Ferrofluids belong to an important class of highly functional soft matter, benefiting from their magnetically controllable physical properties. Therefore, it is of central importance to quantitatively predict the dynamic magnetic response of ferrofluids. Traditional dynamic theories, however, are often restricted to the near-equilibrium regime and/or only apply to nearly ideal ferrofluids that are monodisperse, dilute enough, and weakly interacting. In this paper I develop a self-consistent and nonperturbative dynamical mean field theory for typical ferrofluids which are often polydisperse, concentrated, and strongly interacting, possibly driven far from equilibrium. I obtain a general nonperturbative expression for the dynamic magnetic susceptibility, quantitatively agreeing with the spectra obtained from Brownian Dynamics simulations on both mono- and bidisperse samples. Furthermore, I derive a generic magnetization relaxation equation (MRE) for both mono- and polydisperse ferrofluids by employing the projection operator technique in nonequlibrium statistical mechanics. This MRE is in simple closed form and independent of which model is employed to approximate the equilibrium magnetization curve. Existing models can be recovered as low-order approximations of my generic and nonperturbative MRE. My theory can play a key role in studying the dynamics of ferrofluids and other polar fluids. It may also have substantial and immediate consequences to various ferrofluid applications.
An analytical theoretical model for the influence of the magnetically induced nanoparticle chaining on the linear dichroism in ferrofluids was developed. The model is based on a statistical theory for magnetic nanoparticle chaining in ferrofluids. Together with appropriate experimental approach and data processing strategy, the model grounds a magneto-optical granulometry method able to determine the magnetic field dependence of the statistics of magnetically induced particle chains in concentrated ferrofluids.
The influence of the cyclic heating and cooling on properties of the aggregates (aka "ferrofluid clusters") in a ferrofluid, which made on the basis of magnetite nanoparticles, are investigated. The heating of the ferrofluid layer with such aggregates leads to equalization of the concentration between high- and low-concentrated phases. The temperature of the equalization of the phase concentrations was determined at different values of an external constant magnetic field, which was applied parallel to the layer of the ferrofluid. The temperature of the destruction of a periodic structure of th…
The ferrofluid dynamics theory is applied to thermodiffusive problems in magnetic fluids in the presence of magnetic fields. The analytical form for the magnetic part of the chemical potential and the most general expression of the mass flux are given. By employing these results to experiments, global Soret coefficients in agreement with measurements are determined. Also an estimate for a hitherto unknown transport coefficient is made.
Ferrofluids currently are the only type of magnetic liquid materials with wide practical use. The theory on ferrofluids is an example of success to apply statistics to science. Ferrofluids are two-phase liquids consisting of dispersed nanoscale ferromagnetic particles suspended in a carrier fluid. Due to their tiny size, individual ferromagnetic particles clearly exhibit Brownian motions. Only when a large number of randomly-moving particles are subject to an external magnetic field, can they collectively exhibit magnetization at a macroscale. Using statistical theory, the magnetization of a f…
Influence of magnitude and direction of static magnetic field applied on a drying drop of a laboratory synthesized water base ferrofluid placed on a plane glass plate is investigated. Like all other multi-component fluid this drop also exhibited familiar coffee ring pattern in absence of field while, this pattern is modulated by applying magnetic field and thickness of the ring modulated by the applied field and thickness of the ring decreases exponentially with increase in field when direction of field is normal to the plane of the substrate. Effect of the field on the evaporation rate and te…
The phase transition between a massive dense phase and a diluted superparamagnetic phase has been studied by means of a direct molecular dynamics simulation. The equilibrium structures of the ferrofluid aggregate nucleus are obtained for different values of a temperature and an external magnetic field magnitude. An approximate match of experiment and simulation has been shown for the ferrofluid phase diagram coordinates "field-temperature". The provided phase coexistence curve has an opposite trend comparing to some of known theoretical results. This contradiction has been discussed. For given…
The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematical model: It does not rely on assuming a particular distribution function of the particles.
In the present work we report on the behavior of ferrofluid microdrops in an immiscible nonmagnetic carrier fluid and vice versa subjected to the action of magnetic fields. Our experiments evidence previously unexplored instability and flow patterns. We investigated the instabilities initiated by constant magnetic field and by combined action of constant and rotating magnetic fields. The observed instabilities lead to the formation of various microdrop configurations such as star-like and comb-like shapes, bending deformation, ridges and crests, spiral arms and rings, etc. The reviled peculiar…
A novel type of hybrid colloids is presented, based on the association of several polymeric systems and ferrofluids. On the one hand, we use inorganic nanoparticles made of magnetic iron oxide prepared at the LI2C, which response to a magnetic field of low intensity. On the other hand the organic part is made either of long linear polyacrylamide chains or of mesoscopic structures (vesicles and micelles) self-assembled from amphiphile polybutadiene-b-poly(glutamic acid) di-block copolymers, which conformation is pH-sensitive.
Taking into account the structural transition and long-range interaction (lattice effect), we resort to the Ewald-Kornfeld formulation and developed Maxwell-Garnett theory for uniaxially anisotropic suspensions to calculate the effective permeability of inverse ferrofluids. And we also consider the effect of volume fraction to the magnetophoretic force on the nonmagnetic spherical particles submerged in ferrofluids in the presence of nonuniform magnetic field. We find that the coupling of ac and dc field case can lead to fundamental and third harmonic response in the effective magnetophoresis …
On the basis of the mean spherical approximation of multicomponent dipolar hard sphere mixtures an analytical expression is proposed for the magnetic field dependence of the magnetization of size polydisperse ferrofluids. The polydispersity of the particle diameter is described by the gamma distribution function. Canonical ensemble Monte Carlo simulations have been performed in order to test these theoretical results for the initial susceptibility and the magnetization. The results for the magnetic properties of the polydisperse systems turn out to be in quantitative agreement with our present…
In the paper the novel soft magnetic composite system is investigated. A ferrofluid emulsion studied demonstrates the strong magnetic properties which are atypical for commonly known emulsions. Interaction of ferrofluid emulsions with a magnetic field is considered. Structural transformations in these media, such as deformation of emulsion microdroplets and emulsion inversion, are studied. The changes in the relative permeability of emulsion associated with structural transformations are investigated. The theory of the observed phenomena is developed, and the feasibility of effectively control…
Ferrofluids are liquids exhibiting remarkably strong response to magnetic fields, which leads to fascinating properties useful in various applications. Understanding the wetting properties and spreading of ferrofluids is important for their use in microfluidics and magnetic actuation. However, this is challenging as magnetically induced deformation of the ferrofluid surface can affect contact angles, which are commonly used to characterize wetting properties in other systems. In addition, interaction of the magnetic nanoparticles and solid surface at nanoscale can have surprising effects on fe…
Manipulation of small-scale matter is a fundamental topic in micro- and nanorobotics. Numerous magnetic robotic systems have been developed for the manipulation of microparticles in an ambient environment, liquid as well as on the air-liquid interface. These systems move intrinsically magnetic or magnetically tagged objects by inducing a magnetic torque or force. However, most of the materials found in nature are non-magnetic. Here, we report a ferrofluidic manipulator for automatic two-dimensional manipulation of non-magnetic objects floating on top of a ferrofluid. The manipulation system em…
We investigate how ferrofluid droplets suspended in a wall-bounded shear flow can organise when subjected to an external magnetic field. By tuning the magnitude of the external magnetic field, we find that the ferrofluid droplets form chain-like structures in the flow direction when the magnetic field is weak, while forming a crystal-like pattern in a strong magnetic field. We provide the phase diagram and the critical conditions for this chain-to-crystal transition, by applying both numerical simulations and analytic calculations. We also examine how the organised patterns of the ferrofluid d…
An ordered hexagonal array of aggregates can form in thin ferrofluid layers when an external magnetic field is applied. Using the Helmholtz free energy for this system, we calculate the optimum spacing for these aggregates. Results show excellent agreement with experimental findings as a function of field strength and layer thickness. Our analysis yields a crossover in the exponent for the scaling behavior of the aggregate spacing as a function of plate separation, in agreement with experiment. For the first time, we report a similar crossover in the scaling behavior of the aggregate spacing a…
The linear stability analysis of the Faraday instability on a viscous ferrofluid in a horizontal magnetic field is performed. Strong dipole-dipole interactions lead to the formation of chains elongated in the field direction. The formation of chains results in a qualitative new behaviour of the ferrofluid. This new behaviour is characterized by a neutral stability curve similar to that observed earlier for Maxwell viscoelastic liquids and causes a significant weakening of the energy dissipation at high frequencies. In the case of a ferrofluid with chains in a horizontal magnetic field, the eff…
In the presence of a magnetic field applied perpendicular to a thin sample layer, a suspension of magnetic colloidal particles (ferrofluid) can form spatially modulated phases with a characteristic length determined by the competition between dipolar forces and short-range forces opposing density variations. We introduce models for thin-film ferrofluids in which magnetization and particle density are viewed as independent variables and in which the non-magnetic properties of the colloidal particles are described either by a lattice-gas entropy or by the Carnahan-Starling free energy. Our descr…
Effects of pulse magnetic field on the optical transmission properties of thin ferrofluid (FF) layers were experimentally investigated. It was observed that, under an influence of an external uniform magnetic field, pulses applied to the samples surfaces in normal direction decrease the optical transmission with further returning it to its original state, even before the end of the field pulse. The dependencies of the observed effects on the magnetic pulse magnitude and the samples thickness were investigated. The experimental results are explained using FF columnar aggregates growth and later…
Convective instability in a ferrofluid layer heated from below or from above in the presence of a uniform vertical magnetic field is investigated theoretically. Convection is caused by a magnetic mechanism based on the temperature and concentration dependence of magnetization. An imposed temperature gradient establishes (by the Soret effect) a concentration gradient of magnetic particles of which the ferrofluid is composed. Both these gradients cause a spatial variation in magnetization, which induces a gradient of magnetic field intensity within the fluid layer. The field gradient induces in …
A second-order Taylor series expansion of the free energy functional provides analytical expressions for the magnetic field dependence of the free energy and of the magnetization of ferrofluids, here modelled by dipolar Yukawa interaction potentials. The corresponding hard core dipolar Yukawa reference fluid is studied within the framework of the mean spherical approximation. Our findings for the magnetic and phase equilibrium properties are in quantitative agreement with previously published and new Monte Carlo simulation data.
Ferrofluids are strongly magnetic fluids consisting of magnetic nanoparticles dispersed in a carrier fluid. Besides their technological applications, they have a tendency to form beautiful and intriguing patterns when subjected to external static and dynamic magnetic fields. Most of the patterns occur in systems consisting of two fluids: one ferrofluidic and one non-magnetic (oil, air, etc.), wherein the fluid-fluid interface deforms as a response to magnetic fields. Usually, the fluids are completely immiscible and so the interfacial energy in this systems is very large. Here we show that it …
We investigate the deformation of soft spherical elastic capsules filled with a ferrofluid in external uniform magnetic fields at fixed volume by a combination of numerical and analytical approaches. We develop a numerical iterative solution strategy based on nonlinear elastic shape equations to calculate the stretched capsule shape numerically and a coupled finite element and boundary element method to solve the corresponding magnetostatic problem, and employ analytical linear response theory, approximative energy minimization, and slender-body theory. The observed deformation behavior is qua…
Ferrofluids are a synthetic magnetic colloid consisting of magnetized nanoparticles surrounded by a repulsive surfactant layer. When subjected to an external magnetic field the ferrofluid acquires a macroscopic magnetization density which leads to magnetic behavior that is intricately coupled to the ambient fluid dynamics. Ferrofluids share several features with the chiral active fluids composed of unidirectionally spinning hematite cubes, which have been shown to possess a 2D non-dissipative odd viscosity term (Nature Physics, 15, 1188-1194(2019)). In standard ferrofluid dynamics, 3D versions…
Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial …
The spontaneous motion of liquid droplets on solid surfaces is the result of an unbalanced surface tension force, which is sometimes called the "Marangoni effect". This can be triggered by either a difference in surface temperature or a heterogeneity in the topography or chemistry of the surface passively or actively. The imbibition of liquid within capillary tubes, horizontal ice wicking on either hydrophilic or hydrophobic substrates, and inkjet printing for example are just some classic illustrations of where the Lucas-Washburn equation can predict droplet behavior characteristics fairly we…
We present a new system based on alginate gels for the encapsulation of a ferrofluid drop, which allows us to create millimeter-sized elastic capsules that are highly deformable by inhomogeneous magnetic fields. We use a combination of experimental and theoretical work in order to characterize and quantify the deformation behavior of these ferrofluid-filled capsules. We introduce a novel method for the direct encapsulation of unpolar liquids by sodium alginate. The addition of polar alcohol molecules allows us to encapsulate a ferrofluid as a single phase. This encapsulation method increases t…
We report on the observation of the polygonal whirlpools in the thin layer of ferrofluid under illumination with a laser beam carrying optical vortex and in the presence of a vertical magnetic field. This kind of structures have attracted attention after discovering a hexagonal storm in Saturns atmosphere. Our polygonal whirlpools were created in a closed system (no free surfaces) in micro scale (whirlpool diameter less than 20 micrometers) by the use of holographic optical tweezers. The polygonal shape was changed by varying the magnetic field strength or value of the optical vortex topologic…
Nonmagnetic spheres confined in a ferrofluid layer (magnetic holes) present dipolar interactions when an external magnetic field is exerted. The interaction potential of a microsphere pair is derived analytically, with a precise care for the boundary conditions along the glass plates confining the system. Considering external fields consisting of a constant normal component and a high frequency rotating in-plane component, this interaction potential is averaged over time to exhibit the average interparticular forces acting when the imposed frequency exceeds the inverse of the viscous relaxatio…
Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.)
We exploit magnetostriction in polydisperse ferrofluids in order to generate nonlinear responses, and apply a thermodynamical method to derive the desired nonlinear magnetic susceptibility. For an ideal gas, this method has been demonstrated to be in excellent agreement with a statistical method. In the presence of a sinusoidal ac magnetic field, the magnetization of the polydisperse ferrofluid contains higher-order harmonics, which can be extracted analytically by using a perturbation approach. We find that the harmonics are sensitive to the particle distribution and the degree of field-induc…
We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a non-uniform, azimuthal magnetic field, applied tangential to the cell, tends to stabilize the interface. We verify that maximum growth rate selection of initial patterns is influenced by the applied field, which tends to decrease the number of i…
Viscous fingering occurs in the flow of two immiscible, viscous fluids between the plates of a Hele-Shaw cell. Due to pressure gradients or gravity, the initially planar interface separating the two fluids undergoes a Saffman-Taylor instability and develops finger-like structures. When one of the fluids is a ferrofluid and a perpendicular magnetic field is applied, the labyrinthine instability supplements the usual viscous fingering instability, resulting in visually striking, complex patterns. We consider this problem in a rectangular flow geometry using a perturbative mode-coupling analysis.…
The effect of a spatially uniform magnetic field on the shear rheology of a dilute emulsion of monodispersed ferrofluid droplets, immersed in a non-magnetizable immiscible fluid, is investigated using direct numerical simulations. The direction of the applied magnetic field is normal to the shear flow direction. The droplets extra stress tensor arising from the presence of interfacial forces of magnetic nature is modeled on the basis of the seminal work of G. K. Batchelor, J. Fluid Mech., 41.3 (1970) under the assumptions of a linearly magnetizable ferrofluid phase and negligible inertia. The …
The recently proposed dynamical effective field model (DEFM) is quantitatively accurate for describing dynamical magnetic response of ferrofluids. In paper I it is derived under the framework of dynamical density functional theory, via which the original ensemble of bare Brownian particles is mapped to an ensemble of dressed particles. However, it remains to clarify how the characteristic rotational relaxation time of a dressed particle, denoted by $τ_r$, is quantitatively related to that of a bare particle, denoted by $τ^0_r$. By building macro-micro connections via two different routes, I re…
The observed magnetic tunability of light transmission through a ferrofluid can be effectively understood in terms of the inter-particle interaction that can be estimated from the magnetic and rheological properties of these fluids. The present study reports complementary magnetic and rheological measurements of aqueous dispersions of ferrite nanoparticles and a commercial ferrofluid. The room temperature magnetization measured in a SQUID magnetometer up to fields of 1 to 2 Tesla showed superparamagnetic behaviour of the particles and the dispersion with the background signal of the liquid sho…
The paper is devoted to the theoretical investigation of the magnetodipolar interparticle interaction effect on remagnetization dynamics in moderately concentrated ferrofluids. We consider a homogeneous (without particle aggregates) ferrofluid consisting of identical spherical particles and employ a rigid dipole model, where magnetic moment of a particle is fixed with respect to the particle itself. In particular, for the magnetization relaxation after the external field is instantly switched off, we show that the magnetodipolar interaction leads to the increase of the initial magnetization re…
We investigate in detail the initial susceptibility, magnetization curves, and microstructure of ferrofluids in various concentration and particle dipole moment ranges by means of molecular dynamics simulations. We use the Ewald summation for the long-range dipolar interactions, take explicitly into account the translational and rotational degrees of freedom, coupled to a Langevin thermostat. When the dipolar interaction energy is comparable with the thermal energy, the simulation results on the magnetization properties agree with the theoretical predictions very well. For stronger dipolar cou…
Hydrodynamics and Thermal Multiphysics Lab (HTML), Department of Mechanical Engineering, Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校机械工程系水动力学与热多物理实验室）
Nonmagnetic particles in magnetized ferrofluids have been denoted magnetic holes and are in many ways ideal model systems to test various forms of particle self assembly and dynamics. Some case studies to be reviewed here include: Chaining of magnetic holes Braid theory and Zipf relation used in dynamics of magnetic microparticles Interactions of magnetic holes in ferrofluid layers The objectives of these works have been to find simple characterizations of complex behavior of particles with dipolar interactions.
A mean-field Fokker-Planck equation approach to the dynamics of ferrofluids in the presence of a magnetic field and velocity gradients is proposed that incorporates magnetic dipole-dipole interactions of the colloidal particles. The model allows to study the combined effect of a magnetic field and dipolar interactions on the viscosity of the ferrofluid. It is found that dipolar interactions lead to additional non-Newtonian contributions to the stress tensor, which modify the behavior of the non-interacting system. The predictions of the present model are in qualitative agreement with experimen…
Materials with continuous dissipation can exhibit responses and functionalities that are not possible in thermodynamic equilibrium. While this concept is well-known, a major challenge has been the implementation: how to rationally design materials with functional non-equilibrium states and quantify the dissipation? Here we address these questions for the widely used colloidal nanoparticles that convey several functionalities. We propose that useful non-equilibrium states can be realised by creating and maintaining steady-state nanoparticle concentration gradients by continuous injection and di…
