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In this study, three-dimensional computational analysis is performed to investigate the magnetoconvection of ferrofluid ($F{e}_3{O}_4$-water) within a cubical enclosure heated by an inner spherical hot block. The ferrofluid, considered as a working fluid, is modeled as a single-phase fluid. The inner spherical block is put at high temperature while all the remaining walls of the enclosure are exposed to low temperature. Two radii values ($\mathrm{\text{rs}}=0.1$ and $0.2$) of the inner hot sphere are examined. Governing equations with corresponding boundary conditions are solved numerically applying a second-order accurate finite volume method on a staggered grid system, using an accelerated multigrid model. Simulations are carried out based on various flow-governing parameters such as Rayleigh number $(10^3<\text{Ra}<10^7)$, Hartmann number $(0<\text{Ha}<50)$ and ferrofluid nanoparticle volume fraction $(0<\varphi <4\%)$. The effects of the pertinent parameters in the performance of the system are also studied. The flow and thermal fields, the local and surface-averaged Nusselt numbers on the sphere and the enclosure for both configurations are detailed. The flow remains steady and laminar for all Rayleigh numbers regardless of the sphere radius. Obviously, heat transfer rate improves with $\text{Ra}$ augmentation and minimizes with Ha decrease. At the highest Ra and lowest Ha, higher inner sphere radius shows significantly better heat transfer rate (more than $30\%$). Useful correlations are presented to quantify the surface-averaged heat transfer rate through the cubical enclosure.

Recent experimental as well as theoretical investigations have shown that the formation of structures of magnetic nanoparticles has significant influence on the behaviour of ferrofluids. The dependence of this structure formation on the magnetic field strength and shear stress applied to the fluid leads to strong changes of the viscosity and to the appearance of viscoelastic effects in the fluids. The actual approaches for a description of the effects vary in the basic modeling of the fluid and its behaviour. Some models base on microscopic assumptions, other model the fluid on a mesoscale and even macroscopic descriptions abstaining from microscopic assumptions have been suggested. A point in which the predictions of the models differ is the question of an appearance of a magnetic field dependent yield stress in ferrofluids. For investigations concerning the appearance and field dependence of a yield stress a special stress controlled rheometer for ferrofluids has been designed. The preliminary results presented here, show a dependence of the yield stress on magnetic field strength for different kind of ferrofluids and magnetorheological fluids.

This paper reports two basic microfluidic strategies for the magnetic manipulation of unlabeled nonmagnetic particles/cells. One is the deflection induced by a single magnet, and the other is the confusing effect produced by two magnets of opposite polarity. They can be combined into more completed particle manipulations like continuous flow separation, counting and detection, which are essential steps in biomedical applications. We experimentally studied the dynamics of 10.4 and 20 $\mu$m nonmagnetic polystyrene particles within a flow rate range of 30, 50, 70 and 90 $\mu$L/min in a straight channel. We defined the cross-section length that the particles occupy as the “particle bandwidth” to characterize the extent of deflection and focusing. To predict the trajectories of the particles, we established a simple theoretical model by considering the magnetic force and viscous drag force. Compared with the experimental results, the maximum deviation of the simulation is 9.28%. The influences of magnetic nanoparticle concentration, magnetic field parameters, size of microparticles and flow rate are systematically investigated. We also demonstrated that the effective deflection and focusing could be realized at low Fe₃O₄ nanoparticle concentrations, which means that this method can reduce the damage on cells in the practical applications.

The dipole–dipole interactions may lead to the linear chain formation in the ferrofluids. When the dipolar interaction energy is much larger than the thermal energy, the average length of the chains 〈n〉 becomes much larger than 1. This strongly influences on the magnetic susceptibility χ which is enhanced in comparison to its Langevin value χ_L by a factor of 2〈n〉.

The unsteady Micropolar Navier–Stokes Equations (MNSE) are a system of parabolic partial differential equations coupling linear velocity and pressure with angular velocity: material particles have both translational and rotational degrees of freedom. We propose and analyze a first-order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier–Stokes equations. With the help of our scheme, we explore some qualitative properties of the MNSE related to ferrofluid manipulation and pumping. Finally, we propose a second order scheme and show that it is almost unconditionally stable.

We discuss the equations describing the motion of ferrofluids subject to an external magnetic field. We concentrate on the model proposed by Rosensweig, provide an appropriate definition for the effective magnetizing field, and explain the simplifications behind this definition. We show that this system is formally energy stable, and devise a numerical scheme that mimics the same stability estimate. We prove that solutions of the numerical scheme always exist and, under further simplifying assumptions, that the discrete solutions converge. We also discuss alternative formulations proposed in pre-existing work, primarily involving a regularization of the magnetization equation and supply boundary conditions which lead to an energy stable system. We present a series of numerical experiments which illustrate the potential of the scheme in the context of real applications.

The average density of CoFe₂O₄ particles treated by using ferric nitrate is decided from specific saturation magnetization of both untreated and treated particles. Besides, some characteristic parameters, depending on the density of particles, are determined for CoFe₂O₄ ionic ferrofluids. The magnetization of the ferrofluids exhibits abnormal behaviors and is interpreted in relation to aggregates self-assembled from particles in the ferrofluids. Ringlike aggregates in which particles' moments linked into closed flux cause the saturation magnetization measured to be less than the theoretical value. The aggregates with opposed-parallel moments ordering will break up into isolated particles in the first magnetization process, so that the second magnetization will be easier than the first. For the aggregates with head-to-tail linked moments ordering, the magnetization behavior of the self-assembly structure may be hard to distinguish from field-induced aggregates.

The Cr_xFe${}_{3-x}$O₄ ferrofluids have been successfully synthesized using natural iron sand through co-precipitation method as a voltage sensor. The use of chromium dopants is intended to increase the ferrofluids response when used as a voltage sensor. A series of characterizations were carried out to support this justification, including structure, morphology, functional groups, optical properties, and sensor performance of the Cr_xFe${}_{3-x}$O₄ ferrofluids. The increase in the Cr${}^{3+}$ molar fraction has an impact on decreasing in structural parameters of the Cr_xFe${}_{3-x}$O₄ ferrofluids. Visually, the particles show an agglomeration phase by the presence of interparticle forces. The study of functional groups showed that the Cr_xFe${}_{3-x}$O₄ ferrofluids had been successfully formed, marked by the appearance of all precursor functional groups. Analysis of optical properties based on absorption shows the phenomenon of intervalence charge transfer and causes a decrease in the value of the gap energy. Interestingly, the Cr_xFe${}_{3-x}$O₄ ferrofluids sensor sensitivity shows a good and prospective response making them suitable for new sensor candidates in the future.

The paper is devoted to a new extension in Gegenbauer wavelet method (GWM) to investigate the transfer of heat and MHD boundary-layer flow of ferrofluids beside a flat plate with velocity slip. A homogenous model study is conducted in which we assumed the heat transfer and forced convective flow of ferrofluids along a flat plate with a uniform wall heat flux. In the direction of transverse to plate, a magnetic field is imposed. Three various magnetic nanoparticle types including Mn–ZnFe₂O₄, CoFe₂O₄, Fe₃O₄ are incorporated inside the base fluid. Two types of base fluids (water and kerosene) with bad thermal conductivity as compared to nanoparticles of solid magnetic have been assumed. The mathematical model is tackled via modified Gegenbauer wavelet method (MGWM). A simulation is accomplished for individual ferrofluid mixture by assuming the prevailing impacts of uniform and slip heat fluxes. The variation of heat transfers and skin friction were also observed at the surface of the plate and we analyzed the better heat transfer for every mixture. Kerosene-based magnetite (Fe₃O₄) delivers the better rate of heat transfer at wall due to its association with the kerosene-based Mn–Zn and cobalt ferrites. The slip velocity and magnetic field effects on the temperature, dimensionless velocity, rate of heat transfer and skin friction are examined for various magnetic nanoparticles inside the kerosene oil and water. We observed that the primary influence of magnetic field reduces the dimensionless surface temperature and accelerates the dimensionless velocity as compared to the hydrodynamic case, thus enhancing the rate of heat transfer and skin friction ferrofluids. Moreover, a detailed evaluation of outcomes obtained by MGWM, already published work and numerical RK-4 were found to be in excellent agreement. The error and convergence analysis are presented. Comparison of results, graphical plots, error and convergence analysis reveal the appropriateness of proposed method. The proposed algorithm can be extended for other nonlinear problems.

Droplet actuation is an essential mechanism for droplet-based microfluidic systems. On-demand electromagnetic actuation is used in a ferrofluid-based microfluidic system for water droplet displacement. Electropermanent magnets (EPMs) are used to induce 50 mT magnetic fields in a ferrofluid filled microchannel with gradients up to 6.4 × 10⁴ kA/m². Short 50 µs current pulses activate the electropermanent magnets and generate negative magnetophoretic forces that range from 10 to 70 nN on 40 to 80 µm water-in-ferrofluid droplets. Maximum droplet displacement velocities of up to 300 µm/s are obtained under flow and no-flow conditions. Electropermanent magnet-activated droplet sorting under continuous flow is demonstrated using a split-junction microfluidic design.