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.     

Microfluidic separation of magnetic particles with soft magnetic microstructures

This paper demonstrates simple and cost-effective microfluidic devices for enhanced separation of magnetic particles by using soft magnetic microstructures. By injecting a mixture of iron powder and polydimethylsiloxane (PDMS) into a prefabricated channel, an iron–PDMS microstructure was fabricated next to a microfluidic channel. Placed between two external permanent magnets, the magnetized iron–PDMS microstructure induces localized and strong forces on the magnetic particles in the direction perpendicular to the fluid flow. Due to the small distance between the microstructure and the fluid channel, the localized large magnetic field gradients result a vertical force on the magnetic particles, leading to enhanced separation of the particles. Numerical simulations were developed to compute the particle trajectories and agreed well with experimental data. Systematic experiments and numerical simulation were conducted to study the effect of relevant factors on the transport of superparamagnetic particles, including the shape of iron–PDMS microstructure, mass ratio of iron–PDMS composite, width of the microfluidic channel, and average flow velocity.     

Lagrangian particle model for multiphase flows

A Lagrangian particle model for multiphase multicomponent fluid flow, based on smoothed particle hydrodynamics (SPH), was developed and used to simulate the flow of an emulsion consisting of bubbles of a non-wetting liquid surrounded by a wetting liquid. In SPH simulations, fluids are represented by sets of particles that are used as discretization points to solve the Navier-Stokes fluid dynamics equations. In the multiphase multicomponent SPH model, a modified van der Waals equation of state is used to close the system of flow equations. The combination of the momentum conservation equation with the van der Waals equation of state results in a particle equation of motion in which the total force acting on each particle consists of many-body repulsive and viscous forces, two-body (particle-particle) attractive forces, and body forces such as gravitational forces. Similar to molecular dynamics, for a given fluid component the combination of repulsive and attractive forces causes phase separation. The surface tension at liquid-liquid interfaces is imposed through component dependent attractive forces. The wetting behavior of the fluids is controlled by phase dependent attractive interactions between the fluid particles and stationary particles that represent the solid phase. The dynamics of fluids away from the interface is governed by purely hydrodynamic forces. Comparison with analytical solutions for static conditions and relatively simple flows demonstrates the accuracy of the SPH model.     

Computational and performance analysis of a continuous magnetophoretic bioseparation chip with alternating magnetic fields

This paper presents the modeling and optimization of a magnetophoretic bioseparation chip for isolating cells, such as circulating tumor cells from the peripheral blood. The chip consists of a continuous-flow microfluidic platform that contains locally engineered magnetic field gradients. The high-gradient magnetic field produced by the magnets is spatially non-uniform and gives rise to an attractive force on magnetic particles flowing through a fluidic channel. Simulations of the particle–fluid transport and the magnetic force are performed to predict the trajectories and capture lengths of the particles within the fluidic channel. The computational model takes into account key forces, such as the magnetic and fluidic forces and their effect on design parameters for an effective separation. The results show that the microfluidic device has the capability of separating various cells from their native environment. An experimental study is also conducted to verify and validate the simulation results. Finally, to improve the performance of the separation device, a parametric study is performed to investigate the effects of the magnetic bead size, cell size, number of beads per cell, and flow rate on the cell separation performance.     

Lift and multiple equilibrium positions of a single particle in Newtonian and Oldroyd-B fluids

A heavy particle is lifted from the bottom of a channel in a plane Poiseuille flow when the Reynolds number is larger than a critical value. In this paper we obtain correlations for lift-off of particles in Oldroyd-B fluids. The fluid elasticity reduces the critical shear Reynolds number for lift-off. The effect of the gap size between the particle and the wall, on the lift force, is also studied. A particle lifted from the channel wall attains an equilibrium height at which its buoyant weight is balanced by the hydrodynamic lift force. Choi and Joseph [Choi HG, Joseph DD. Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation. J Fluid Mech 2001;438:101-128] first observed multiple equilibrium positions for a particle in Newtonian fluids. We report several new results for the Newtonian fluid case based on a detailed study of the multiple equilibrium solutions, e.g. we find that at a given Reynolds number there are regions inside the channel where no particle, irrespective of its weight, can attain a stable equilibrium position. This would result in particle-depleted zones in channels with Poiseuille flows of a dilute suspension of particles of varying densities. Multiple equilibrium positions of particles are also found in Oldroyd-B fluids. All the results in this paper are based on 2D direct numerical simulations.     

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.     

An immersed boundary method based on the lattice Boltzmann approach in three dimensions,with application

The immersed boundary (IB) method originated by Peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid. The Navier–Stokes (N–S) equations in the IB method are usually solved using numerical methods such as FFT and projection methods. Here in our work, the N–S equations are solved by an alternative approach, the lattice Boltzmann method (LBM). Compared to many conventional N–S solvers, the LBM can be easier to implement and more convenient for modeling additional physics in a problem. This alternative approach adds extra versatility to the immersed boundary method. In this paper we discuss the use of a 3D lattice Boltzmann model (D3Q19) within the IB method. We use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3D channel and determine a drag scaling law for the sheet. Our main conclusions are: (1) the hybrid method is convergent with first-order accuracy which is consistent with the immersed boundary method in general; (2) the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow.     

Mathematical modelling of tidal currents in mangrove forests

The effects of mangrove forests on the flow structure in estuaries have been studied in this paper. An existing two-dimensional depth-integrated mathematical model has been refined to include both the effects of drag force induced by mangrove trees and the blockage effects on the mass fluxes through mangrove forests. To investigate the influence of mangrove trees on the flow structure two idealised cases have been considered. These include: (i) steady channel flow, with mangrove trees distributed within the middle reach of the channel along both sides, and (ii) tidal flow in a straight creek, fringed by mangrove swamps. Comparisons of velocity profiles at a cross-section for the case of steady channel flow, and of the time series of velocities in both the creek and its floodplain for the case of tidal flow in the straight creek–mangrove swamp system, have been undertaken. Six cases of different diameters and densities of mangrove trees have been studied to examine the significance of the drag force and blockage on the flow structure in the mangrove swamp system. It was found that mangrove trees have a significant impact on the flow structure in a mangrove system. The drag force induced by the mangrove trees plays a key role, and the blockage from the mangrove trees also plays an important role when the porosity of the mangrove trees is less than 0.8. The model has also been applied to simulate tidal flows in the Merbok Estuary, Malaysia. Simulations have been undertaken, both with and without mangrove tree effects, as well as for an extreme case of complete removal of mangrove areas from flooding, termed ‘complete bunding’, to study the effects of the mangrove trees on the hydrodynamic processes in the basin. The results show that the model provides an ideal management tool for mangrove systems.     

Theoretical analysis of a new, efficient microfluidic magnetic bead separator based on magnetic structures on multiple length scales

We present a theoretical analysis of a new design for microfluidic magnetic bead separation. It combines an external array of mm-sized permanent magnets with magnetization directions alternating between up and down with μm-sized soft magnetic structures integrated in the bottom of the separation channel. The concept is studied analytically for simple representative geometries and by numerical simulation of an experimentally realistic system geometry. The array of permanent magnets provides long-range magnetic forces that attract the beads to the channel bottom, while the soft magnetic elements provide strong local retaining forces that prevent captured beads from being torn loose by the fluid drag. The addition of the soft magnetic elements increases the maximum retaining force by two orders of magnitude. The design is scalable and provides an efficient and simple solution to the capture of large amounts of magnetic beads on a microsystem platform.     

Size-dependent microparticles separation through standing surface acoustic waves

This study presents a method that uses a standing surface acoustic wave (SSAW) to continuously separate particles in a size-gradient manner in a microchannel flow. The proposed method was applied to a colloidal suspension containing poly dispersed particles with three different sizes (1, 5, and 10 μm) but the same density and compressibility. Particle suspension was focused hydrodynamically at an entrance region, and particles were forced actively toward the side wall where SSAW-pressure nodes were generated by two interdigital transducers (IDTs) across the channel. The particles placed in the middle stream, in which the shear rate was minimized, were separated successfully in a size-gradient manner by acoustic force. In addition, this study further developed an analytical model to predict the displacement of particles in microchannel flow by considering viscous, acoustic, and diffusive forces. The predicted values of particle displacement showed excellent agreement with the experimental results, and diffusion was found to be important and not negligible. The advantage of this method is to minimize the shear rate on particles, which would be useful for potential applications of shear-dependent cells such as platelets.     

Cell separation in a microfluidic channel using magnetic microspheres

Magnetophoretic isolation of biological cells in a microfluidic environment has strong relevance in biomedicine and biotechnology. A numerical analysis of magnetophoretic cell separation using magnetic microspheres in a straight and a T-shaped microfluidic channel under the influence of a line dipole is presented. The effect of coupled particle–fluid interactions on the fluid flow and particle trajectories are investigated under different particle loading and dipole strengths. Microchannel flow and particle trajectories are simulated for different values of dipole strength and position, particle diameter and magnetic susceptibility, fluid viscosity and flow velocity in both the microchannel configurations. Residence times of the captured particles within the channel are also computed. The capture efficiency is found to be a function of two nondimensional parameters, α and β. The first parameter denotes the ratio of magnetic to viscous forces, while the second one represents the ratio of channel height to the distance of the dipole from the channel wall. Two additional nondimensional parameters γ (representing the inverse of normalized offset distance of the dipole from the line of symmetry) and σ (representing the inverse of normalized width of the outlet limbs) are found to influence the capture efficiency in the T-channel. Results of this investigation can be applied for the selection of a wide range of operating and design parameters for practical microfluidic cell separators.     

Flow field analysis in a spiral viscous micropump

The paper presents a stream function solution and a computational analysis for the flow field of a viscous spiral pump, which employs a rotating spiral channel to achieve pumping action. This pump is fabricated using surface micromachining technology. The stream function solution employs a simplified 2D model for the flow field in its spiral channel that neglects the curvature of the spiral, and replaces it with an equivalent straight channel. The effect of spiral wall height on flow rate is analyzed and discussed. 3D computational analyses are obtained and are compared with analytical predictions.     

Three-dimensional microscale flow simulation and colloid transport modeling in saturated soil porous media

Transport of sub-micron colloid particles in soil porous media has been mostly studied numerically with unit-cell-based grain-scale geometries. In this study, we develop a more general approach by combining a multiple-grain pore-scale flow simulation with Lagrangian tracking of individual colloids. First, two numerical methods are applied simultaneously to solve viscous flows in a channel partially or fully packed with spherical grain particles, this allows cross-validation of the numerical methods for considered model geometries. It is demonstrated that the mesoscopic lattice Boltzmann approach can more accurately simulate three-dimensional pore-scale flows with multiple grain–grain and grain–wall contact points. Colloid transport is simulated under the combined influence of hydrodynamic forces, Brownian force, and physicochemical forces. Preliminary results demonstrate the capture of colloids by the secondary energy minimum (SEM) well. The local hydrodynamic retardation is shown to reduce the ability for colloids to move into the SEM well, but does not prevent this. Trajectories before and after the capture are also discussed.     

Optical separation of droplets on a microfluidic platform

This paper describes the optical separation of microdroplets according to their refractive indices. The behavior of the droplets was characterized in terms of the optical force and the hydrodynamic effects present upon illumination of the droplets in a direction normal to the flow direction in a rectangular microfluidic channel. The optical forces acting on the droplets and the resultant droplet trajectories were analyzed and compared with the numerically predicted values. The relationship between the drag force and optical force was examined to understand the system performance properties in the context of screening applications involving the removal of unwanted droplets. Two species of droplets were compared for their photophoretic displacements by varying the illumination intensity. Because the optical forces exerted on the droplets were functions of the refractive indices and sizes of the droplets, a variety of chemical species could be separated simultaneously.     

Flow control for cell growth by movement of magnetic particles utilizing electromagnetic force

Three-dimensional (3D) cell structures are required to fabricate artificial organ. Inkjet technology is applied for fabrication of 3D cell structures in order to fabricate artificial organ and investigate biochemical characteristics of cells in 3D cell structures. Usually cells located inside 3D cell structures get nutrition via blood vessels. In case that there are no blood vessels in the 3D cell structures, cells located inside the 3D cell structures will die of nutrition shortage. So, blood vessels are essential to fabricate 3D cell structures. When the amount and flow of nutrition is controlled, growth speed of cells will be changed. We control the flow around the cells utilizing magnetic particles and magnetic force. The magnetic particles are installed in the dish that is filled with medium, nutrition and living cells. When the magnetic particles are trapped and transported by magnetic force, the cell growth will be controlled. In this paper, we challenge to control the flow utilizing magnetic particles and magnetic force.     

Dynamic adhesion characterization of cancer cells under blood flow-mimetic conditions: effects of cell shape and orientation on drag force

Cell adhesion to and detachment from the endothelium plays an essential role in numerous biological processes such as cancer cell metastasis, cell migration, and cell–cell communication. However, little is known about the effect of cell shape and orientation on the drag force leading to cell detachment. To further investigate these factors, we cultured cancer cells in a microfluidic channel, and recorded the shape and orientation of the cells under constant fluid flow rate. Results showed that cell morphology varied dynamically with respect to time. In particular, we discovered two distinct shapes of cells at the moment of detachment: the circular shape, and the elongated shape whose long axis is perpendicular to the flow. Based on the experimental observations, we designed and reconstructed two cellular solid models (a hemispherical model and an elongated model) to calculate the drag force using a finite-element method. The hemispherical model yielded much higher pressure drag force than that of the elongated models irrespective of orientation, though the total drag force of the hemispherical model was slightly lower. We also examined the effect of the orientation on the drag force using five different orientations to the flow. The cells of which the long axes were perpendicular to the flow exhibited larger pressure drag force than cells oriented in other directions, though the friction drag force was comparable. In summary, when cells detach from the surface, the fraction of the pressure force becomes larger, demonstrating the determinative role of cell adhesion and/or detachment. Significantly, our observation that two cancer cell subpopulations exist exhibiting different morphological dynamics and required drag forces for detachment implies redundant mechanisms for cancer cells to achieve the transition from the adherent type to the circulating type during metastasis.     

Dynamic motion analysis of magnetic particles in microfluidic systems under an external gradient magnetic field

To gain an insightful understanding of motion behavior of paramagnetic particles suspended in a nonmagnetic fluid under a gradient magnetic field, a coupled fluid–structure model based on a direct numerical scheme is developed in this work. The governing equations of magnetic field, fluid flow field and particle motion are simultaneously solved using an Arbitrary Lagrangian–Eulerian method, taking into account magnetic and hydrodynamic interactions between particles in a fully coupled manner. The accuracy of the proposed method is validated using the magnetic particulate flows of two particles under a uniform magnetic field as the test problem and is then applied to investigate effects of magnetic and hydrodynamic interactions between particles on the particle motion behavior. Results show that neighboring magnetic particles are easy to form chain-like clusters along field direction due to magnetic interactions between particles and then move together toward the surface of magnetic source under the action of gradient magnetic force. More importantly, it has been found that both magnetic and hydrodynamic interactions between particles are conducive to the acceleration of particles and the chain formation of particles. The present method and results could help in understanding the basic mechanism underlying the low-gradient magnetophoretic separation process and designing magnetic aggregate-based microfluidic devices.     

The modeling of colloidal fluids by the real-coded lattice gas

We model colloid-dispersed fluids using the real-coded lattice gas, in which colloidal particles are treated as hard spheres interacting with solvents of the lattice gas particles. We simulate the Brownian motion of a colloidal particle and compare its velocity distribution with that from the theoretical prediction. Both agree well showing that thermal fluctuation is naturally incorporated. We also measured the drag force acting on a colloidal particle and compare the drag coefficient with existing data. It is found that higher space and time resolutions are required in order to model the correct colloidal fluids interactions.     

Numerical simulation of Newtonian and non-Newtonian flows in bypass

This paper deals with the numerical solution of Newtonian and non-Newtonian flows with biomedical applications. The flows are supposed to be laminar, viscous, incompressible and steady or unsteady with prescribed pressure variation at the outlet. The model used for non-Newtonian fluids is a variant of power law. Governing equations in this model are incompressible Navier–Stokes equations. For numerical solution we use artificial compressibility method with three stage Runge–Kutta method and finite volume method in cell centered formulation for discretization of space derivatives. The following cases of flows are solved: steady Newtonian and non-Newtonian flow through a bypass connected to main channel in 2D, steady Newtonian flow in angular bypass in 3D and unsteady non-Newtonian flow through bypass in 2D. Some 2D and 3D results that could have application in the area of biomedicine are presented.     

Separation of highly viscous fluid threads in branching microchannels

We experimentally study the transport properties of threads made of high-viscosity fluids flowing in a sheath of miscible, low-viscosity fluids in bifurcating microchannels. A viscous filament is generated using a square hydrodynamic focusing section by injecting a ‘thick’ fluid into the central channel and a ‘thin’ fluid from the side channels. This method allows us to produce miscible fluid threads of various sizes and lateral positions in a straight channel and enables the systematic study of the downstream thread’s response to flow partitioning in branching microfluidic networks at low Reynolds numbers. A phase diagram detailing the various flow patterns observed at the first bifurcation, including thread folding, transport, and fouling, is presented along with transition lines. We also examine the role of viscous buckling instabilities on thread behavior and the formation of complex viscous mixtures and stratifications at the small scale. This work shows the possibility to finely control thread trajectory and stability as well as manipulate the structural arrangement of high-viscosity multiphase flows in complex microfluidic systems.