Reynolds number, power-law index, and blockage ratio on the formation of particle trains are explored. The results show that single particle with different initial positions reach the same equilibrium position for the same power-law index. The stable equilibrium position moves closer to the centerline under the higher power-law index and blockage ratio. One-line of eight particles distributed initially at a vertical position will migrate laterally to the vicinity of the wall and form single-line particle trains. The particle spacing is unstable and increases when particles migrate to the equilibrium position. The inertial focusing length is an important factor for analyzing the formation of particle trains, which will be longer with increasing the power-law index. The mean particle spacing will be reduced with increasing Re and blockage ratio. Two-lines of 12 particles distributed initially and abreast along both sides of the centerline will migrate to the vicinity of the wall and form staggered particle trains. Due to the multiparticles interaction, the final particle equilibrium position will deviate from the single particle equilibrium position. The axial spacing between two neighboring particles is stable or fluctuates within a certain range. The particle spacing decreases with increasing the power-law index and blockage ratio, and with decreasing Re. The shear-thinning fluid is beneficial to the formation of single-line particle trains and staggered particle trains.

A novel model for the lift force acting on a prolate spheroidal particle in an arbitrary non-uniform flow. Part I. Lift force due to the streamwise flow shear

The paper proposes a generic method to extend lift force models that were originally devised for single linear shear flow, to arbitrary flow conditions. The method computes the lift force due to the dominant streamwise flow shear in the Stokes flow regime by implementing a series of coordinate transformations, facilitating the computation of the lift force from dominant streamwise flow shear. The derived numerical algorithm is applied to the computation of a dedicated shear lift force model for prolate spheroidal particles (or axisymmetric ellipsoidal particles) and a novel generalised Saffman-type lift force model for spherical particles in a general shear flow. In order to verify the proposed shear lift force for prolate spheroidal particles, numerical simulations of a particle moving in Poiseuille flow at four different initial positions and two aspect ratios are perfomed. The new generalised Saffman-type lift model is compared with an established generalised Saffman-type lift model by simulating the axial migration of a spherical particle in Poiseuille flow. The computational results confirm the correctness of the proposed shear lift force models.

Swinging motion of active deformable particles in Poiseuille flow.

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Lateral migration and nonuniform rotation of suspended ellipse in Poiseuille flow

Suspensions of an elliptical particle in Poiseuille flow are investigated by using the multiple-relaxation-time lattice Boltzmann method coupled with the Galilean-invariant momentum exchange method. The elliptical particle shows lateral migration and final equilibrium, which are similar to the classical Segré–Silberberg effect. Because the elliptical shape interacts with the parabolic velocity distribution of the Poiseuille flow, the particulate behaviors remarkably contain regular wave accompanied by nonuniform rotation. When the blockage ratio grows up, the equilibrium position of the particle moves towards the channel centerline and the rotation period becomes long. With the increase of the aspect ratio, the rotation period becomes short; the equilibrium position shows a shape of saddle and reaches its bottom at nearby aspect ratio 0.5. Surprisingly, the numerical results show that the equilibrium position is insensitive to Reynolds number (Re) of Poiseuille flows in the range 3≤Re≤300. This work can make active promotions to the researches of blood circulation of birds, whose red blood cell is oval or elliptical in shape.

High-frequency effective viscosity of a dilute suspension of particles in Poiseuille flow between parallel walls

It is shown that the formal expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in Poiseuille flow contains a novel quadrupole term, besides the expected stresslet. This term becomes important for a very confined geometry. For a high-frequency flow field (in the sense used in Feuillebois et al. (J. Fluid Mech., vol. 764, 2015, pp. 133–147), the suspension rheology is Newtonian at first order in volume fraction. The effective viscosity is calculated for suspensions of $N$-bead rods and of prolate spheroids with the same length, volume and aspect ratio (up to 6), entrained by the Poiseuille flow between two infinite parallel flat hard walls. The numerical computations, based on solving the Stokes equations, indicate that the quadrupole term gives a significant positive contribution to the intrinsic viscosity $[{\it\mu}]$ if the distance between the walls is less than ten times the particle width, or less. It is found that the intrinsic viscosity in bounded Poiseuille flow is generally smaller than the corresponding value in unbounded flow, except for extremely narrow gaps when it becomes larger because of lubrication effects. The intrinsic viscosity is at a minimum for a gap between walls of the order of 1.5–2 particle width. For spheroids, the intrinsic viscosity is generally smaller than for chains of beads with the same aspect ratio, but when normalized by its value in the bulk, the results are qualitatively the same. Therefore, a rigid chain of beads can serve as a simple model of an orthotropic particle with a more complicated shape. The important conclusion is that the intrinsic viscosity in shear flow is larger than in the Poiseuille flow between two walls, and the difference is significant even for relatively wide channels, e.g. three times wider than the particle length. For such confined geometries, the hydrodynamic interactions with the walls are significant and should be taken into account.

Using Shear and Direct Current Electric Fields to Manipulate and Self-Assemble Dielectric Particles on Microchannel Walls

Manipulating suspended neutrally buoyant colloidal particles of radii a = O (0.1–1 μm) near solid surfaces, or walls, is a key technology in various microfluidics devices. These particles, suspended in an aqueous solution at rest near a solid surface, or wall, are subject to wall-normal “lift” forces described by the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory of colloid science. The particles experience additional lift forces, however, when suspended in a flowing solution. A fundamental understanding of such lift forces could therefore lead to new methods for the transport and self-assembly of particles near and on solid surfaces. Various studies have reported repulsive electroviscous and hydrodynamic lift forces on colloidal particles in Poiseuille flow (with a constant shear rate γ· near the wall) driven by a pressure gradient. A few studies have also observed repulsive dielectrophoretic-like lift forces in electroosmotic (EO) flows driven by electric fields. Recently, evanescent-wave particle tracking has been used to quantify near-wall lift forces on a = 125–245 nm polystyrene (PS) particles suspended in a monovalent electrolyte solution in EO flow, Poiseuille flow, and combined Poiseuille and EO flow through ∼30 μm deep fused-silica channels. In Poiseuille flow, the repulsive lift force appears to be proportional to γ·, a scaling consistent with hydrodynamic, versus electroviscous, lift. In combined Poiseuille and EO flow, the lift forces can be repulsive or attractive, depending upon whether the EO flow is in the same or opposite direction as the Poiseuille flow, respectively. The magnitude of the force appears to be proportional to the electric field magnitude. Moreover, the force in combined flow exceeds the sum of the forces observed in EO flow for the same electric field and in Poiseuille flow for the same γ·. Initial results also imply that this force, when repulsive, scales as γ·1/2. These results suggest that the lift force in combined flow is fundamentally different from electroviscous, hydrodynamic, or dielectrophoretic-like lift. Moreover, for the case when the EO flow opposes the Poiseuille flow, the particles self-assemble into dense stable periodic streamwise bands with an average width of ∼6 μm and a spacing of 2–4 times the band width when the electric field magnitude exceeds a threshold value. These results are described and reviewed here.

Nonlinear dynamics of spherical particles in Poiseuille flow under creeping-flow condition

We study the nonlinear dynamics of spherical colloids under the influence of a pressure driven flow at vanishing Reynolds number. The colloids are confined between two parallel planar walls with a distance comparable to the particle diameter and they interact hydrodynamically via the solvent. We show that the bounded Poiseuille flow gives rise to new classes of trajectories resulting in cross-streamline migration. Two particles moving on these new trajectories exhibit either bound or unbound states. In the first case they oscillate on closed trajectories in the center-of-mass frame. In the second case, they exhibit cross-swapping trajectories in addition to swapping trajectories which were already observed in unbounded or bounded linear shear flow. The different classes of trajectories occur depending on the initial positions of the two particles and their size. We present state diagrams in the lateral positions, where we categorize the trajectories and color code the oscillation frequencies of the bound states. Finally we discuss how the results on the two-particle system help to understand the stability of particle trains composed of several particles.

Numerical investigation of the character of the lift on a cylindrical particle in Poiseuille flow of a plane channel

Numerical investigation of the character of the lift on a cylindrical particle in Poiseuille flow of a plane channel

Nanoparticle Brownian motion and hydrodynamic interactions in the presence of flow fields

We consider the Brownian motion of a nanoparticle in an incompressible Newtonian fluid medium (quiescent or fully developed Poiseuille flow) with the fluctuating hydrodynamics approach. The formalism considers situations where both the Brownian motion and the hydrodynamic interactions are important. The flow results have been modified to account for compressibility effects. Different nanoparticle sizes and nearly neutrally buoyant particle densities are also considered. Tracked particles are initially located at various distances from the bounding wall to delineate wall effects. The results for thermal equilibrium are validated by comparing the predictions for the temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical and experimental results where available. The equipartition theorem for a Brownian particle in Poiseuille flow is verified for a range of low Reynolds numbers. Numerical predictions of wall interactions with the particle in terms of particle diffusivities are consistent with results, where available.

Inertial migration and multiple equilibrium positions of a neutrally buoyant spherical particle in Poiseuille flow

The radial migration of a single neutrally buoyant particle in Poiseuille flow is numerically investigated by direct numerical simulations. The simulation results show that the Segre and Silberberg equilibrium position moves towards the wall as the Reynolds number increases and as the particle size decreases. At high Reynolds numbers, inner equilibrium positions are found at positions closer to the centerline and move towards the centerline as the Reynolds number increases. At higher Reynolds numbers, the Segre and Silberberg equilibrium position disappears and only the inner equilibrium position exists. We prove that the inner annuluses in the measurements of Matas, Morris & Guazzelli (J. Fluid Mech. 515, 171-195, 2004) are not transient radial positions, but are real equilibrium positions. The results on the inner equilibrium positions and unstable equilibrium positions are new and convince us of the existence of multiple equilibrium radial positions for neutrally buoyant particles.