Equilibrium Positions Of Particles Research Articles

A correlation-based approach for fast prediction of the equilibrium position of particles within a spiral microchannel

ABSTRACT As inertial microfluidics is a proven technique for manipulating particles within microchannels, a deep understanding of hydrodynamics forces acting on particles in these systems is crucial for optimal manipulation. However, existing numerical techniques for examining particle equilibrium positions are often time-intensive and require high-memory systems, limiting accessibility due to complexity and cost. To address this issue, this study proposes a method to develop a correlation for fast estimation of particle equilibrium positions. An algorithm is devised to develop the correlation in three main steps: first, a dataset is created by conducting simulations using the finite element method, considering width, height, flow rate, particle size, and curvature radius. The computed distance between the equilibrium position of the particle and the inner channel wall serves as input for the next step where a general form of the correlation is established using Buckingham’s Π-theorem. The unknown coefficients of the correlation are calculated using 80 percent of the dataset from the first step and the least sum squares errors method. Finally, the obtained correlation is validated using the remaining data and previous experimental studies. The proposed correlation reduces the computational burden associated with predicting particle focus positions, with a 3.7 percent mean absolute error.

Deciphering the Evolution of Inertial Migration in Serpentine Channels.

Serpentine channels coupling inertial and secondary flows enable effective particle focusing and separation, showing great potential in clinical diagnostics and drug screening. However, the nonsteady secondary flows in the serpentine channel make the evolution of inertial migration unclear, hindering the development and application of the serpentine channel. Herein, to refine the inertial migration mechanism, we established a model with varying curvature ratios to study the effect of secondary flow on particle migration in the serpentine channel. This method used direct numerical simulation (DNS) to calculate inertial lift, mapped the inertial lift to cross sections of the serpentine channel, and deciphered the inertial migration by using the Lagrangian particle tracking (LPT) method. The inertial migration of microparticles is experimentally investigated to validate the established numerical model. The results indicate that particle migration in serpentine channels follows a two-stage migration. An increase in secondary flow accelerates the second stage of the migration process while slowing the first stage process. Subsequently, we investigated the effects of different parameters, including Reynolds number, aspect ratio, and blockage ratio, on the equilibrium positions of particles, providing guidelines for the high-resolution separation of particles. Taking flow resistance into account, the dimensionless study makes the separation of arbitrary-sized particles possible. This work reveals the migration mechanism in serpentine channels, paving the way for the inertial separation of the particles.

Bifurcation of equilibrium positions for ellipsoidal particles in inertial shear flows between two walls

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Fox et al., J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles.

Inertial migration and control force in pulsatile flow- a computational study

ABSTRACT The current work proposes a numerical model for analysing the inertial migration of cylindrical-shaped rigid particles in pulsatile flow. The particle is non-neutrally buoyant, and the numerical model is built using a feedback forcing-based immersed boundary scheme. For shifting particle equilibrium position towards the channel centre, an opposing flow control force is applied. The relationship between control force and parameters such as particle diameter, Reynolds number, and density ratio is thoroughly investigated and reported here. The magnitude of the control force increases with Reynolds number and decreases with particle diameter. With density ratio, on the other hand, the magnitude of the control force first drops and then rises. Based on the results of the parametric study a prediction model for the control force is developed with the help of a linear regression algorithm.

Thomson-Einstein's Tea Leaf Paradox Revisited: Aggregation in Rings.

A distinct particle focusing spot occurs in the center of a rotating fluid, presenting an apparent paradox given the presence of particle inertia. It is recognized, however, that the presence of a secondary flow with a radial component drives this particle aggregation. In this study, we expand on the examination of this "Thomson-Einstein's tea leaf paradox" phenomenon, where we use a combined experimental and computational approach to investigate particle aggregation dynamics. We show that not only the rotational velocity, but also the vessel shape, have a significant influence on a particle's equilibrium position. We accordingly demonstrate the formation of a single focusing spot in a vessel center, as has been conclusively demonstrated elsewhere, but also the repeatable formation of stable ring-shaped particle arrangements.

Numerical study on heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion

Janus particle is a research hotspot due to its novelty and settlement in acid liquid during wastewater treatment. Heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion are numerically investigated based on immersed boundary lattice Boltzmann method. Chemical reaction heat ratio, Damkohler number, Peclet number, and particle number effects on temperature field, concentration field, Janus particle mass reduction, position, and velocity are investigated. The uniform particle has an equilibrium position of about 1/4 times the channel width for two corroded uniform particle settlement processes. The Janus particle horizontal position deviates from the uniform particle equilibrium position due to the force caused by nonuniform buoyancy and particle rotation. When the chemical reaction heat ratio is more than 1, the Janus particle horizontal position is closer to the channel centerline and has a positive deviation. However, the converse trend happens when the chemical reaction heat ratio is less than 1, and the Janus particle horizontal position has a negative deviation. The Janus particle horizontal position deviation magnitude increases with increasing Damkohler number and decreasing Peclet number. The horizontal position deviation phenomenon exists for the single corroded Janus particle and two corroded Janus particle settlement processes.

High-throughput isolation of cancer cells in spiral microchannel by changing the direction, magnitude and location of the maximum velocity

Circulating tumor cells (CTCs) are scarce cancer cells that rarely spread from primary or metastatic tumors inside the patient's bloodstream. Determining the genetic characteristics of these paranormal cells provides significant data to guide cancer staging and treatment. Cell focusing using microfluidic chips has been implemented as an effective method for enriching CTCs. The distinct equilibrium positions of particles with different diameters across the microchannel width in the simulation showed that it was possible to isolate and concentrate breast cancer cells (BCCs) from WBCs at a moderate Reynolds number. Therefore we demonstrate high throughput isolation of BCCs using a passive, size-based, label-free microfluidic method based on hydrodynamic forces by an unconventional (combination of long loops and U-turn) spiral microfluidic device for isolating both CTCs and WBCs with high efficiency and purity (more than 90%) at a flow rate about 1.7 mL/min, which has a high throughput compared to similar ones. At this golden flow rate, up to 92% of CTCs were separated from the cell suspension. Its rapid processing time, simplicity, and potential ability to collect CTCs from large volumes of patient blood allow the practical use of this method in many applications.

Numerical Study of the Effects of Asymmetric Velocity Profiles in a Curvilinear Channel on Migration of Neutral Buoyant Particle

The microstructure and suspended particle behavior should be considered when studying the flow properties exhibited by particle suspension. In addition, particle migration, also known as Segré–Silberberg effects, alters the microstructure of the suspension and significantly affects the viscosity properties of the suspension. Therefore, particle behavior with respect to the changes in mechanical factors should be considered to better understand suspension. In this study, we investigated the particle behavior in asymmetric velocity profiles with respect to the channel center numerically using the lattice Boltzmann method and a two-way coupling scheme. Our findings confirmed that the final equilibrium position of particles in asymmetric velocity profiles converged differently between the outer and inner wall sides with respect to the channel center. This indicates that the mechanical equilibrium position of particles can be changed by asymmetric velocity profiles. In addition, centrifugal force acting on the particles is also important in the study of equilibrium position. These results suggest that the microstructure and viscosity characteristics of a suspension in a pipe could be handled by changes in velocity profiles.

Numerical study of microscopic particle arrangement of suspension flow in a narrow channel for the estimation of macroscopic rheological properties

In a narrow channel, the apparent relative viscosity of a suspension with finite-size particles is strongly dependent on its microscopic particle arrangement. Relative viscosity increases when suspended particles flow near the channel wall; thus, a suspension in a narrow channel does not always exhibit the same rheological properties even if the concentration is the same. In this study, we focus on the inertia and concentration of particles in a narrow channel and consider their effects on the microscopic particle arrangement and macroscopic suspension rheology. Two-dimensional pressure-driven suspension flow simulations were performed using a two-way coupling scheme, and normalized particle density distribution (PDD) were implemented to consider their particle arrangements. The results demonstrated that the velocity profiles for the particle suspension were changed by the Reynolds number and particle concentration because of the interactions between particles according to the power-law index. These changes affected the particle equilibrium positions in the channel, and the subsequent changes in solvent layer thickness caused changes in the macroscopic apparent viscosity. The behavior of microscopic particles played important roles in determining macroscopic rheology. Thus, we have confirmed that a normalized PDD can be used to estimate and assess the macroscopic rheology of a suspension.

Self-trapping of nanoparticles by bound states in the continuum

In the first tutorial part of the paper, we show that equilibrium positions of small dielectric particles inside the Fabry-Perot resonator (FPR) are sensitive to a frequency of incident electromagnetic wave and size of particle. That elucidates basic principles of resonant trapping of nanoparticles by excitation of high-$Q$ resonances of FPR. In the second part, we consider a long dielectric cylinder with submicron radius (primary cylinder) integrated into a metallic waveguide which supports symmetry-protected bound states in the continuum (BICs). We consider the case of a slightly shifted cylinder relative to the axis of symmetry of a waveguide that controls the $Q$ factor of quasi-BIC. Then, the extra nanoparticle perturbs quasi-BIC as dependent on the size of the nanoparticle and position relative to the primary cylinder. An interplay between the resonant width of quasi-BIC and a degree of frequency perturbation defines whether a dragging nanoparticle is terminated at a surface of the primary cylinder for an ultrasmall size of nanoparticles or at the definite distances from the cylinder for the larger size of nanoparticles. Thereby, we demonstrate a paradigm of resonant self-trapping and sorting of nanoparticles by use of quasi-BICs. We also show extremal sensitivity of self-trapping to the frequency of an electromagnetic (EM) wave propagating over waveguide.

Inertial focusing patterns and equilibrium position of particles in symmetric CEA microchannels

Inertial focusing patterns and equilibrium position of particles in symmetric CEA microchannels

Effect of neutrally buoyant oblate spheroid's aspect ratio on its equilibrium position in a square duct

The inertial migration of a neutrally buoyant oblate spheroid in a square duct is numerically simulated via the multiple-relaxation-time lattice Boltzmann method. This study aims to investigate the effect of a particle's aspect ratio $(AR)$ on its equilibrium position at different initial positions, orientations, and Reynolds numbers $(Re)$. The spheroid's equatorial radius remains unchanged here, and its $AR$ is adjusted by changing its polar radius, which is distinct from previous studies. Therefore, the particle's volume and mass increase with the $AR$. At a low $Re$ $(Re~=~80)$, the particle's initial position and orientation affect its final motion. There are three possible motion modes, tumbling, log-rolling and inclined log-rolling. Although the oblate spheroids with different $ARs$ may experience different motion modes at their final equilibrium states, their rotational diameters are constant. For the tumbling mode, the $AR$ affects the equilibrium position, and the particle gradually approaches the duct center as the $AR$ increases. For the inclined log-rolling mode, the $AR$ partially affects the equilibrium position, where the corresponding equilibrium positions remain unchanged for the spheroids with $AR~=~0.5$ and $0.75$, approaching closer to the duct center for the spherical particle with $AR~=~1$. Finally, for the log-rolling mode, $AR$ has a negligible effect on the equilibrium positions. Furthermore, in the same motion mode, the particle's equilibrium position approaches the wall as the $Re$ increases from 40 to 160.

Active control of particle position by boundary slip in inertial microfluidics

Inertial microfluidic is able to focus and separate particles in microchannels based on the characteristic geometry and intrinsic hydrodynamic effect. Yet, the vertical position of suspended particles in the microchannel cannot be manipulated in real time. In this study, we utilize the boundary slip effect to regulate the parabolic velocity distribution of fluid in the microchannel and present a scheme to active control the vertical position of particles in inertial microfluidics. The flow field of a microchannel with a unilateral slip boundary is equivalent to that of the microchannel widened by the relevant slip length, and the particle equilibrium positions in the two microchannels are consistent consequently. Then, we simulate the lateral migrations of three kinds of typical particles, namely circle, ellipse, and rectangle in the microchannel. Unlike the smooth trajectories of circular particles, the motions of the elliptical and rectangular particles are accompanied by regular fluctuations and non-uniform rotations due to their non-circular geometries. The results demonstrate that the unilateral slip boundary can effectively control the vertical equilibrium position of particles. Thus, the present scheme enables to active manipulate the particles positions in vertical direction and can promote more accurate focusing, separating, and transport in inertial microfluidics.

Exploiting Heteroaggregation to Quantify the Contact Angle of Charged Colloids at Interfaces

We exploit the aggregation between oppositely charged particles to visualize and quantify the equilibrium position of charged colloidal particles at the fluid-water interface. A dispersion of commercially available charge-stabilized nanoparticles was used as the aqueous phase to create oil-water and air-water interfaces. The colloidal particles whose charge was opposite that of the nanoparticles in the aqueous phase were deposited at the chosen fluid-water interface. Heteroaggregation, i.e., aggregation between oppositely charged particles, leads to the deposition of nanoparticles onto the larger particle located at the interface; however, this only occurs on the surface of the particle in contact with the aqueous phase. This selective deposition of nanoparticles on the surfaces of the particles exposed to water enables the distinct visualization of the circular three-phase contact line around the particles positioned at the fluid-water interface. Since the electrostatic association between the nanoparticles and the colloids at interfaces is strong, the nanoparticle assembly on the larger particles is preserved even after being transferred to solid substrates via dip-coating. This facilitates the easy visualization of the contact line by electron microscopy and the determination of the equilibrium contact angle of colloidal particles (θ) at the fluid-water interface. The suitability of the method is demonstrated by the measurement of the three-phase contact angle of positively and negatively charged polystyrene particles located at fluid-water interfaces by considering particles with sizes varying from 220 nm to 8.71 μm. The study highlights the effect of the size ratio between the nanoparticles in the aqueous phase and the colloidal particles on the accuracy of the measurement of θ.

Fluid-Structure Interaction Approach to Single Particle in a Square Microchannel

Inertial microfluidic technique has been widely applied on particle/cell manipulation and detection. To understand the physical principle of this technique more detailed, the interaction of fluid and particle was studied through the Fluid-Structure Interaction (FSI) method. The equilibrium positions of finite-size particles with different diameters were simulated at moderate Reynolds numbers. The flow structure around two typical particles was analysed. The vortex in the front of the particle retards particle’s translation leading to the lag velocity increasing. Finally, the rotation velocity and the rotational-induced force analysed quantitatively to demonstrate that particle’s self-rotation significantly promotes its inertial migration.

Effects of sample rheology on the equilibrium position of particles and cells within a spiral microfluidic channel

Effects of sample rheology on the equilibrium position of particles and cells within a spiral microfluidic channel

Inertial migration of a non-neutrally buoyant particle in a linear shear flow with thermal convection

Inertial migration of a nonneutrally buoyant disk particle in a linear shear flow under thermal convection (TC) is studied numerically. Particle dynamics and equilibrium position depend on competition between the inertial lift force, the gravitational force (buoyancy), and the TC lift force. When the particle is heavier than the fluid, inertial lift-off is observed and a modified phase diagram is established in terms of the channel Reynolds number Re and density ratio \ensuremath{\sigma}. When the particle is lighter than the fluid, TC induced re-suspension and sedimentation are observed, where the normalized critical Grashof number, Gr${}_{\mathrm{crit}}$/\ensuremath{\sigma}, depends linearly on Re for all particle densities studied.

Dynamics of self-organizing single-line particle trains in the channel flow of a power-law fluid

The formation of self-organizing single-line particle train in a channel flow of a power-law fluid is studied using the lattice Boltzmann method with power-law index 0.6 ≤ n ≤ 1.2, particle volume concentration 0.8% ≤ Φ ≤ 6.4%, Reynolds number 10 ≤ Re ≤ 100, and blockage ratio 0.2 ≤ k ≤ 0.4. The numerical method is validated by comparing the present results with the previous ones. The effect n, Φ, Re and k on the interparticle spacing and parallelism of particle train is discussed. The results showed that the randomly distributed particles would migrate towards the vicinity of the equilibrium position and form the ordered particle train in the power-law fluid. The equilibrium position of particles is closer to the channel centerline in the shear-thickening fluid than that in the Newtonian fluid and shear-thinning fluid. The particles are not perfectly parallel in the equilibrium position, hence IH is used to describe the inclination of the line linking the equilibrium position of each particle. When self-organizing single-line particle train is formed, the particle train has a better parallelism and hence benefit for particle focusing in the shear-thickening fluid at high Φ, low Re and small k. Meanwhile, the interparticle spacing is the largest and hence benefit for particle separation in the shear-thinning fluid at low Φ, low Re and small k.

Three-Dimensional Numerical Simulation of Particle Focusing and Separation in Viscoelastic Fluids.

Particle focusing and separation using viscoelastic microfluidic technology have attracted lots of attention in many applications. In this paper, a three-dimensional lattice Boltzmann method (LBM) coupled with the immersed boundary method (IBM) is employed to study the focusing and separation of particles in viscoelastic fluid. In this method, the viscoelastic fluid is simulated by the LBM with two sets of distribution functions and the fluid–particle interaction is calculated by the IBM. The performance of particle focusing under different microchannel aspect ratios (AR) is explored and the focusing equilibrium positions of the particles with various elasticity numbers and particle diameters are compared to illustrate the mechanism of particle focusing and separation in viscoelastic fluids. The results indicate that, for particle focusing in the square channel (AR = 1), the centerline single focusing becomes a bistable focusing at the centerline and corners as El increases. In the rectangular channels (AR < 1), particles with different diameters have different equilibrium positions. The equilibrium position of large particles is closer to the wall, and large particles have a faster lateral migration speed and few large particles migrate towards the channel center. Compared with the square channel, the rectangular channel is a better design for particle separation.

Motion and equilibrium position of elliptical and rectangular particles in a channel flow of a power-law fluid

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.