Ferrofluid Flow Research Articles

The stability of ferrofluid flow in a vertical layer subject to lateral heating and horizontal magnetic field

We use the Langevin law of magnetization to study the linear stability of a convective flow in a flat vertical layer of ferrofluid subject to a transverse temperature gradient and a uniform magnetic field. The stability of the flow against planar, spiral and three-dimensional perturbations is examined, and the stability boundaries and characteristics of critical disturbances are determined. The competition between the monotonic mode and two types of wave modes is analyzed taking into account the properties of the fluid (magnetic susceptibility and Prandtl number) and the magnetic field strength. The domain of parameters where the oscillatory thermomagnetic wave instability exists is found.

Taylor–Couette flow of ferrofluid: Spin field and spin boundary condition effects

We solve for the steady flow solutions of a ferrofluid between concentric cylinders (the Taylor-Couette problem) and consider the effects of the spin field and the spin boundary conditions on the flow. In particular, our model includes the full spin equations. We analyze families of solutions for a range of realistic flow parameters and radial magnetic fields. Particular attention is paid to regimes in which different spin boundary conditions lead to significantly different flow profiles.

Fabrication and testing of a CoNiCu/Cu CPP-GMR nanowire-based microfluidic biosensor

Giant magneto resistance (GMR)-based microfluidic biosensors are used in applications involving the detection, analysis, enumeration and characterization of magnetic nano-particles attached to biological mediums such as antibodies and DNA. Here we introduce a novel multilayered CoNiCu/Cu nanowire GMR-based microfluidic biosensor. The current perpendicular to the plane of multilayers (CPP)-nanowires GMR was used as the core sensing material in the biosensor which responds to magnetic fields depending on the concentration and the flow velocity of bio-nano-magnetic fluids. The device was tested with different control solutions such as DI-water, mineral oil, phosphate buffered saline (PBS), ferrofluid, polystyrene superparamagnetic beads (PSB) and Dynabeads sheep anti-rabbit IgG. The nanowire array resistance decreased with an increase in the ferrofluid concentration, and a maximum 15.8% relative GMR was observed for the undiluted ferrofluid. The sensor was also responding differently to various ferrofluid flow rates. The GMR device showed variation in the output signal when the PSB and Dynabeads of different dilutions were pumped through it. When the tests were performed with pulsing potentials (150 mV and 200 mV), an increased GMR response was identified at higher voltages for PSB and Dynabeads sheep anti-rabbit IgG.

Global analysis for strong solutions to the equations of a ferrofluid flow model

In this paper we are concerned with the differential system proposed by Shliomis to describe the motion of an incompressible ferrofluid submitted to an external magnetic field. The system consists of the Navier–Stokes equations, the magnetization equations and the magnetostatic equations. No regularizing term is added to the magnetization equations. We prove the local existence of unique strong solution for the Cauchy problem and establish a finite time blow-up criterion of strong solutions. Under the smallness assumption of the initial data and the external magnetic field, we prove the global existence of strong solutions and derive a decay rate of such small solutions in L 2 -norm.

Lattice Boltzmann model for simulating temperature-sensitive ferrofluids

In this paper, a lattice Boltzmann model for simulating temperature-sensitive ferrofluids is presented. The lattice Boltzmann equation for modeling the magnetic field is formulated using a scalar magnetic potential. Introducing a time derivative into the original elliptic equation for the scalar potential leads to an advection-diffusion equation, with an effective velocity determined by the temperature gradient. The time derivative is multiplied by an adjustable preconditioning parameter to ensure that the lattice Boltzmann solution remain close to a solution of the original elliptic equation for the scalar potential. To test the present lattice Boltzmann model, numerical simulations for the thermomagnetic nature convection of the ferrofluids in a cubic cavity are carried out. Good agreement between the obtained results and experimental data shows that the present lattice Boltzmann model is promising for studying temperature-sensitive ferrofluid flows.

Strong solutions to the equations of a ferrofluid flow model

We study the differential system introduced by M.I. Shliomis to describe the motion of a ferrofluid driven by an external magnetic field. The system is a combination of the Navier–Stokes equations, the magnetization equation and the magnetostatic equations. No regularizing term is added to the magnetization equation. We prove the local-in-time existence of strong solutions to the system.

Non-Newtonian flow of dilute ferrofluids in a uniform magnetic field

Nonequilibrium magnetization states predict non-Newtonian ferrofluid properties. It is desirable to understand the corresponding flow fields and characteristics. In this study, we derive a magnetoviscosity expression coming from the effective-field method and describing the shear-thinning non-Newtonian behavior of dilute ferrofluids with finite magnetic anisotropy. A mathematical model is developed of non-Newtonian plane flow with respect to shear and pressure driving mechanisms in the presence of an applied stationary uniform magnetic field oriented in the direction perpendicular to vorticity. The results reveal that the non-Newtonian effect tends to increase the velocity and angular velocity but to reduce the magnetization strength. Moreover, an enhanced flow rate and reduced flow drag may be obtained. The maximum non-Newtonian effect is found at a ratio of the Néel relaxation time to the Brownian relaxation time of the order of 0.1.

Hydrodynamic modeling of ferrofluid flow in magnetic targeting drug delivery

Among the proposed techniques for delivering drugs to specific locations within human body, magnetic drug targeting prevails due to its non-invasive character and its high targeting efficiency. Magnetic targeting drug delivery is a method of carrying drug-loaded magnetic nanoparticles to a target tissue target under the applied magnetic field. This method increases the drug concentration in the target while reducing the adverse side-effects. Although there have been some theoretical analyses for magnetic drug targeting, very few researchers have addressed the hydrodynamic models of magnetic fluids in the blood vessel. A mathematical model is presented to describe the hydrodynamics of ferrofluids as drug carriers flowing in a blood vessel under the applied magnetic field. In this model, magnetic force and asymmetrical force are added, and an angular momentum equation of magnetic nanoparticles in the applied magnetic field is modeled. Engineering approximations are achieved by retaining the physiclaly most significant items in the model due to the mathematical complexity of the motion equations. Numerical simulations are performed to obtain better insight into the theoretical model with computational fluid dynamics. Simulation results demonstrate the important parameters leading to adequate drug delivery to the target site depending on the magnetic field intensity, which coincident with those of animal experiments. Results of the analysis provide important information and suggest strategies for improving delivery in clinical application.

Stability of Ferrofluid Flows in a Horizontal Channel Subjected to a Longitudinal Temperature Gradient and an Oblique Magnetic Field

The stability of thermoconvective flows of a ferrofluid in a horizontal channel subjected to a longitudinal temperature gradient and an oblique strong magnetic field is studied. The flows are governed by the mass, momentum, heat balance and Maxwell equations, in the Boussinesq approximation. Strong magnetic fields are characterized by a small parameter measuring the deviation of the magnetization across the layer from the external magnetic field. An approximate solution of the stationary hydrodynamic problem was found in analytical form in Hennenberg et al. (Phys Fluids 18:093602, 2006). The flow depends on the thermal (gravitational) and magnetic Rayleigh numbers. In the present paper the linear stability of that basic flow is studied by the Galerkin method. The analysis shows that for large Prandtl numbers, typical for ferrofluids, and relatively small magnetic Rayleigh numbers, only oscillatory instability can appear. For a given magnetic Rayleigh number, the critical wavenumber does not depend on the inclination of the magnetic field, while the critical thermal Rayleigh number slightly changes. For horizontal and vertical magnetic fields, both critical numbers decrease when increasing the magnetic Rayleigh number.

Parametric modulation in the Taylor–Couette ferrofluid flow

A parametric instability of the Taylor–Couette ferrofluid flow excited by a periodically oscillating magnetic field, has been investigated numerically. The Floquet analysis has been employed. It has been found that the modulation of the applied magnetic field affects the stability of the basic flow. The instability response has been found to be synchronous with respect to the frequency of periodically oscillating magnetic field.

Spin-up flow of ferrofluids: Asymptotic theory and experimental measurements

We treat the flow of ferrofluid in a cylindrical container subjected to a uniform rotating magnetic field, commonly referred to as spin-up flow. A review of theoretical and experimental results published since the phenomenon was first observed in 1967 shows that the experimental data from surface observations of tracer particles are inadequate for the assessment of bulk flow theories. We present direct measurements of the bulk flow by using the ultrasound velocity profile method, and torque measurements for water and kerosene based ferrofluids, showing the fluid corotating with the field in a rigid-body-like fashion throughout most of the bulk region of the container, except near the air-fluid interface, where it was observed to counter-rotate. We obtain an extension of the spin diffusion theory of Zaitsev and Shliomis, using the regular perturbation method. The solution is rigorously valid for αK⪡3∕2, where αK is the Langevin parameter evaluated by using the applied field magnitude, and provides a means for obtaining successively higher contributions of the nonlinearity of the equilibrium magnetization response and the spin-magnetization coupling in the magnetization relaxation equation. Because of limitations in the sensitivity of our apparatus, experiments were carried out under conditions for which α∼1. Still, under such conditions the predictions of the analysis are in good qualitative agreement with the experimental observations. An estimate of the spin viscosity is obtained from comparison of flow measurements and theoretical results of the extrapolated wall velocity from the regular perturbation method. The estimated value lies in the range of 10−8–10−12kgms−1 and is several orders of magnitude higher than that obtained from dimensional analysis of a suspension of noninteracting particles in a Newtonian fluid.

Homogeneous turbulence in ferrofluids with a steady magnetic field

The general equations necessary for a basic theoretical interpretation of the physics of turbulence in ferrofluids are presented. The equations are examined and show multiple novel turbulence aspects that arise in ferrofluids. For example, two new modes of turbulent kinetic energy and turbulent kinetic energy dissipation rate occur, and unique modes of energy conversion (rotational to/from translational kinetic energy and magnetic energy to/from turbulent kinetic energy) are exhibited in turbulent ferrofluid flows. Furthermore, it is shown that potential models for turbulence in ferrofluids are complicated by additional closure requirements from the five additional nonlinear terms in the governing equations. The equations are applied to turbulence of a ferrofluid in the presence of a steady magnetic field (as well as the case of no magnetic field) in order to identify the importance of the new terms. Results are presented for the enhanced anisotropy in the presence of a magnetic field, and results show how turbulence properties (both classical ones and new ones) vary with the strength of the magnetic field. Three different equations for the magnetization are examined and lead to different results at large magnitudes of the applied magnetic field.

Global weak solutions to a ferrofluid flow model

AbstractWe are concerned with the global solvability of the differential system introduced by Shliomis to describe the flow of a colloidal suspension of magnetized nanoparticles in a nonconducting liquid, under the action of an external magnetic field. The system is a combination of the Navier–Stokes equations, the magnetization equation, and the magnetostatic equations. We prove, by using a method of regularization, the existence of global‐in‐time weak solutions with finite energy to an initial boundary‐value problem and establish the long‐time behaviour of such solutions. The main difficulty is due to the singularity of the gradient magnetic force and the torque. Copyright © 2007 John Wiley & Sons, Ltd.

Global Weak Solutions to Equations of Motion for Magnetic Fluids

We study the differential system governing the flow of an incompressible ferrofluid under the action of a magnetic field. The system consists of the Navier–Stokes equations, the angular momentum equation, the magnetization equation, and the magnetostatic equations. We prove, by using the Galerkin method, a global in time existence of weak solutions with finite energy of an initial boundary-value problem and establish the long-time behavior of such solutions. The main difficulty is due to the singularity of the gradient magnetic force.

Ferrofluid magnetoviscous control of wall flow channeling in porous media

We analyzed the phenomenon of ferrofluid magnetoviscosity in high-permeability wall-region non-magnetic porous media of the Müller kind. After upscaling the pore-level ferrohydrodynamic model, we obtained a simplified volume-average zero-order axisymmetric model for non-Darcy non-turbulent flow of steady-state isothermal incompressible Newtonian ferrofluids through a porous medium experiencing external constant bulk-flow oriented gradient magnetic field, ferrofluid self-consistent demagnetizing field and induced magnetic field in the solid. The model was explored in contexts plagued by wall flow maldistribution due to low column-to-particle diameter ratios. It was shown that for proper magnetic field arrangement, wall channeling can be reduced by inflating wall flow resistance through magnetovisco-thickening and Kelvin body force density which reroute a fraction of wall flow towards bed core.

Torque and Bulk Flow of Ferrofluid in an Annular Gap Subjected to a Rotating Magnetic Field

We report analysis and measurements of the torque and flow of a ferrofluid in a cylindrical annulus subjected to a rotating magnetic field perpendicular to the cylinder axis. The presence of the inner cylinder results in a nonuniform magnetic field in the annulus. An asymptotic analysis of the ferrohydrodynamic torque and flow assuming linear magnetization and neglecting the effect of couple stresses indicated that the torque should have a linear dependence on field frequency and quadratic dependence on field amplitude. To the order of approximation of the analysis, no bulk flow is expected in the annular gap between stationary cylinders. Experiments measured the torque required to restrain a polycarbonate spindle surrounded by ferrofluid in a cylindrical container and subjected to the rotating magnetic field generated by a two-pole magnetic induction motor stator, as a function of the applied field amplitude and frequency, and for various values of the geometric aspect ratios of the problem. The ultrasound velocity profile method was used to measure the azimuthal and axial velocity profiles in the ferrofluid contained in the annular gap of the apparatus. Flow measurements show the existence of a bulk azimuthal ferrofluid flow between stationary coaxial cylinders with a negligible axial velocity component. The fluid was found to corotate with the applied magnetic field. Both the torque and flow measurements showed power-of-one dependence on frequency and amplitude of the applied magnetic field. This analysis and these experiments indicate that the action of antisymmetric stresses is responsible for the torque measured on the inner cylinder, whereas the effect of body couples is likely responsible for bulk motion of the ferrofluid.

Ferrofluid induced-field effects in inhomogeneous porous media under linear-gradient dc magnetic fields

Numerical simulations of ferrofluid flows through porous media with low column-to-grain diameter ratios are obtained for fluids experiencing external linear-gradient magnetic fields, ferrofluid self-consistent demagnetizing field and induced magnetic field in the non-magnetic granular phase. Analysis of the macroscopic volume-average ferrohydrodynamic model identified the conditions for decoupling magnetostatics from hydrodynamics. Order-of-magnitude calculations of the applied magnetic field versus the self-consistent demagnetizing field and the corresponding Kelvin body force densities showed that such decoupling is fulfilled only for large and positive gradient magnetic field.

Rheological properties of ferrofluids with microstructures

This paper presents results of a theoretical study of the effects of linear chain-like as well asbulk drop-like heterogeneous aggregates on the rheological properties and behaviour offerrofluids. The results demonstrate that the appearance of both these internal structuresleads to a strong (one–two orders of magnitude) increase of the ferrofluid effectiveviscosity under the action of the magnetic field applied parallel to the gradient ofthe ferrofluid flow. When the ferrofluid fills a thin channel (gap) placed into anormal magnetic field, the drop-like structures can overlap with the channel. In thecase of a rigid connection between the drop-like domains and the channel walls,the appearance of elastic and yield stress effects on the ferrofluid is expected.

Magnetoviscosity in suspensions of grains with finite magnetic anisotropy

Coupling between magnetic and mechanical rotational degrees of freedom of fine ferromagnetic grains is provided by the energy of their magnetic anisotropy. In the limiting case of strong anisotropy, an applied stationary magnetic field induces the greatest obstacles to the "rigid dipole" spin in a vortex ferrofluid flow, while in the opposite ideal case, the "soft dipoles" twist freely with the liquid. As a result, the field-dependent part of the ferrofluids viscosity depends not only on the external magnetic field strength but also on the particle magnetic anisotropy. An explicit expression coming from simple physical arguments and describing both these dependencies of magnetoviscosity is derived and discussed.

Investigations of convective heat transfer in ferrofluid microflows using lattice-Boltzmann approach

By using the lattice-Boltzmann method, the mesoscopic models for the ferrofluid are developed to simulate flow and thermal processes of the ferrofluid flowing through a micro channel. The models include a variety of forces and potentials acting on the ferrofluid system as well as heat exchange between the suspended magnetic nanoparticles and the ambient liquid. Some numerical examples are given to discuss the enhancement or suppression mechanism of heat transfer of the ferrofluid by adjusting the orientation and magnitude of the magnetic field gradient.