Experimental observations of bands of suspended colloidal particles subject to shear flow and steady electric field

Manipulating suspended colloidal particles flowing through a microchannel is of interest in microfluidics and nanotechnology. However, the flow itself can affect the dynamics of these suspended particles via wall-normal “lift” forces. The near-wall dynamics of particles suspended in shear flow and subject to a dc electric field was quantified in combined Poiseuille and EO flow through a?~?30 μm deep channel. When the two flows are in opposite directions, the particles are attracted to the wall. They then assemble into very high aspect ratio structures, or concentrated streamwise “bands,” above a minimum electric field magnitude, and, it appears, a minimum near-wall shear rate. These bands only exist over the few micrometers next to the wall and are roughly periodic in the cross-stream direction, although there are no external forces along this direction. Experimental observations and dimensional analysis of the time for the first band to form and the number of bands over a field of view of ~?200 μm are presented for dilute suspensions of polystyrene particles over a range of particle radii, concentrations, and zeta potentials. To our knowledge, there is no theoretical explanation for band assembly, but the results presented here demonstrate that it occurs over a wide range of different particle and flow parameters.     

Efficient computation of micro-particle dynamics including wall effects

This study describes an effective method for one-way coupled Eulerian-Lagrangian simulations of spherical micro-size particles, including particle-wall interactions and the quantification of near-wall stasis at possibly elevated concentrations. The focus is on particle-hemodynamics simulations where particle suspensions are composed of critical blood cells, such as monocytes, and the carrier fluid is non-Newtonian. Issues regarding adaptive time-step integration of the particle motion equation, relevant point-force model terms, and adaptation of surface-induced particle forces to arbitrary three-dimensional geometries are outlined. By comparison to available experimental trajectories, it is shown that fluid-element pathlines may be used to simulate non-interacting blood particles removed from wall boundaries under dilute transient conditions. However, when particle-wall interactions are significant, an extended form of the particle trajectory equation is required which includes terms for Stokes drag, near-wall drag modifications, or lubrication forces, pressure gradients, and near-wall particle lift. Still, additional physical and/or biochemical wall forces in the nano-meter range cannot be readily calculated; hence the near-wall residence time (NWRT) model indicating the probability of blood particle deposition is presented. The theory is applied to a virtual model of a femoral bypass end-to-side anastomosis, where profiles of the Lagrangian-based NWRT parameter are illustrated and convergence is verified. In order to effectively compute the large number of particle trajectories required to resolve regions of particle stasis, the proposed particle tracking algorithm stores all transient velocity field solution data on a shared memory architecture (SGI Origin 2400) and computes particle trajectories using an adaptive parallel approach. Compared to commercially available particle tracking packages, the algorithm presented is capable of reducing computational time by an order of magnitude for typical transient one-way coupled blood particle simulations in complex cyclical flow domains.     

Inertial effects on cylindrical particle migration in linear shear flow near a wall

Micro-/nanoparticle-based systems are regarded as one of the possible candidates due to the engineerability and multifunctionality to maximize the accumulation of the nano-/microparticle-based drug delivery system on the target. Recent advances in nanotechnology enable the fabrication of diverse particle shapes from simple spherical particles to more complex shapes. The particle dynamics in blood flow and endocytosis characteristics of non-spherical particles change as the non-sphericity effect increases. We used a numerical approach to investigate the particle dynamics in linear shear flow near a wall. We examined the dynamics of slender cylindrical particles with aspect ratio γ = 5.0 in terms of particle trajectory, velocity, and force variation for different Stokes numbers over time. We identified the rotating inertia of particle near a wall as the source of inertial migration toward the wall. The drift velocity of slender cylindrical particles is comparable to that of discoidal particles. We discuss the possibilities and limitations of using slender cylindrical particles as a drug delivery system.     

An immersed interface method for the Vortex-In-Cell algorithm

The paper presents a two-dimensional immersed interface technique for the Vortex-In-Cell (VIC) method for simulation of flows past bodies of complex geometry. The particle–mesh VIC algorithm is augmented by a local particle–particle correction term in a Particle–Particle Particle–Mesh (P³M) context to resolve sub-grid scales incurred by the presence of the immersed interface. The particle–particle correction furthermore allows to disjoin mesh and particle resolution by explicitly resolving sub-grid scales on the particles. This P³M algorithm uses an influence matrix technique to annihilate the anisotropic sub-grid scales and adds an exact particle–particle correction term. Free-space boundary conditions are satisfied through the use of modified Green’s functions in the solution of the Poisson equation for the streamfunction. The concept is extended such as to provide exact velocity predictions on the mesh with free-space boundary conditions.The random walk technique is employed for the diffusion in order to relax the need for a remeshing of the computational elements close to solid boundaries. A novel partial remeshing technique is introduced which only performs remeshing of the vortex elements which are located sufficiently distant from the immersed interfaces, thus maintaining a sufficient spatial representation of the vorticity field.Convergence of the present P³M algorithm is demonstrated for a circular patch of vorticity. The immersed interface technique is applied to the flow past a circular cylinder at a Reynolds number of 3000 and the convergence of the method is demonstrated by a systematic refinement of the spatial parameters. Finally, the flow past a cactus-like geometry is considered to demonstrate the efficient handling of complex bluff body geometries. The simulations offer an insight into physically interesting flow behavior involving a temporarily negative total drag force on the section.     

Design of microfluidic channels for magnetic separation of malaria-infected red blood cells

This study is motivated by the development of a blood cell filtration device for removal of malaria-infected, parasitized red blood cells (pRBCs). The blood was modeled as a multi-component fluid using the computational fluid dynamics discrete element method (CFD-DEM), wherein plasma was treated as a Newtonian fluid and the red blood cells (RBCs) were modeled as soft-sphere solid particles which move under the influence of drag, collisions with other RBCs, and a magnetic force. The CFD-DEM model was first validated by a comparison with experimental data from Han and Frazier (Lab Chip 6:265–273, 2006) involving a microfluidic magnetophoretic separator for paramagnetic deoxygenated blood cells. The computational model was then applied to a parametric study of a parallel-plate separator having hematocrit of 40 % with 10 % of the RBCs as pRBCs. Specifically, we investigated the hypothesis of introducing an upstream constriction to the channel to divert the magnetic cells within the near-wall layer where the magnetic force is greatest. Simulations compared the efficacy of various geometries upon the stratification efficiency of the pRBCs. For a channel with nominal height of 100 µm, the addition of an upstream constriction of 80 % improved the proportion of pRBCs retained adjacent to the magnetic wall (separation efficiency) by almost twofold, from 26 to 49 %. Further addition of a downstream diffuser reduced remixing and hence improved separation efficiency to 72 %. The constriction introduced a greater pressure drop (from 17 to 495 Pa), which should be considered when scaling up this design for a clinical-sized system. Overall, the advantages of this design include its ability to accommodate physiological hematocrit and high throughput, which is critical for clinical implementation as a blood-filtration system.     

Inertial focusing of microparticles in curvilinear microchannels with different curvature angles

Inertial microfluidics has become one of the emerging topics due to potential applications such as particle separation, particle enrichment, rapid detection and diagnosis of circulating tumor cells. To realize its integration to such applications, underlying physics should be well understood. This study focuses on particle dynamics in curvilinear channels with different curvature angles (280°, 230°, and 180°) and different channel heights (90, 75, and 60 µm) where the advantages of hydrodynamic forces were exploited. We presented the cruciality of the three-dimensional particle position with respect to inertial lift forces and Dean drag force by examining the focusing behavior of 20 µm (large), 15 µm (medium) and 10 µm (small) fluorescent polystyrene microparticles for a wide range of flow rates (400–2700 µL/min) and corresponding channel Reynolds numbers. Migration of the particles in lateral direction and their equilibrium positions were investigated in detail. In addition, in the light of our findings, we described two different regions: transition region, where the inner wall becomes the outer wall and vice versa, and the outlet region. The maximum distance between the tight particle stream of 20 and 15 µm particles was obtained in the 90 high channel with curvature angle of 280° at Reynolds number of 144 in the transition region (intersection of the turns), which was the optimum condition/configuration for focusing.     

Quantitative characterization of the focusing process and dynamic behavior of differently sized microparticles in a spiral microchannel

In this paper, a spiral microchannel was fabricated to systematically investigate particle dynamics. The focusing process or migration behavior of different-sized particles in the outlet region was presented. Specifically, for focused microparticles, quantitative characterization and analysis of how particles migrate towards the equilibrium positions with the increase in flow rate (De = 0.31–3.36) were performed. For unfocused microparticles, the particle migration behavior and the particle-free region’s formation process were characterized over a wide range of flow rates (De = 0.31–4.58), and the emergence of double particle-free regions was observed at De ≥ 3.36. These results provide insights into the design and operation of high-throughput particle/cell filtration and separation. Furthermore, using the location markers pre-fabricated along with the microchannel structures, the focusing or migration dynamics of different-sized particles along the spiral microchannel was systematically explored. The particle migration length effects on focusing degree and particle-free region width were analyzed. These analyses may be valuable for the optimization of microchannel structures. In addition, this device was successfully used to efficiently filter rare particles from a large-volume sample and separate particles of two different sizes according to their focusing states.     

Molecular dynamics simulation of nanofluid’s flow behaviors in the near-wall model and main flow model

The flow behaviors of nanofluids were studied in this paper using molecular dynamics (MD) simulation. Two MD simulation systems that are the near-wall model and main flow model were built. The nanofluid model consisted of one copper nanoparticle and liquid argon as base liquid. For the near-wall model, the nanoparticle that was very close to the wall would not move with the main flowing due to the overlap between the solid-like layer near the wall and the adsorbed layer around the nanoparticle, but it still had rotational motion. When the nanoparticle is far away from the wall (d > 11 Å), the nanoparticle not only had rotational motion, but also had translation. In the main flow model, the nanoparticle would rotate and translate besides main flowing. There was slip velocity between nanoparticles and liquid argon in both of the two simulation models. The flow behaviors of nanofluids exhibited obviously characteristics of two-phase flow. Because of the irregular motions of nanoparticles and the slip velocity between the two phases, the velocity fluctuation in nanofluids was enhanced.     

A novel method for modeling of complex wall geometries in smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) has become increasingly important during recent decades. Its meshless nature, inherent representation of convective transport and ability to simulate free surface flows make SPH particularly promising with regard to simulations of industrial mixing devices for high-viscous fluids, which often have complex rotating geometries and partially filled regions (e.g., twin-screw extruders). However, incorporating the required geometries remains a challenge in SPH since the most obvious and most common ways to model solid walls are based on particles (i.e., boundary particles and ghost particles), which leads to complications with arbitrarily-curved wall surfaces. To overcome this problem, we developed a systematic method for determining an adequate interaction between SPH particles and a continuous wall surface based on the underlying SPH equations. We tested our new approach by using the open-source particle simulator “LIGGGHTS” and comparing the velocity profiles to analytical solutions and SPH simulations with boundary particles. Finally, we followed the evolution of a tracer in a twin-cam mixer during the rotation, which was experimentally and numerically studied by several other authors, and ascertained good agreement with our results. This supports the validity of our newly-developed wall interaction method, which constitutes a step forward in SPH simulations of complex geometries.     

Inertial particle focusing dynamics in a trapezoidal straight microchannel: application to particle filtration

Inertial microfluidics has emerged recently as a promising tool for high-throughput manipulation of particles and cells for a wide range of flow cytometric tasks including cell separation/filtration, cell counting, and mechanical phenotyping. Inertial focusing is profoundly reliant on the cross-sectional shape of channel and its impacts on not only the shear field but also the wall-effect lift force near the wall region. In this study, particle focusing dynamics inside trapezoidal straight microchannels was first studied systematically for a broad range of channel Re number (20 < Re < 800). The altered axial velocity profile and consequently new shear force arrangement led to a cross-lateral movement of equilibration toward the longer side wall when the rectangular straight channel was changed to a trapezoid; however, the lateral focusing started to move backward toward the middle and the shorter side wall, depending on particle clogging ratio, channel aspect ratio, and slope of slanted wall, as the channel Reynolds number further increased (Re > 50). Remarkably, an almost complete transition of major focusing from the longer side wall to the shorter side wall was found for large-sized particles of clogging ratio K ~ 0.9 (K = a/H_min) when Re increased noticeably to ~ 650. Finally, based on our findings, a trapezoidal straight channel along with a bifurcation was designed and applied for continuous filtration of a broad range of particle size (0.3 < K < 1) exiting through the longer wall outlet with ~ 99% efficiency (Re < 100).     

Coupled RapidCell and lattice Boltzmann models to simulate hydrodynamics of bacterial transport in response to chemoattractant gradients in confined domains

The RapidCell (RC) model was originally developed to simulate flagellar bacterial chemotaxis in environments with spatiotemporally varying chemoattractant gradients. RC is best suited for motility simulations in unbounded nonfluid environments; this limits its use in biomedical applications hinging on bacteria-fluid dynamics in microchannels. In this study, we eliminated this constraint by coupling the RC model with the colloidal lattice Boltzmann (LB) model. RC–LB coupling was accomplished by tracking positions of chemoreceptors on particle surfaces that vary with particles’ angular and translational velocities, and by including forces and torques due to particles’ tumbling and running motions in particle force- and torque-balance equations. The coupled model successfully simulated trajectories of particles in initially stagnant fluids in bounded domains, involving a chemoattractant contained in a confined zone with a narrow inlet or concentric multiringed inline obstacles, mimicking tumor vasculature geometry. Chemotactically successful particles exhibited higher attractant concentrations near the receptor clusters, transient increases in the motor bias, and transient fluctuations in methylated proteins at the cell scale, while exhibiting more frequent higher particle translation velocities and smaller angular velocities than chemotactically unsuccessful particles at the particle scale. In these simulations, the chemotactic particles reached the chemoattractant with the success rates of 20–72 %, whereas nonchemotactic particles would be unsuccessful. The coupled RC–LB model is the first step toward development of a multiscale simulation tool that bridges cell-scale signal and adaptation dynamics with particle-scale fluid-particle dynamics to simulate chemotaxis-driven bacterial motility in microchannel networks, typically observed in tumor vasculatures, in the context of targeted drug delivery.     

Numerical investigation of polygonal particle separation in microfluidic channels

We numerically investigate the separation of polygonal particles through an array of solid obstacles in microfluidic devices. Particle–fluid, particle–particle and particle–wall interactions are all considered in our numerical method. Firstly, the separation of circular particles based on size is simulated and the relationship of the migration angle and forcing angle by our simulations is coincided with the experimental results. Then, the simulations of polygon particle separation based on shape are carried out. The results show that the shape of particles can be used for particle separation through an array of solid obstacles. Through reasonable design of the shape of obstacles, separation of polygon particles can be achieved. In addition, the results indicate that our numerical method has the potential to substantially improve the design and optimization of microfluidic devices for the separation of particles.     

Selective particle and cell clustering at air–liquid interfaces within ultrasonic microfluidic systems

In this study, we demonstrate particle and cell clustering in distinct patterns on the free surface of microfluidic volumes. Employing ultrasonic actuation, submersed microparticles are forced to two principal positions: nodal lines (pressure minima) of a standing wave within the liquid bulk, and distinct locations on the air–liquid interface (free surface); the latter of which has not been previously demonstrated using ultrasonic standing waves. As such, we unravel the fundamental mechanisms behind such patterns, showing that the contribution of fluid particle velocity variations on the free surface (acoustic radiation force) results in patterned particle clustering. In addition, by varying the size and density of the microparticles (3.5–31 μm polystyrene and 1–5 μm silica), acoustic streaming is found to increase the tendency for a smaller and lighter particle to cluster at the air–liquid interface. This selectivity is exploited for the isolation of multiple microparticle and cell types on the free surface from their nodally aligned counterparts. Free surface clustering is demonstrated in both an open microfluidic chamber and a sessile droplet, as well as using a range of biological species Escherichia coli, blood cells, Ragweed pollen and Paper Mulberry pollen). The ability to selectively cluster submersed microparticles and cells in distinct patterns on the free surface showcases the excellent suitability of this method to lab-on-a-chip systems.     

Field, force and transport analysis for magnetic particle-based gene delivery

Magnetic particles are used to deliver gene vectors to target cells for uptake in a process known as magnetofection. Magnetic particle-based gene delivery has been successfully demonstrated for all types of nucleic acids and across a broad range of cell lines. It is well suited for multiwell culture plate systems wherein magnetic particles with surface-bound gene vectors are introduced into culture wells, and a magnetic force provided by rare-earth magnets beneath and aligned with the wells attracts the particles to the cells for uptake. In this paper, models are presented for analyzing and optimizing this process. These include closed-form equations for predicting the magnetic field and force and a drift–diffusion equation for predicting the transport and accumulation of particles in a well. The closed-form equations enable rapid parametric analysis of the spatial distribution of the field and force in a well as a function of key parameters including its dimensions, the magnet-to-well spacing, the strength of the magnet, the influence of neighboring magnets and the properties of the particles. The particle transport equation accounts for the field-induced drift of particles as well as fluidic drag and Brownian diffusion. It is solved numerically using the finite volume method. The theory is demonstrated via application to a multiwall plate magnetofection system and the impact of various factors that govern gene delivery is assessed. The models provide insight into gene delivery and are well suited for parametric analysis of particle accumulation in the wells. They enable the rational design of novel magnetofection systems.     

On the importance of carrier fluid viscosity and particle–wall interactions in magnetic-guided assembly of quasi-2D systems

We demonstrate the influence of experimental conditions (carrier fluid viscosity and particle–wall interactions—friction) on the quasi-2D deterministic aggregation kinetics of carbonyl iron magnetic suspensions in rectangular microchannels. On the one hand, the carrier fluid viscosity determines the time scale for aggregation. On the other hand, friction strongly determines the aggregation rate and therefore the kinetic exponent (mean cluster size vs. time dependence). When particle–wall interactions are weak, the mean cluster size increases with a power of 0.65 ± 0.06, for open cavities (≥500 microns channel width), in very good agreement with theories and particle-level simulations. However, when the particle–wall interactions are strong, the kinetic exponent decreases and the aggregation is eventually arrested. This work suggests that particle–wall interactions may be one of the reasons for the discrepancies found in the experimental determination of the aggregation kinetic exponents in the literature.     

Improved particle concentration by cascade AC electroosmotic flow

The importance of electrokinetics in microfluidic technology has been growing owing to its versatility and simplicity in fabrication, implementation, and handling. Alternating-current electroosmosis (ACEO), which is the motion of fluid due to the ion movement by an interaction between AC electric field and an electrical double layer on the electrode surface, has a potential for a particle concentration method to detecti rare samples flowing in a microchannel. This study investigates an improved ACEO-based particle concentration by cascade electrokinetic approach. Flow field induced by ACEO and accumulation behavior of particles were parametrically measured to discuss the concentrating mechanism. The accumulation of particles by ACEO can be explained by a balance between the attenuating electroosmotic flow to transport particles and the inherent diffusive motion of the particles, which is hindered due to the near-wall location. Although a parallel double-gap electrode geometry enables particles to be collected at the center of electrode very sharply, it has scattering zones with accumulated particles at sidewalls of the channel. This drawback can be overcome by applying sheath flow or introducing cascade electrode pattern upstream of the focusing zone. As a result, total concentration efficiency was 98.4 % for all the particles flowing in the cascade device. The resultant concentrated particles exist on the electrode surface within 5 μm, and three-dimensional concentration of particle with the concentration factor as large as 700 is possible using a monolithic channel, co-planar electrode, and sheathless solution feeding. This cascade electrokinetic method provides a new and effective preconcentrator for ultra-sensitive detection of rare samples.     

Experimental and numerical investigation on particle–particle interaction of multi-particle separation in an alternating and repetitive microchannel

Inertial focusing plays a major role in size-based cell separation or enrichment for microfluidic applications in many medical areas such as diagnostics and treatment. These applications often deal with suspensions of different particles which cause interactions between particles with different diameters such as particle–particle collision. In this study, particle–particle interaction in a laminar flow through a low aspect ratio alternating and repetitive microchannel is investigated both numerically and experimentally. It is revealed that particle–particle collision affects high quality particle focusing. computational fluid dynamics simulations are conducted for demonstrating the effect of the flow field in the transverse cross-section on the focusing quality and position. The experiments and simulations both revealed that if the flow is seeded with a mixture of particles of 3.3 and 9.9 µm diameters, the quality of focusing intensity is degenerated compared to the focusing features obtained by particles with a diameter of 9.9 µm solely. The results clearly show that particle–particle collision between the 3.3 and 9.9 µm particles has a negative effect on particle focusing behavior of the 9.9 µm particles.

     

“Law of the nano-wall” in nano-channel gas flows

Molecular dynamics simulations of force-driven nano-channel gas flows show two distinct flow regions. While the bulk flow region can be determined using kinetic theory, transport in the near-wall region is dominated by gas–wall interactions. This duality enables definition of an inner-layer scaling, \(y^{*}\), based on the molecular dimensions. For gas–wall interactions determined by Lennard–Jones potential, the velocity distribution for \(y^{*} \le 3\) exhibits a universal behavior as a function of the local Knudsen number and gas–wall interaction parameters, which can be interpreted as the “law of the nano-wall.” Knowing the velocity and density distributions within this region and using the bulk flow velocity profiles from Beskok–Karniadakis model (Beskok and Karniadakis in Microscale Thermophys Eng 3(1):43–77, 1999), we outline a procedure that can correct kinetic-theory-based mass flow rate predictions in the literature for various nano-channel gas flows.