Axial particle displacements in fluid slugs after passing a simple serpentiform microchannel

In this work, we designed a simple microchannel to separate particles in fluids by size. We found that mixtures of polystyrene 2 and 0.5 μm particles in a fluid slug can be differentiated by size after passing a long serpentiform microchannel. In contrast to the tubular pinch effect, which separates the particle in radial direction, we found that the particle suspensions in fluid slugs are displaced along the flow directions. The separation performance increases with the increasing flow velocity. The feature of differentiation along the flow directions in our device leads to the result that the separation process can be easily improved by stretching the slug before cutting the slug into pieces. Furthermore, the alternative air slugs between working fluid slugs can also prevent clogging inside the microchannels.     

Inertial microfluidics for continuous particle filtration and extraction

In this paper, we describe a simple passive microfluidic device with rectangular microchannel geometry for continuous particle filtration. The design takes advantage of preferential migration of particles in rectangular microchannels based on shear-induced inertial lift forces. These dominant inertial forces cause particles to move laterally and occupy equilibrium positions along the longer vertical microchannel walls. Using this principle, we demonstrate extraction of 590 nm particles from a mixture of 1.9 μm and 590 nm particles in a straight microfluidic channel with rectangular cross-section. Based on the theoretical analysis and experimental data, we describe conditions required for predicting the onset of particle equilibration in square and rectangular microchannels. The microfluidic channel design has a simple planar structure and can be easily integrated with on-chip microfluidic components for filtration and extraction of wide range of particle sizes. The ability to continuously and differentially equilibrate particles of different size without external forces in microchannels is expected to have numerous applications in filtration, cytometry, and bioseparations.     

Particle handling in straight microfluidic channels via opposing electroosmotic and pressure-driven flows

The current study presents a method for producing recirculation zones in a straight microchannel using opposing pressure-driven and electrokinetically driven flows. The interaction of these two flow streams causes flow recirculation structures, which restricts the flow passage within the microchannel and causes a nozzle-like effect, thereby increasing the separation distance between particles in the fluid stream. Theoretical and experimental investigations are performed to investigate the effects of the applied electrical field intensity on the flow recirculation size, and the nozzle-like effect, respectively. In general, the results confirm that the proposed approach provides an effective means of achieving particle acceleration and separation distance within straight microchannels, and therefore provides a viable technique for improving particle manipulation and optical detection in conventional microfluidic devices. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Three-dimensional analysis and enhancement of continuous magnetic separation of particles in microfluidics

In continuous magnetic separation process, particles can be deflected and separated from the direction of laminar flow by means of magnetic force depending on their magnetic susceptibility and size as well as the flow rate. To analyze and control dynamic behavior of these particles flowing in microchannels, a three-dimensional numerical model was proposed and solved for obtaining the particle trajectories under the action of a gradient magnetic field and flow field. The magnetic force distribution and particle trajectories obtained were firstly verified by analytical and experimental results. Then, a detailed analysis for the enhancement of the continuous magnetic separation efficiency by optimizing the flow parameters and microchannel configurations was carried out. The results show that the separation efficiency can be greatly improved by controlling the flow rate ratio of the two fluid streams and introducing a broadened segment in the T-shaped microchannel. And it has been demonstrated to be effective through the sorting of 2-μm and 5-μm non-magnetic particles suspended in a dilute ferrofluid by a permanent magnet. The results reported could be encouraging for the design and optimization of efficient microfluidic separation systems.     

Spiral microchannel with stair-like cross section for size-based particle separation

Particle separation has a variety of applications in biology, chemistry and industry. Among them, circulating tumor cells (CTCs) separation has drawn significant attention to itself due to its high impact on both cancer diagnosis and therapeutics. In recent years, there has been growing interest in using inertial microfluidics to separate micro/nano particles based on their sizes. This technique offers label-free, high-throughput and efficient separation and can be easily fabricated. However, further improvements are needed for potential clinical applications. In this study, a novel inertial separation technique using spiral microchannel having stair-like cross section is introduced. The design fundamental concepts, design criteria and efficacy are investigated thoroughly using a robust numerical model; moreover, it is experimentally tested on the fabricated spiral microchannel. Based on the results, in contrast to conventional spiral microchannels, in which the flow vortices are located latitudinal, the two vortices are uniquely placed longitudinally in the stair-like cross section. The numerical and experimental results indicate that there is a size-dependent volume flow rate threshold defined for each particle size determining which vortices become equilibrated and consequently facilitate their separation. According to the results, using stair-like cross section, the separation throughput and resolution, as the two important design criteria in CTCs’ separation techniques, are significantly improved compared to the conventional spiral microchannels.     

Size scale effects on cavitating flows through microorifices entrenched in rectangular microchannels

Cavitating flow of deionized water through various microorifices and microchannels has been investigated. Multifarious cavitating flow patterns, including incipient, choking and supercavitation have been detected. Effects of microorifice and microchannel size on cavitation have been discussed and results indicate the existence of strong size scale effects. Incipient and choking cavitation numbers are observed to increase with the area ratio between the microorifice and the microchannel while the orifice discharge coefficient plummets once cavitation activity erupts. Additionally, for a fixed microchannel width, the incipient and the choking cavitation numbers rise with the ratio between the hydraulic diameters of the microorifice and the microchannel. In addition, velocity and pressure effects on cavitation have been investigated for several microorifices and the observed trends have been compared with established macroscale results. Furthermore, the flow patterns encountered at choking and supercavitation are significantly influenced by the microorifice and microchannel size. Flow rate choking occurs irrespective of the inlet pressures and is a direct consequence of cavitation inside the microorifice. The predicted choked cavitation number is always higher than the experimental data. This discrepancy is suspected to be the result of exceedingly small residence time for nuclei growth and the ability of the liquid to withstand low pressures at such scales. Flow and cavitation hysteresis is observed but its effects are more pronounced for the smallest microorifice.     

Particle transport in patterned cylindrical microchannels

An Eulerian model (convection–diffusion–migration equation) to evaluate particle transport in patchy heterogeneous cylindrical microchannels is presented. The objective of this model is to capture the effect of surface chemical heterogeneity on deposition and particle transport in cylindrical microchannels with fully developed Poiseuille flow velocity profile. Surface heterogeneity is modeled as alternate bands of attractive and repulsive regions on the channel wall to facilitate systematic continuum type evaluation. The results indicate that particles tend to preferentially collect at the leading edge of the favorable sections and the extent of this deposition can be controlled by changing Peclet number. Also, it is shown that particles tend to travel further along the microchannel length for heterogeneous channels compared to homogeneously favorable channels. In addition, the study evaluates the effect of the frequency of these stripes on the transport behavior and provides the average collection rate depending on favorable surface coverage fraction. This analysis shows how the existing microchannel/capillary transport models could possibly be modified by incorporating surface interactions and chemical heterogeneity.     

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied ??wall effect?? on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.     

On-chip manipulation of nonmagnetic particles in paramagnetic solutions using embedded permanent magnets

This study develops a method for embedding permanent magnets into poly(dimethylsiloxane) (PDMS)-based microfluidic chips. Magnets can be brought very close to the planar microchannels for enhanced magnetic field and field gradients, which enables on-chip continuous-flow manipulation of nonmagnetic particles in typical paramagnetic solutions. We performed a systematic study of the transport of polystyrene particles suspended in manganese (II) chloride (MnCl₂) solutions through a rectangular microchannel. Owing to their smaller magnetization than the suspending fluid, particles experience negative magnetophoresis and are deflected away from the magnet. The effects of particle position (relative to the magnet), particle size, MnCl₂ salt concentration, and fluid flow velocity on the horizontal magnetophoretic deflection are examined using a combined experimental and theoretical approach. The experimental results agree quantitatively with the predictions of an analytical model. The demonstrated nonmagnetic particle deflection may be used with the potential to focus and sort cells in lab-on-a-chip for bio-applications.     

Improvement of microchannel geometry subject to electrokinesis and dielectrophoresis using numerical simulations

This paper addresses the effects of microchannel geometry with electrically insulating posts on a particle flow driven by electrokinesis and dielectrophoresis. An in-house numerical program is developed using a numerical model proposed in literature to predict particle flows in a microchannel with a circular post array. The numerical program is validated by comparing the results of the present study to those in the literature. Results obtained from a Monte-Carlo simulation confirm the three particle flow types driven by an external DC electric field: electrokinetic flow, streaming dielectrophoretic flow, and trapping dielectrophoretic flow. In addition, we study the effects of electrokinetic and dielectrophoretic forces on particle transports by introducing a ratio of lateral to longitudinal forces exerted on a particle. As a result, we propose an improved microchannel geometry to enhance particle transports across electrokinetic streamlines for a given power dissipation. The improved microchannel has a shorter longitudinal spacing between the circular posts than a reference microchannel. We also discuss the critical values of dimensionless variables that distinguish the three particle flow types for both improved and reference microchannels.     

Analytical investigation of the feasibility of sacrificial microchannel sealing for Chip-Scale Atomic Magnetometers

An alkali metal vapor cell is a crucial component of the highly sensitive Chip Scale Atomic Magnetometers (CSAMs) that are increasingly deployed in a variety of electronic devices. Herein, we propose a novel microfabrication technique utilizing an array of microchannels at a bonded interface, to enable gas feedthrough for evacuation of unwanted gases from a vapor cell and subsequent introduction of an inert gas, followed by permanent sealing of the microchannels by reflow of a glass frit. The characteristics of glass frit reflow are analyzed to investigate the feasibility of using microchannels formed either on a silicon substrate, or embedded in a glass frit layer, with four different cross-sectional shapes considered. Prior to modeling the microchannels for simulation, the minimum cross-sectional size of a microchannel that fulfills gas feedthrough requirements was calculated and a value of 10 μm was determined based on a flow conductance model. The sealing of the microchannels was simulated using the finite element method (FEM) and the results revealed that flow resistance is a crucial design factor. Thus, embedded microchannel designs were more suitable for the proposed sealing technique than microchannel designs fabricated in silicon.     

Enhanced size-dependent trapping of particles using microvortices

Inertial microfluidics has been attracting considerable interest for size-based separation of particles and cells. The inertial forces can be manipulated by expanding the microchannel geometry, leading to formation of microvortices for selective isolation and trapping of particles or cells from a mixture. In this work, we aim to enhance our understanding of particle trapping in such microvortices by developing a model of selective particle entrapment. Design and operational parameters including flow conditions, size of the trapping region, and target particle concentration are explored to elucidate their influence on trapping behavior. Our results show that the size dependence of trapping is characterized by a threshold Reynolds number, which governs the selective entry of particles into microvortices from the main flow. We show that concentration enhancement on the order of 100,000× and isolation of targets at concentrations as low as 1/mL is possible. Ultimately, the insights gained from our systematic investigation suggest optimization solutions that enhance device performance (efficiency, size selectivity, and yield) and are applicable to selective isolation and trapping of large rare cells as well as other applications.     

Slow viscous flow around two particles in a cylinder

This article describes the motion of two arbitrarily located free moving particles in a cylindrical tube with background Poiseuille flow at low Reynolds number. We employ the Lamb’s general solution based on spherical harmonics and construct a framework based on cylindrical harmonics to solve the flow field around the particles and the flow within the tube, respectively. The two solutions are performed in an iterated framework using the method of reflections. We compute the drag force and torque coefficients of the particles which are dependent on the distances among the cylinder wall and the two particles. In addition, we provide detailed flow field in the vicinity of the two particles including streamlines and velocity contour. Our analysis reveals that the particle–particle interaction can be neglected when the separation distance is three times larger than the sum of particles radii when the two particles are identical. Furthermore, the direction of Poiseuille flow, the particle position relative to the axis and the particle size can make the two particles attract or repel. Unlike the single particle case, the two particles can move laterally due to the hydrodynamic interaction. Such analysis can give insights to understand the mechanisms of collision and aggregation of particles in microchannels.     

Tracking microparticle motions in three-dimensional flow around a microcubic array fabricated on the wall surface

This paper describes the application of a microscopic defocusing image system to track 3D particle motions in microflow around a microcubic array near a microchannel wall surface. The measurement principle and calibration method were evaluated to provide accurate 3D microparticle location. Particle trajectories were measured in two microchannels. Measured velocity profiles of Hele–Shaw flows for two Reynolds numbers agreed well with theoretical profiles. Three-dimensional particle tracking in fluid flow around a microcubic array exhibited quasi-periodic and non-periodic trajectory modes. The experimental results indicated that 3D particle motions are spatially and time dependent even when the flow rate is constant, and microparticle trajectories may deviate from steady flow streamlines.     

Analysis of combined pressure-driven electroosmotic flow through square microchannels

In this paper three-dimensional single-phase liquid flow through microchannels with a square-shaped cross-section driven by simultaneous application of pressure gradient and electroosmotic pumping mechanism is studied. The governing system of equations consists of the electric potential field and flow field equations. The solution procedure involves three steps. First, the net charge distribution on the cross-section of the microchannel is computed by solving two-dimensional Poisson–Boltzmann equation using the finite element method. Then, using the computed fluid’s charge distribution, the magnitude of the resulting body force due to interaction of an external electric field with the charged fluid particles is calculated along the microchannel. In the third step, the flow equations are solved by considering three-dimensional Navier–Stokes equations with an electrokinetic body force. The computations reveal that the flow pattern in the microchannel is significantly different from the parabolic velocity profile of the laminar pressure-driven flow. The effect of the liquid bulk ionic concentration and the external electric field strength on flow patterns through the square-shaped microchannels is also investigated.     

Dielectrophoresis in aqueous suspension: impact of electrode configuration

Dielectrophoresis (DEP) allows to moving neutral or charged particles in liquids by supplying a non-uniform electric field. When using alternating current and insulated electrodes, this is possible in conducting media such as aqueous solutions. However, relatively high field strength is required that is discussed to induce also an undesired Joule heating effect. In this paper, we demonstrate boundary conditions for avoiding this side effect and suggest a novel design of an interdigitated electrode (IDE) configuration to reduce the power consumption. Numerical simulation using OpenFOAM demonstrated that, when replacing conventional plate IDE by cylindrical micro-IDE in microchannel systems, the dielectrophoretic force field, i.e., the electric field gradient squared, becomes stronger and more homogeneously distributed along the electrodes array. Also the resulting particle DEP velocities were highest for the cylindrical IDE. The simulations were experimentally confirmed by measuring velocity of resin particle located at the subsurface of demineralized water. Surprisingly the fluid flow induced by electrothermal effect turned out to be negligible in microchannels when compared to the DEP effect and becomes dominant only for distances between particle and IDE larger than 6,000 μm. The well-agreed experimental and simulation results allow for predicting particle motion. This can be expected to pave the way for designing DEP microchannel separators with high throughput and low energy consumption.     

Analysis and experiment of transient filling flow into a rectangular microchannel on a rotating disk

In order to predict the time-dependent behaviors of the moving front in lab-on-a-CD systems or centrifugal pumping, an analytical expression and experimental methods of centrifugal-force-driven transient filling flow into a rectangular microchannel in centrifugal microfluidics are presented in this paper. Considering the effect of surface tension, and neglecting the effect of Coriolis force, the velocity profile, flow rate, the moving front displacement and the pressure distribution along the microchannel are characterized. Experiments are carried out using the image-capturing unit to measure the shift of the flow in rectangular microchannels. The flow characteristics in rectangular microchannels with different cross-sectional dimensions (200, 300 and 400 μm in width and 140, 240 and 300 μm in depth) and length (18 and 25 mm) under different rotational speed are investigated. According to the experimental data, the model can be more reasonable to predict the flow displacement with time, and the errors between theoretical and the experimental will decrease with increasing the cross-section size of the microchannel.     

Self-ordered particle trains in inertial microchannel flows

Controlling the transport of particles in flowing suspensions at microscale is of interest in numerous contexts such as the development of miniaturized and point-of-care analytical devices (in bioengineering, for foodborne illnesses detection, etc.) and polymer engineering. In square microchannels, neutrally buoyant spherical particles are known to migrate across the flow streamlines and concentrate at specific equilibrium positions located at the channel centerline at low flow inertia and near the four walls along their symmetry planes at moderate Reynolds numbers. Under specific flow and geometrical conditions, the spherical particles are also found to line up in the flow direction and form evenly spaced trains. In order to statistically explore the dynamics of train formation and their dependence on the physical parameters of the suspension flow (particle-to-channel size ratio, Reynolds number and solid volume fraction), experiments have been conducted based on in situ visualizations of the flowing particles by optical microscopy. The trains form only once particles have reached their equilibrium positions (following lateral migration). The percentage of particles in trains and the interparticle distance in a train have been extracted and analyzed. The percentage of particles organized in trains increases with the particle Reynolds number up to a threshold value which depends on the concentration and then decreases for higher values. The average distance between the surfaces of consecutive particles in a train decreases as the particle Reynolds number increases and is independent of the particles size and concentration, if the concentration remains below a threshold value related to the degree of confinement of the suspension flow.     

Inertially focused diamagnetic particle separation in ferrofluids

Continuous flow separation of target particles from a mixture is essential to many chemical and biomedical applications. There has recently been an increasing interest in the integration of active and passive particle separation techniques for enhanced sensitivity and flexibility. We demonstrate herein the proof-of-concept of a ferrofluid-based hybrid microfluidic technique that combines passive inertial focusing with active magnetic deflection to separate diamagnetic particles by size. The two operations take place in series in a continuous flow through a straight rectangular microchannel with a nearby permanent magnet. We also develop a three-dimensional numerical model to simulate the transport of diamagnetic particles during their inertial focusing and magnetic separation processes in the entire microchannel. The predicted particle trajectories are found to be approximately consistent with the experimental observations at different ferrofluid flow rates and ferrofluid concentrations.     

Flow-induced deformation of compliant microchannels and its effect on pressure–flow characteristics

We report theoretical and experimental investigations of flow through compliant microchannels in which one of the walls is a thin PDMS membrane. A theoretical model is derived that provides an insight into the physics of the coupled fluid–structure interaction. For a fixed channel size, flow rate and fluid viscosity, a compliance parameter \(f_{\text{p}}\) is identified, which controls the pressure–flow characteristics. The pressure and deflection profiles and pressure–flow characteristics of the compliant microchannels are predicted using the model and compared with experimental data, which show good agreement. The pressure–flow characteristics of the compliant microchannel are compared with that obtained for an identical conventional (rigid) microchannel. For a fixed channel size and flow rate, the effect of fluid viscosity and compliance parameter \(f_{\text{p}}\) on the pressure drop is predicted using the theoretical model, which successfully confront experimental data. The pressure–flow characteristics of a non-Newtonian fluid (0.1 % polyethylene oxide solution) through the compliant and conventional (rigid) microchannels are experimentally measured and compared. The results reveal that for a given change in the flow rate, the corresponding modification in the viscosity due to the shear thinning effect determines the change in the pressure drop in such microchannels.