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We investigate the wall shear stress variation induced by soft particles modeled as capsules migrating in a channel. Interestingly, the wall shear stress exhibits a roughly linear increase in both its global maximum value and variation magnitude with an increase in the normalized overall lateral position of the capsules when they stabilize as a linear train. Furthermore, when a single capsule stabilizes in the channel centerline, the streamlines show an M-like shape in the upper part and a W-like shape in the lower part of the channel. Meanwhile, we use the vertical velocity to explain the typical peak-valley-peak structure in the wall shear stress profile. For multiple capsules, the contours of the vertical velocity can also be employed to determine the locations where the peaks or valleys in the wall shear stress occur. These findings enhance our comprehension of the variation in wall shear stress caused by soft particles. [ABSTRACT FROM AUTHOR]

Pair of particle chain self-organization in a square channel flow of Giesekus viscoelastic fluid is studied by the direct forcing/fictitious domain method. The effects of particle diameter, initial particle distance, shear-thinning (n), Weissenberg number (Wi), and Reynolds number (Re) are explored to analyze the mechanism of particle chain self-organization in Giesekus viscoelastic fluid. The results show that the small particle at the equilibrium position moves faster than the larger one and then catches up with it to form a particle chain, in which the large and small particles are located at the front and the end of the chain, respectively. The particle pair with the same diameter cannot form the chain in Giesekus viscoelastic fluid. In addition, the larger the diameter ratio and the initial particle distance, the larger the absolute value of the particle velocity difference, the earlier the particle chain is formed. The particle chain will be formed early with increasing n, Re, and Wi. [ABSTRACT FROM AUTHOR]

The inertial migration of two-dimensional soft particles initially distributed uniformly in channel flow is numerically studied by employing an immersed-boundary lattice Boltzmann method coupled with a finite element method. To model a soft particle, a capsule with an elastic membrane separating the liquid inside from the outside is used. Validation tests show excellent agreement with previous numerical results of other researchers. Then, the effects of the number of capsules Np, the bending stiffness Eb, the initial position Y 0 ′ , and the Reynolds number Re on the dynamics of the capsules in channel flow are investigated in detail. Interestingly, we discover a new regime (labeled as regime E) in which a few capsules situated near the channel centerline travel much faster than the rest. Moreover, regime E is more prone to vanishing while the capsules are very soft. The normalized overall lateral position of the capsules σ increases almost linearly with Np when the capsules stabilize in a single-line particle train (designated as regime A). We also make an effort to explain the formation of the capsule deformation shape in regime A. The steady dynamics of a single capsule depend on whether the initial position is on the channel centerline. However, if the capsule is not released on the channel centerline, the steady capsule dynamics are independent of the initial position. But, it is not true for multiple capsule dynamics. These findings may help understand the inertial migration of capsules in channel flow. [ABSTRACT FROM AUTHOR]

An immersed boundary-lattice Boltzmann (IB-LB) method is employed to investigate the migration of a two-dimensional cylindrical micro-swimmer in a channel flow. The swimming Reynolds numbers (Re s), the flow Reynolds numbers (Re p), and the blockage ratios (κ) are respectively set being from 0.05 to 2.0, 40 to 160, and 0.11 to 0.5 in the simulations. A two-dimensional archetypal self-propelled model generating tangential surface waves is employed to mimic a micro-swimmer with different Re s swimming in the presence of a channel flow with different Re p and κ , finding four typical locomotion modes, namely, the horizontal mode, the attracted oscillatory mode, the oscillatory mode, and the chaotic mode. At Re p = 100 and κ = 0.25, the squirmer displays an oscillatory motion even though at a lower Re s (Re s = 0.05), indicating a different migration behavior from that of a passive particle; With increasing Re s , the horizontal or the attracted oscillatory mode develops to the oscillatory or the chaotic mode, showing a tendency of motion symmetrical concerning the centreline. On increasing Re p with Re s = 0.1 and κ = 0.25, the squirmer with a lower swimming intensity | β | ≤ 1 maintains the attracted oscillatory mode, whereas the pusher (propelled from the rear) with β = −3 and the puller with β = 3 (propelled from the front) develop to the attracted oscillatory mode from the oscillatory and horizontal modes, respectively. At Re p = 100 and Re s = 0.1, the squirmers with −3 ≤ β ≤ 0 and the puller with β = 5 respectively maintain the attracted oscillatory and the horizontal modes regardless of κ ; On increasing κ , the horizontal mode for the pullers with 1 ≤ β ≤ 3 and the attracted oscillatory mode for the pusher with β = −5 develop to the attracted oscillatory and oscillatory modes, respectively. The transport velocity of the squirmer is also studied with the variations of Re s , Re p , and κ , obtaining a maximum value for the neutral squirmer at Re s = 1.5, Re p = 100, and κ = 0.25. [Display omitted] • Two-dimensional micro-swimmer in a channel flow swims with horizontal or periodic orbit. • Find horizontal motion develop to periodic motion. • Find periodic motion regardless of the width of the channel. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It has been recognized that, generally, large particles enhance the turbulence intensity, while small particles attenuate the turbulence intensity. However, there has been no consensus on the quantitative criterion for particle-induced turbulence enhancement or attenuation. In the present study, interface-resolved direct numerical simulations of particle-laden turbulent flows in an upward vertical channel are performed with a direct forcing/fictitious domain method to establish a criterion for turbulence enhancement or attenuation. The effects of the particle Reynolds number ($Re_p$), the bulk Reynolds number ($Re_b$), the particle size, the density ratio and the particle volume fraction on the turbulence intensity are examined at $Re_b=5746$ (i.e. $Re_\tau =180.8$) and 12 000 ($Re_\tau =345.9$), the ratio of the particle radius to the half channel width $a/H=0.05\text {--}0.15$ , the density ratio 2–100, the particle volume fraction $0.3\,\%$ – $2.36\,\%$ and $Re_p. Our results indicate that at low $Re_p$ the turbulent intensity across the channel is all diminished; at intermediate $Re_p$ the turbulent intensity is enhanced in the channel centre region and attenuated in the near-wall region; and at sufficiently large $Re_p$ the turbulent intensity is enhanced across the channel. The critical $Re_p$ increases with increasing bulk Reynolds number, particle size and particle–fluid density ratio, while increasing with decreasing particle volume fraction, particularly for the channel centre region. Criteria for enhancement or attenuation are provided for the total turbulence intensity in the channel and the turbulence intensity at the channel centre, respectively, and both are shown to agree well with the experimental data in the literature. The reason for the dependence of the critical particle Reynolds number on the other parameters is discussed. [ABSTRACT FROM AUTHOR]

The inertial migration of the elliptical and rectangular particles in a channel flow of a power-law fluid is studied using the lattice Boltzmann method. The numerical method and code are validated by comparing the present results with the previous ones. Effects of power-law index (n) of the fluid, particle shape, particle aspect ratio (α), blockage ratio (k) and Reynolds number (Re) on the particle trajectory and equilibrium position are discussed. The results show that the elliptical and rectangular particles will finally oscillate in a lateral equilibrium position. The distance for the particle from its initial position to the stable equilibrium position is the shortest for the rectangular particle, then followed for the elliptical particle and finally for the circular particle and square particle, the distance is the shortest for the shear-thinning fluid, then followed for the Newtonian fluid and finally for the shear-thickening fluid. This distance for the rectangular particle decreases with increasing Re , but the dependence of the distance on Re for the elliptical particle is not as obvious as that for the rectangular particle. The particle with larger aspect ratio and blockage ratio gets to the equilibrium position faster. The lateral distance from the equilibrium position to the channel centerline is reduced with increasing k, and with decreasing α for both elliptical and rectangular particles. For the particles with larger α , the lateral distance is reduced with the increase of Re , but the relationship between the lateral distance and Re for the particles with smaller α is dependent on n. Unlabelled Image • Elliptical, rectangular particle in power-law fluid reaches equilibrium position. • Found shortest distance of particle focusing for different shape particle. • Found shortest distance of particle focusing in power-law fluid of different index. [ABSTRACT FROM AUTHOR]

The inertial focusing of elliptical particles and the formation of self-organizing trains in a channel flow are studied by using the lattice Boltzmann method. The effects of particle aspect ratio (α), particle concentration (Φ), Reynolds number (Re), and blockage ratio (k) on self-organizing single-line and staggered particle trains are explored. The results show that a single-line particle train is dynamically formed mainly due to the inclination of height (IH) for the particles in the train. The elliptical particle with large α, Φ, Re, and small k facilitates self-organizing of the particle train with relatively stable spacing for a long travel distance. With increasing α, Φ, Re, and k, the value of IH increases and the interparticle spacing decreases. Four kinds of stability conditions for a self-organizing staggered particle train exist depending on Re, k, and α. The threshold Re to form the stable staggered particle train increases with increasing k and is insensitive to α. As Re increases, the spacing of the staggered particle train for the particles with low k and large α is more likely to fluctuate within a certain range. The staggered particle train can be dynamically formed when Re is larger than a critical value. This critical value of Re increases with increasing k and decreasing α. The interparticle spacing of the formed staggered particle train, which is insensitive to Φ, increases with increasing Re and α and decreasing k. [ABSTRACT FROM AUTHOR]

In this paper, the inertial migration of particles in the channel flow of power-law fluid is numerically investigated. The effects of the power-law index (n), Reynolds number (Re), blockage ratio (k), and channel aspect ratio (AR) on the inertial migration of particles and equilibrium position are explored. The results show that there exist two stages of particle migration and four stable equilibrium positions for particles in the cross section of a square channel. The particle equilibrium positions in a rectangular channel are much different from those in a square channel. In shear-thinning fluids, the long channel face equilibrium position and two kinds of particle trajectories are found at low Re. With increasing Re, the short channel face equilibrium position turns to be stable, multiequilibrium positions, and three kinds of particle trajectories along the long wall start to form. Only two stable equilibrium positions exist in shear-thickening fluids. The equilibrium positions are getting closer to the channel centerline with increasing n and k and with decreasing Re. The inertial focusing length L2 in the second stage of particle migration is much longer than inertial focusing length L1 in the first stage. In the square channel, L2 is decreased with increasing Re and k and with decreasing n. In the rectangular channel, L2 is the shortest in the shear-thinning fluid. [ABSTRACT FROM AUTHOR]

• Migration of rigid spheroid is explored in wide range of parameters. • Equilibrium positions of the spheroid in square channel are obtained. • Shear-thinning fluid is beneficial for fast focusing rigid particles. • New rotational mode is captured for the migration of oblate spheroid. • Phase diagram of the rotational mode of oblate spheroid is obtained. The characteristics of rigid spheroid migration in square channel flow of power-law fluids are numerically investigated by the three-dimensional lattice Boltzmann method. The effects of aspect ratio (α), blockage ratio of the particle (k), power-law index (n) and Reynolds number (Re) of the fluid on the inertial migration of rigid prolate and oblate spheroids are explored, respectively. The results show that the shear-thinning fluid with large fluid inertia is beneficial for fast focusing rigid particles to the equilibrium positions in square channel. There are two stages of particle migration and four stable channel face equilibrium positions for migration of spheroid; the channel corner equilibrium positions only exist for the oblate spheroid under a low inertia effect. The prolate spheroid exhibits tumbling and log-rolling (LR) rotational modes, and the LR mode is conditionally stable. For the oblate spheroid, only the LR mode exists when Re is large while two new rotational modes are captured when Re decreases. The equilibrium position of the prolate and oblate spheroids increase when α < 1.0 then decrease at larger α values, escaping the channel centreline with decreasing n and k and increasing Re. The changes of inertial focusing length, angular velocity, and rotational period of the spheroid are systematically analysed to study mechanism of spheroid migration. The current results enrich our understanding of rigid particle accumulation behaviour in channel flow of non-Newtonian fluids and may also shed light on how to efficiently focus and control particles in microfluidic devices. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: Rheological behavior of fiber suspensions in a turbulent channel flow was investigated theoretically and numerically. A model of turbulent fiber suspensions was proposed to predict the orientation distribution of fibers. The fluctuating equation for the orientation distribution function (ODF) of fibers was theoretically solved using the method of characteristics. The self-governed mean equation for orientation distribution function (ODF) was derived by relating the fluctuating ODF and angular velocities-correlated terms to the gradient of mean ODF. Then the ODF of fibers was predicted by numerically solving the mean equation for ODF. Finally the shear stress and first normal stress difference of suspensions were obtained. The results, some of which agree with the available relevant experimental data, show that the orientation distribution of fibers in the vicinity of the center of the flow is relatively broad in turbulent regime, and becomes broader with the increase of Reynolds number. The shear stress of fiber suspensions increases, while the first normal stress difference decreases, from the wall to the center of the flow for varying Reynolds number. [Copyright &y& Elsevier]

• Comparison of ellipsoidal particle migration with equivalent spheres is explored. • Effects of fluid rheology and inertia on the migration behaviour are analysed. • Effects of particle shape and size on the migration behaviour are obtained. • Shear-thinning fluid with high fluid inertia is beneficial for fast focusing particles. We numerically investigate the migration of an ellipsoidal particle in square channel flow of power-law fluids with equivalent spheres. The effects of particle shape and blockage ratio (k), power-law index (n) and Reynolds number (Re) of the fluid on the equilibrium position and travel distance are explored. The results show that the equilibrium positions of prolate ellipsoidal particle, oblate ellipsoidal particle and two equivalent spheres approach the channel centreline with increasing particle size, fluid power-law index, and with decreasing Reynolds number. The second stage travel distance for the ellipsoidal particles to reach the final equilibrium position at the wall bisector decreases with increasing Re , and with decreasing n , while the effect of k depends on the particle shape. The equivalent sphere with the same volume can predict the equilibrium position of prolate ellipsoidal particle in log-rolling (LR) rotational mode, while the second stage travel distance of prolate ellipsoidal particle is greater than two equivalent spheres. The equivalent spheres with the same rotational diameter can be used to predict the equilibrium position and the second stage travel distance of oblate ellipsoidal particle. The results are helpful for designing microfluidic devices with high precious and efficiency. [Display omitted] [ABSTRACT FROM AUTHOR]

Highlights • Particle migration in Giesekus viscoelastic rectangular channel flow is studied. • Particle migrates toward channel centerline or corner at low Reynolds numbers. • Particles migrate toward face centers of shorter walls by elasto-inertial effect. • Particle migration trajectories are significantly affected by the secondary flow. Abstract In this paper, the lateral migration of a neutrally buoyant spherical particle in a pressure-driven rectangular-shaped channel flow of Giesekus viscoelastic fluids is numerically investigated with a fictitious domain method. The particle trajectories are shown for the channel aspect ratio 2, the ratio of the particle diameter to the channel height 0.15, the Reynolds number 1 and 50, and the Weissenberg number up to 2.5. When the fluid inertial effect is negligible, the particle migrates toward the channel centerline or the closest corner depending on its initial position, and the corner-attraction region is enlarged as the Weissenberg number increases. When both fluid inertial and elastic effects are important, most particles migrate toward the face centers of the shorter walls. The particle migration trajectories are significantly affected by the secondary flow. [ABSTRACT FROM AUTHOR]