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.     

Numerical investigation of dynamics of elliptical magnetic microparticles in shear flows

We study the rotational dynamics of magnetic prolate elliptical particles in a simple shear flow subjected to a uniform magnetic field, using direct numerical simulations based on the finite element method. Focusing on paramagnetic and ferromagnetic particles, we investigate the effects of the magnetic field strength and direction on their rotational dynamics. In the weak field regime (below a critical field strength), the particles are able to perform complete rotations, and the symmetry property of particle rotational speed is influenced by the direction and strength of the magnetic field. In the strong field regime (above a critical strength), the particles are pinned at steady angles. The steady angle depends on both the direction and strength of the magnetic field. Our results show that paramagnetic and ferromagnetic particles exhibit markedly different rotational dynamics in a uniform magnetic field. The numerical findings are in good agreement with theoretical prediction. Our numerical investigation further reveals drastically different lateral migration behaviors of paramagnetic and ferromagnetic particles in a wall-bounded simple shear flow under a uniform magnetic field. These two kinds of particles can thus be separated by combining a shear flow and a uniform magnetic field. We also study the lateral migration of paramagnetic and ferromagnetic particles in a pressure-driven flow (a more practical flow configuration in microfluidics), and observe similar lateral migration behaviors. These findings demonstrate a simple but useful way to manipulate non-spherical microparticles in microfluidic devices.     

A rapid magnetic particle driven micromixer

Performances of a magnetic particle driven micromixer are predicted numerically. This micromixer takes advantages of mixing enhancements induced by alternating actuation of magnetic particles suspended in the fluid. Effects of magnetic actuation force, switching frequency and channel’s lateral dimension have been investigated. Numerical results show that the magnetic particle actuation at an appropriate frequency causes effective mixing and the optimum switching frequency depends on the channel’s lateral dimension and the applied magnetic force. The maximum efficiency is obtained at a relatively high operating frequency for large magnetic actuation forces and narrow microchannels. If the magnetic particles are actuated with a much higher or lower frequency than the optimum switching frequency, they tend to add limited agitation to the fluid flow and do not enhance the mixing significantly. The optimum switching frequency obtained from the present numerical prediction is in good agreement with the theoretical analysis. The proposed mixing scheme not only provides an excellent mixing, even in simple microchannel, but also can be easily applied to lab-on-a-chip applications with a pair of external electromagnets.     

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.     

Numerical study of an explosion in a non-homogeneous medium with and without magnetic fields

A version of the two step Lax-Wendroff difference method with second order accuracy is used to seek solutions of the unsteady magnetohydrodynamic (MHD) equationsfor the study of an explosion in a non-homogeneous medium with and without magnetic fields. The explosion is initiated by introducing a finite amount of energy in a small volume of gas which leads to an instantaneous increase of gas temperature. Two types of magnetic field configurations (i.e. open and closed) are considered to illustrate the dependence and differences of magnetic and a non-magnetic flow motion. Numerical results show the strong dependence of induced MHD flow field on the magnetic field configuration and strength. The development and decay of the fast and slow MHD shock waves, as well as the ordinary gasdynamic shock waves, are also represented well by the present computer simulations. In conclusion, we have demonstrated that the numerical scheme we have used is a reliable one for studying 2-dimensional MHD problems in non-homogeneous medium.     

Effects of particle–fluid coupling on particle transport and capture in a magnetophoretic microsystem

A numerical analysis is presented of the effects of particle–fluid coupling on the transport and capture of magnetic particles in a microfluidic system under the influence of an applied magnetic field. Particle motion is predicted using a computational fluid dynamic CFD-based Lagrangian–Eulerian approach that takes into account dominant particle forces as well as two-way particle–fluid coupling. Two dimensionless groups are introduced that characterize particle capture, one that scales the magnetic and hydrodynamic forces on the particle and another that scales the distance to the magnetic field source. An analysis is preformed to parameterize capture efficiency with respect to the dimensionless numbers for both one-way and two-way particle–fluid coupling. For one-way coupling, in which the flow field is uncoupled from particle motion, correlations are developed that provide insight into system performance towards optimization. The difference in capture efficiency for one-way versus two-way coupling is analyzed and quantified. The analysis demonstrates that one-way coupling, in the dilute limit, provides a conservative estimate of capture efficiency in that it overpredicts the magnetic force needed to ensure particle capture as compared with a more rigorous fully coupled analysis. In two-way coupling there is a cooperative effect between the magnetic force and a particle-induced fluidic force that enhances capture efficiency. Thus, while one-way coupling is useful for rapid parametric screening of particle capture performance, more accurate predictions require two-way particle–fluid coupling. This is especially true when considering higher capture efficiencies and/or higher particle concentrations.     

Numerical simulation of two-phase flows in the presence of a magnetic field

A set of non-dimensional model equations, which can simulate incompressible, immiscible two-phase flows in the presence of a magnetic field, has been derived and solved numerically with a finite difference method using the HSMAC algorithm. In this study, dynamics of a falling droplet of liquid metal into a horizontal liquid metal layer and of a rising air bubble in water subject to a magnetic field are presented as examples. The numerical results reveal that the Lorentz force acts to dampen the motion of electric conducting fluid as the Hartmann number increases. On the other hand, even for ordinary non-conducting fluids such as water and air, a substantial body force due to magnetization influences the air bubble behaviour in water under a gradient magnetic field.     

Mathematical modelling for pulsatile flow of Casson fluid along with magnetic nanoparticles in a stenosed artery under external magnetic field and body acceleration

In the present paper, the magnetohydrodynamics effects on flow parameters of blood carrying magnetic nanoparticles flowing through a stenosed artery under the influence of periodic body acceleration are investigated. Blood is assumed to behave as a Casson fluid. The governing equations are nonlinear and solved numerically using finite difference schemes. The effects of stenotic height, yield stress, magnetic field, particle concentration and mass parameters on wall shear stress, flow resistance and velocity distribution are analysed. It is found that wall shear stress and flow resistance values are considerably enhanced when an external magnetic field is applied. The velocity values of fluid and particles are appreciably reduced when a magnetic field is applied on the model. It is significant to note that the presence of nanoparticles, magnetic field and yield stress tend to increase the plug core radius. Increased wall shear stress and flow resistance affects the circulation of blood in the human cardiovascular system. The results obtained from the study can be used in normalizing the values of the model parameters and hence can be used for medical applications. The presence of magnetic field helps to slow down the flow of fluid and magnetic particles associated with it. The magnetic particles of nanosize developed in recent days are biodegradable and used in biomedical applications. Biomagnetic principles and biomagnetic particles as drug carriers are used in cancer treatments.

     

An efficient and robust method for Lagrangian magnetic particle tracking in fluid flow simulations on unstructured grids

In this paper we report on a newly developed particle tracking scheme for fluid flow simulations on 3D unstructured grids, aiming to provide detailed insights in the particle behaviour in complex geometries. A possible field of applications is the magnetic drug targeting (MDT) technique, on which this paper will be focused. MDT is a promising medical technique that uses locally applied magnetic fields to capture magnetic drug carriers at the desired locations in the human body, strongly increasing the efficiency of medical drugs. The new particle tracking scheme combines the advantages of existing methods and is easy for implementation in a generic numerical code. The scheme is tested and validated for simple MDT cases that include effects of a non-homogeneous magnetic field on deposition of magnetic particles in laminar flow. The first test case is a validation study of the magnetic particle trajectories released in a horizontal circular pipe flow with a current-carrying wire parallel to the flow, for which analytical solutions are reported in literature. The second test case involves particle capture efficiencies in a 90° bent tube for different configurations of the imposed magnetic field. This configuration corresponds more closely to the conditions inside blood vessels, because of the presence of secondary motions. These results are compared with numerical studies from literature too. The obtained results demonstrate that the developed particle tracking scheme is a very robust, efficient and accurate method, which can give detailed insights in particle behaviour in complex geometries. As such it is a good candidate for future applications and optimisations of MDT technique for loco-regional cancer treatment or treatment of cardiovascular diseases.     

Numerical study of unsteady hydromagnetic Generalized Couette flow of a reactive third-grade fluid with asymmetric convective cooling

Unsteady hydromagnetic Generalized Couette flow and heat transfer characteristics of a reactive variable viscosity incompressible electrically conducting third grade fluid in a channel with asymmetric convective cooling at the walls in the presence of uniform transverse magnetic field is studied. It is assumed that the chemical kinetics in the flow system is exothermic and the convective heat transfer at the channel surface with the surrounding environment follow the Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using an unconditionally stable and convergent semi-implicit finite difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system.     

Magnetophoretic mixing for in situ immunochemical binding on magnetic beads in a microfluidic channel

Functionalized magnetic beads offer promising solutions to a host of micro-total analysis systems ranging from immunomagnetic biosensors to cell separators. Immunochemical binding of functional biochemical agents or target biomolecules serves as a key step in such applications. Here we show how magnetophoretic motion of magnetic microspheres in a microchannel is harnessed to promote in situ immunochemical binding of short DNA strands (probe oligonucleotide) on the bead surface via streptavidin–biotin bonds. Using a transverse magnetic field gradient, the particles are transported across a co-flowing analyte stream containing biotinylated probe oligonucleotides that are labeled with a Cy3-fluorophore. Quantification of the resulting biotin–streptavidin promoted binding has been achieved through fluorescence imaging of the magnetophoretically separated magnetic particles in a third stream of phosphate buffered saline. Both the experimental and numerical data indicate that for a given flow rate, the analyte binding per bead depends on the flow fraction of the co-flowing analyte stream through the microchannel, but not on the fluid viscosity. Parametric studies of the effects of fluid viscosity, analyte flow fraction, and total flow rate on the extent of binding and the overall analyte separation rate are also conducted numerically to identify favorable operating regimes of a flow-through immunomagnetic separator for biosensing, cell separation, or high-throughput applications.     

Eccentric electrophoretic motion of a sphere in circular cylindrical microchannels

The eccentric electrophoretic motion of a spherical particle in an aqueous electrolyte solution in circular cylindrical microchannels is studied in this paper. The objective is to investigate the influences of separation distance and channel size on particle motion. A theoretical model is developed to describe the electric field, the flow field and the particle motion. A finite element based direct numerical simulation method is employed to solve the model. Numerical results show that, when the particle is eccentrically positioned in the channel, the electric field and the flow field are not symmetric, and the strongest electric field and the highest flow velocity occur in the small gap region. It is shown that the rotational velocity of the particle increases with the decrease of the separation distance. With the decrease of the separation distance, the translational velocity increases in a smaller channel; while it decreases first and then increases in a relatively large channel. When a particle moves eccentrically at a smaller separation distance from the channel wall, both the translational velocity and the rotational velocity increase with the decrease of the channel size.     

A chaotic mixer for magnetic bead-based micro cell sorter

An efficient magnetic force driven mixer with simple configuration is designed, fabricated, and tested. It is designed to facilitate the mixing of magnetic beads and biomolecules in a microchannel, where mixing is unavoidably inefficient due to its low Reynolds number. With appropriate temporal variations of the force field, chaotic mixing is achieved, hence the mixing becomes effective. The mixing device consists of embedded microconductors as a magnetic field source and a microchannel that guides the streams of working fluid. It is demonstrated that a pair of integrated micro conductors provides a local magnetic field strong enough to attract nearby magnetic beads. Mixing of magnetic beads is accomplished by applying a time-dependent control signal to a row of conductors, at the Reynolds number of as low as 10/sup -2/. Two-dimensional numerical simulation has been performed to design the configuration of the channel and electrodes, which creates chaotic motion of beads. It is found that a simple two-dimensional serpentine channel geometry with the transverse electrodes is able to create the stretching and folding of material lines, which is a manifestation of chaos. The mixing pattern predicted by the simulation has been confirmed by both flow visualization and PTV (particle tracking velocimetry) in the chaotic mixer fabricated, which should greatly increase the attachment of beads onto the target biomolecules. The optimum frequency of applied control signal is searched by evaluating the Lyapunov exponent in both numerical and experimental particle tracking. It is found that the range of optimum Strouhal number is 5相似文献   

Size-selective separation of magnetic nanospheres in a microfluidic channel

This paper reported an efficient method to size-selective separate magnetic nanospheres using a self-focusing microfluidic channel equipped with a permanent magnet. Under external magnetic field, the magnetophoresis force exerted on particles leads to size-dependent deflections from their laminar flow paths and results in effective particles separation. By adjusting the distance between magnet and main path of channel, we obtained two monodisperse nanosphere samples (Ca. 90 nm, Ca. 160 nm) from polydispersing particles solution whose diameters varied from 40 to 280 nm. Based on the magnetostatic and laminar flow models, numerical simulations were also used to predict and optimize the nanospheres migrations. Two thresholds of particles diameters were obtained by the simulations and diverse at each position of magnet. Therefore, appropriate position of the magnet could be determined at a certain particle sizes’ range when the flow rate of the two inlets remains unchanged.     

Deformation and migration of a leaky-dielectric droplet in a steady non-uniform electric field

This work numerically investigates the dynamics of an initially uncharged droplet freely suspended in another immiscible fluid and influenced by a steady non-uniform electric field. Both the droplet and the suspending fluid are assumed leaky dielectric. A three-dimensional spectral boundary element method is employed. It is validated by comparing with other numerical results and experimental findings for droplet deformation in a uniform electric field. This work reveals the dominant influence of the relative conductivity of fluids on the droplet migration direction in a non-uniform electric field. We have also explored the complicated behavior of the droplet deformation and speed affected by the relative permittivity and conductivity. In addition, the impact of the electric capillary number and viscosity ratio on the droplet dynamics has also been investigated. Results found and numerical algorithms developed in this study pave ways for investigations on droplet motion in an electric field created by co-planar electrodes, which has direct applications in digital microfluidics.     

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls.     

Electrophoretic motion of two spherical particles in a rectangular microchannel

The electrophoretic motion of two spherical particles in an aqueous electrolyte solution in a small rectangular microchannel was studied in this paper. A theoretical model was developed to describe the electric field, the flow field, and the particle motion. A direct numerical simulation method using the finite element method is employed to solve the model. The simulation results clearly show how the presence of one particle influences the electric field, the flow field, and the motion of the adjacent particle. Such an influence weakens with the separation distance. In addition to the zeta potentials, the particles motion depends on their sizes: the smaller particle moves slightly faster. For a faster particle moving from behind of a slower particle, the simulation results show that the faster particle will climb and then pass the slower particle when the two particles centers are not located on the same line parallel to the applied electric field.     

Dissipative particle dynamics simulation of circular and elliptical particles motion in 2D laminar shear flow

The dissipative particle dynamics (DPD) method is a relatively new computational method for modeling the dynamics of particles in laminar flows at the mesoscale. In this study, we use the DPD approach to model the motion of circular and elliptical particles in a 2D shear laminar flow. Three examples are considered: (i) evaluation of the drag force exerted on a circular particle moving in a stagnant fluid, (ii) rotation of an elliptical particle around its center in a shear flow, and (iii) motion of an ellipsoidal particle in a linear shear flow. For all cases, we found a good agreement with theoretical and finite element solutions available. These results show that the DPD method can effectively be applied to model motion of micro/nano-particles at the mesoscale. The method proposed can be used to predict the performances of intravascularly administered particles for drug delivery and biomedical imaging.     

3D-printed microfluidic manipulation device integrated with magnetic array

This paper reported a transparent, high-precision 3D-printed microfluidic device integrated with magnet array for magnetic manipulation. A reserved groove in the device can well constrain the Halbach array or conventional alternating array. Numerical simulations and experimental data indicate that the magnetic flux density ranges from 30 to 400 mT and its gradient is about 0.2–0.4 T/m in the manipulation channel. The magnetic field parameters of Halbach array in the same location are better than the other array. Diamagnetic polystyrene beads experience a repulsive force and move away from the magnetic field source under the effect of negative magnetophoresis. It is undeniable that as the flow rate increases, the ability of Halbach array to screen particle sizes decreases. Even so, it has a good particle size discrimination at a volumetric flow rate of 1.08 mL/h, which is much larger than that of a conventional PDMS device with a single magnet. The observed particle trajectories also confirm these statements. The deflection angle is related to the magnetic field, flow rate, and particle size. This 3D-printed device integrated with Halbach array offers excellent magnetic manipulation performance.     

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.