Measurements of ferrofluid surface tension in confined geometry

Magnetic field effects on the surfactant concentration over ferrofluid droplet surfaces in shear flows

We investigate the impact of a magnetic field on surfactant concentration and interfacial forces across droplet surfaces within shear flows. Our analysis centers on a single two-dimensional ferrofluid droplet covered with surfactants, suspended in an immiscible, non-magnetizable liquid. The model combines incompressible Navier-Stokes equations and Maxwell's equations in the superparamagnetic limit in the single-fluid formulation, augmented by terms accounting for Marangoni, capillary, and magnetic forces at the droplet interface. We solve the surfactant convection-diffusion equation at the surface, while a non-linear Langmuir equation of state relates surfactant concentration to surface tension. The model is numerically solved using finite differences, a level-set method for multiphase flow computation, and the closest-point method for concentration equation. Our findings reveal that even though the surfactant is magnetically neutral, the presence of a magnetic field significantly modifies its distribution at the interface. A magnetic field perpendicular to the primary flow direction shifts the maximum concentration zone from the droplet tips toward the flow vorticity direction, while a parallel field produces the opposite effect. Alterations in surfactant distribution directly impact the surface tension field, offering a potential wireless means of controlling droplet dynamics.

Does Magnetic Field Influence the Surface Tension of Ferrofluid?

Studying the physical properties of ferrofluids is a challenging task, especially when conventional experimental techniques are adapted to the presence of a magnetic field. To date, there has been no definitive understanding of how the magnetic field affects the surface energy of ferrofluid interfaces. In this study, we perform a direct experimental investigation to assess the effect of magnetic fields on the surface tension of ferrofluids. For this purpose, a modified capillary wave technique was modified for use in the presence of an external magnetic field. A decrease in the wavelength of the capillary wave was observed when the magnetic field was oriented perpendicular to the ferrofluid surface, and an increase was recorded when the magnetic field was parallel. We note that the capillary wave pattern elongates along the magnetic field force lines. The observed effect is attributed to the varying influence of the magnetic field along and across the propagating capillary wave. Analysis of the dispersion relation and evaluation of the impacts of various mechanisms influencing capillary waves revealed, that the changes in the surface tension of ferrofluids in the presence of a magnetic field are responsible for the observed behavior. It is shown that the surface tension of the MK 8-40 ferrofluid gradually increases with the applied magnetic field and reaches a grouth up to 10% in a magnetic field of ∼10 kA/m. Thus, the surface tension is found to be influenced by an external magnetic field.

Ferrofluid annulus in crossed magnetic fields

We study the dynamics and pattern formation of a ferrofluid annulus enveloped by two nonmagnetic fluids in a Hele-Shaw cell, subjected to an in-plane crossed magnetic field configuration involving the combination of radial and azimuthal magnetic fields. A perturbative, second-order mode-coupling analysis is employed to investigate how the ferrofluid annulus responds to variations in the relative strength of the radial and azimuthal magnetic field components, as well as in the thickness of magnetic fluid ring. By tuning the magnetic field components and the annulus' thickness, we have found the development of several stationary annular shapes, presenting polygon-shaped structures typically having skewed, peaked fingers. Such fingered structures may vary their skewness, sharpness, and number and arise on the inner, outer, or even both boundaries of the annulus. In addition to controlling the morphologies of the ferrofluid annuli, the external field can be used to put the annulus into a rotational motion, with an angular velocity having prescribed magnitude, and direction. Our second-order theory is utilized to obtain a correction to the linear stability analysis prediction of such angular velocity, usually resulting in a decreased weakly nonlinear value as compared with the magnitude predicted by purely linear theory. These theoretical results suggest the use of magnetic-field-controlled ferrofluid annuli in Hele-Shaw cells as a potential laboratory for microscale applications related to the manipulation of shape-programmable magnetic fluid objects and tunable fluidic-mixing devices in confined environments.

Magnetowetting dynamics of sessile ferrofluid droplets: a review

The fascinating behavior of ferrofluids in a magnetic field has been intriguing researchers for many years. With the advancement in digital microfluidics, ferrofluid droplets have been extensively used in different applications ranging from biomedical to mechanical systems. Notably, the magnetic field can change the wetting dynamics of sessile ferrofluid droplets, leading to a plethora of interesting hydrodynamic phenomena. In the recent past, the spatiotemporal evolution of the droplet shape and contact line dynamics of a ferrofluid droplet in different magnetowetting scenarios has been explored widely. The relevant studies elucidate several critical aspects, such as the role of magnetic nanoparticles, carrier fluid, and the interaction of the magnetic fluid with the solid surface, among many others. Hence a systematic review of the progress made in understanding the fundamental and practical aspects of magnetowetting in the past decade (2010-2020) would be a helpful resource to the scientific community in the near future. Drawn by this motivation, an honest effort has been made in this Review to highlight the significant scientific findings concerning the sessile droplet magnetowetting phenomena within the timeline of interest. Several cutting-edge applications developed from the scientific findings in the purview of magnetowetting have also been discussed before outlining the conclusions and future areas of scope.

Shape instabilities in confined ferrofluids under crossed magnetic fields

We analyze the morphology and dynamic behavior of the interface separating a ferrofluid and a nonmagnetic fluid in a Hele-Shaw cell, when crossed radial and azimuthal magnetic fields are applied. In addition to inducing the formation of a variety of eye-catching, complex interfacial structures, the action of the crossed fields makes the deformed ferrofluid droplet to rotate. Numerical simulations and perturbative mode-coupling theory are employed to look into early linear, intermediate weakly nonlinear, and fully nonlinear dynamic regimes of the pattern-forming process. We investigate how the system responds to variations in the viscosity difference between the fluids, the magnetic susceptibility of the ferrofluid, the effects of surface tension, and in the relative strength between radial and azimuthal applied magnetic fields. The role played by random perturbations at the initial conditions in determining the ultimate shape and dynamic stability of the spinning ferrofluid patterns is also studied.

Magnetically induced interfacial instabilities in a ferrofluid annulus

We investigate the flow of a viscous ferrofluid annulus surrounded by two nonmagnetic fluids in a Hele-Shaw cell when subjected to an external radial magnetic field. The interfacial pattern formation dynamics of the system is determined by the interplay of magnetic and surface tension forces acting on the inner and outer boundaries of the annulus, favoring the coupling of the disjoint interfaces. Mode-coupling analysis is employed to examine both linear and weakly nonlinear stages of the flow. Linear stability analysis indicates that the trailing and leading annular boundaries are coupled already at the linear regime, revealing that perturbations arising in the outer interface may induce the emergence of deformed structures in the inner boundary. Moreover, second-order weakly nonlinear analysis is utilized to identify key nonlinear morphological features of the ferrofluid annulus. Our theoretical results show that linear, n-fold symmetric annular patterns having rounded edges are replaced by nonlinear polygonal-like shapes, presenting fairly sharp fingers. It is found that, as opposed to the linear patterns, the nonlinear peaky structures reach a stationary state, characterized by a growth saturation process induced by nonlinear effects. Furthermore, the response of the ferrofluid ring to changes in the thickness of the annulus, in the relative strength of magnetic and surface tensions forces, as well as in the magnetic susceptibility of the ferrofluid material, are also discussed.

Magnetic Field-Driven Deformation, Attraction, and Coalescence of Nonmagnetic Aqueous Droplets in an Oil-Based Ferrofluid

Stimuli-responsive compartments are attracting more and more attention through the years motivated by their wide applications in different fields including encapsulation, manipulation, and triggering of chemical reactions on demand. Among others, magnetic responsive compartments are particularly attractive due to the numerous advantages of magnetic fields compared to other external stimuli. In this article, we used an oil-based ferrofluid where the magnetic nanoparticles have been coated with different polymers to increase their amphiphilic character and surface activity, consequently rendering the interface magnetically responsive. Microliter aqueous nonmagnetic droplets dispersed in the oil-based ferrofluid were used as a model of microreactors. A comprehensive experimental and theoretical study of the deformation, attraction, and coalescence processes of the nonmagnetic water droplets coated with the magnetic nanoparticles under an applied magnetic field in the continuous oil-based ferrofluid phase is provided. To manipulate the packing of the nanoparticles at the water/oil interface, the ionic strength of the aqueous droplets was varied using different NaCl concentrations, and its effect on modulating the coalescence of the droplets was probed. Our results show that the water droplets deform along the magnetic field depending on the magnetic properties of the ferrofluid itself and on the surface properties of the interface, attract in pairs under the action of the magnetic dipole force, and coalesce by the action of the same force with a stochastic behavior. We have studied all of these phenomena as a function of the magnetic field applied, evaluating in each case the forces and/or pressures acting on the droplets with particular attention to roles of magnetic attraction, interface properties, and viscosity in the system. This work offers an overall set of tools to understand and predict the behavior of multiple water droplets in an oil-based ferrofluid for lab-on-a-chip applications.

A new method of interface tension measurement of a magnetic fluid drop

A new method for determining the interfacial tension of a magnetic fluid (MF) is proposed on the basis of deformation of a MF drop lying on a liquid substrate and subjected to a vertical uniform magnetic field. The results show that the drop elongates in the direction of the field with an increase of its intensity. As soon as the field strength reaches a certain value, the interface and the free surface of the drop become unstable, which causes the peaks of different height to form. It has been found that the ratio of the corresponding critical values of magnetic field intensity is determined by the ratio of surface tension at the interface to that on the free boundary of the drop. Surface and interfacial tension of liquids used in the experiment were measured with the help of tensiometer by the ring detachment method to verify the experimental data. The presented results on the ferrofluid interface tension measurements can be of interest for the specialists in the field of ferrohydrodynamics.•

The magnetic field causes the drop to elongate till the peak instability.

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The critical values of the field strength respond to the ferrofluid initial magnetic susceptibility.

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The ratio of the critical magnetic field values is determined by the ratio of the interfacial tension.

Generation of droplet arrays with rational number spacing patterns driven by a periodic energy landscape

The generation of droplets at low Reynolds numbers is driven by nonlinear dynamics that give rise to complex patterns concerning both the droplet-to-droplet spacing and the individual droplet sizes. Here we demonstrate an experimental system in which a time-varying energy landscape provides a periodic magnetic force that generates an array of droplets from an immiscible mixture of ferrofluid and silicone oil. The resulting droplet patterns are periodic, owing to the nature of the magnetic force, yet the droplet spacing and size can vary greatly by tuning a single bias pressure applied on the ferrofluid phase; for a given cycle period of the magnetic force, droplets can be generated either at integer multiples (1, 2, ...), or at rational fractions (3/2, 5/3, 5/2, ...) of this period with mono- or multidisperse droplet sizes. We develop a discrete-time dynamical systems model not only to reproduce the phenotypes of the observed patterns but also to provide a framework for understanding systems driven by such periodic energy landscapes.

Single-mode instability of a ferrofluid-mercury interface under a nonuniform magnetic field

This work reports an experimental and a numerical study of the interfacial instability in a mercury-ferrofluid system caused by a spatially nonuniform magnetic field against the action of gravity and interfacial tension. The interface evolution is observed to be continuous till its movement is hindered by a physical boundary. In contrast to the behavior of the ferrofluid interface under uniform field, we noted the instability growth to be monotonic under a field gradient. A steepness in the growth curve is noticed during the later stages of the instability, indicating a high magnitude of the growth velocities. Some unique phenomena, such as similarity of the growth at the initial stage, a slope transition in the growth curve at a later stage, and wrapping and pinning of the interface are observed, both in experiments and simulations.

Static Magnetowetting of Ferrofluid Drops

We report results of a comprehensive study of the wetting properties of sessile drops of ferrofluid water solutions at various concentrations deposited on flat substrates and subjected to the action of permanent magnets of different sizes and strengths. The amplitude and the gradient of the magnetic field experienced by the ferrofluid are changed by varying the magnets and their distance to the surface. Magnetic forces up to 100 times the gravitational one and magnetic gradients up to 1 T/cm are achieved. A rich phenomenology is observed, ranging from flattened drops caused by the magnetic attraction to drops extended normally to the substrate because of the normal traction of the magnetic field. We find that the former effect can be conveniently described in terms of an effective Bond number that compares the effective drop attraction with the capillary force, whereas the drop's vertical elongation is effectively expressed by a dimensionless number S, which compares the pressure jump at the ferrofluid interface because of the magnetization with the capillary pressure.

Magnetofluidic control of the breakup of ferrofluid droplets in a microfluidic Y-junction

Breakup of the ferrofluid droplets at the Y-junction divergence under various flow rate ratios.

Magnetically induced behaviour of ferritin corpuscles in avian ears: can cuticulosomes function as magnetosomes?

Magnetoreception is an enigmatic, poorly understood sensory ability, described mainly on the basis of behavioural studies in animals of diverse taxa. Recently, corpuscles containing superparamagnetic iron-storage protein ferritin were found in the inner ear hair cells of birds, a predominantly single ferritin corpuscle per cell. It was suggested that these corpuscles might represent magnetosomes and function as magnetosensors. Here we determine ferritin low-field paramagnetic susceptibility to estimate its magnetically induced intracellular behaviour. Physical simulations show that ferritin corpuscles cannot be deformed or rotate in weak geomagnetic fields, and thus cannot provide magnetoreception via deformation of the cuticular plate. Furthermore, we reached an alternative hypothesis that ferritin corpuscle in avian ears may function as an intracellular electromagnetic oscillator. Such an oscillator would generate additional cellular electric potential related to normal cell conditions. Though the phenomenon seems to be weak, this effect deserves further analyses.

Nonlinear traveling waves in confined ferrofluids

We study the development of nonlinear traveling waves on the interface separating two viscous fluids flowing in parallel in a vertical Hele-Shaw cell. One of the fluids is a ferrofluid and a uniform magnetic field is applied in the plane of the cell, making an angle with the initially undisturbed interface. We employ a mode-coupling theory that predicts the possibility of controlling the speed of the waves by purely magnetic means. The influence of the tilted magnetic field on the waves shape profile and the establishment of stationary traveling wave structures are investigated.

Nonmonotonic field-dependent magnetic permeability of a paramagnetic ferrofluid emulsion

The ferrofluid emulsion, made of kerosene-based ferrofluid droplets suspended in nonmiscible aviation oil, demonstrates experimentally the nonmonotonic dependence of the effective magnetic permeability as a function of the uniform static magnetic field. In weak fields the emulsion permeability rapidly grows; it reaches its maximum at fields on the order of 1 kA/m; after that, it decays to zero. The theoretical explanation of the effect, as we show here, could be based on the following idea: In a weak magnetic field the growth of the induced droplet magnetic moment is faster than the linear one due to the droplet elongation accompanied by the reduction of the demagnetizing field. Further increase of the external magnetic field strength cannot lead to a significant decrease of the demagnetizing field, as the droplets are already highly elongated. On the other hand, the magnetic susceptibility of the ferrofluid reduces with the field strength. Thus, the effective magnetic permeability of the ferrofluid suspension starts decreasing. The developed theoretical model describes well the experimental observations.

Generation and manipulation of monodispersed ferrofluid emulsions: the effect of a uniform magnetic field in flow-focusing and T-junction configurations

This paper demonstrates the use of magnetically controlled microfluidic devices to produce monodispersed ferrofluid emulsions. By applying a uniform magnetic field on flow-focusing and T-junction configurations, the size of the ferrofluid emulsions can be actively controlled. The influences of the flow rates, the orientation, and the polarity of the magnetic field on the size of ferrofluid emulsions produced in both flow-focusing and T-junction configurations are compared and discussed.

Weakly nonlinear study of normal-field instability in confined ferrofluids

Similar to the classic three-dimensional Rosensweig instability, a ferrofluid confined in a vertical Hele-Shaw cell subjected to an in-plane normal magnetic field develops a periodic array of peaked interfacial structures. We perform a weakly nonlinear analysis that is able to reproduce the morphology of such pattern formation phenomenon at lowest nonlinear order. A mode-coupling theory is applied to compare the early nonlinear evolution of the interface with static shapes obtained when relevant forces equilibrate. Our nonlinear results indicate that the time-evolving shapes tend to approach stable stationary solutions.

Meniscus of a ferrofluid around a vertical cylindrical wire carrying electric current

We study the meniscus profiles of ferrofluids in the magnetic field of a vertical current-carrying wire. Measurements of the free ferrofluid surface profile are quantitatively compared with numerical calculations. The theoretical model leads to a second-order ordinary differential equation. All material parameters are determined in independent experiments, therefore no fitting parameters are involved in the calculations. The experimental results can be modeled by the equilibrium of magnetic, gravitational, and interface tension forces. The classical model that neglects interface tension yields significant deviations from the experimental profiles in the parameter range studied.

Magnetodeformation effects and the swelling of ferrogels in a uniform magnetic field

Magnetic field sensitive gels (ferrogels or magnetoelastic gels) are three-dimensional cross-linked networks of flexible polymers swollen by ferrofluids or magnetic fluids. We have studied the response of magnetic field sensitive polymer gels to an external magnetic field. Two phenomena were investigated in detail: deformation and swelling under a uniform magnetic field. Gel spheres containing magnetic particles distributed randomly in the gel matrix as well as pearl chain aggregates chemically fixed in the network were exposed to a static homogeneous magnetic field. It was found that the spatial distribution of the magnetic particles plays an essential role in the magnetodeformation effect. A weak effect was observed for gels containing randomly distributed magnetic particles. In response to the magnetic field induction, these gel spheres elongated along the field lines and were compressed in the perpendicular direction. No magnetodeformation was observed for gels containing aligned particles in the polymer matrix. The influence of an external magnetic field on the equilibrium swelling degree was also the subject of this study. Using thermodynamic arguments it was shown that a uniform external field may result in deswelling of the ferrogels at high field intensities.

Rupture of a ferrofluid droplet in external magnetic fields using a single-component lattice Boltzmann model for nonideal fluids

A nonisotropic tensorial extension of the single-component Shan-Chen pseudopotential Lattice Boltzmann method for nonideal fluids is presented. Direct comparison with experimental data shows that this extension is able to capture relevant features of ferrofluid behavior, such as the deformation and subsequent rupture of a liquid droplet as a function of an externally applied magnetic field. The present model offers an economic lattice-kinetic pathway to the simulation of complex ferrofluid hydrodynamics.

Stretching and squeezing of sessile dielectric drops by the optical radiation pressure

We study numerically the deformation of sessile dielectric drops immersed in a second fluid when submitted to the optical radiation pressure of a continuous Gaussian laser wave. Both drop stretching and drop squeezing are investigated at steady state where capillary effects balance the optical radiation pressure. A boundary integral method is implemented to solve the axisymmetric Stokes flow in the two fluids. In the stretching case, we find that the drop shape goes from prolate to near-conical for increasing optical radiation pressure whatever the drop to beam radius ratio and the refractive index contrast between the two fluids. The semiangle of the cone at equilibrium decreases with the drop to beam radius ratio and is weakly influenced by the index contrast. Above a threshold value of the radiation pressure, these "optical cones" become unstable and a disruption is observed. Conversely, when optically squeezed, the drop shifts from an oblate to a concave shape leading to the formation of a stable "optical torus." These findings extend the electrohydrodynamics approach of drop deformation to the much less investigated "optical domain" and reveal the openings offered by laser waves to actively manipulate droplets at the micrometer scale.

Confined ferrofluid droplet in crossed magnetic fields

When a ferrofluid drop is trapped in a horizontal Hele-Shaw cell and subjected to a vertical magnetic field, a fingering instability results in the droplet evolving into a complex branched structure. This fingering instability depends on the magnetic field ramp rate but also depends critically on the initial state of the droplet. Small perturbations in the initial droplet can have a large influence on the resulting final pattern. By simultaneously applying a stabilizing (horizontal) azimuthal magnetic field, we gain more control over the mode selection mechanism. We perform a linear stability analysis that shows that any single mode can be selected by appropriately adjusting the strengths of the applied fields. This offers a unique and accurate mode selection mechanism for this confined magnetic fluid system. We present the results of numerical simulations that demonstrate that this mode selection mechanism is quite robust and "overpowers" any initial perturbations on the droplet. This provides a predictable way to obtain patterns with any desired number of fingers.

Nonlinear deformations of liquid-liquid interfaces induced by electromagnetic radiation pressure

The idea of working with a near-critical phase-separated liquid mixture whereby the surface tension becomes weak, has recently made the field of laser manipulation of liquid interfaces a much more convenient tool in practice. The deformation of interfaces may become as large as several tenths of micrometers, even with the use of conventional laser power. This circumstance necessitates the use of nonlinear geometrical theory for the description of surface deformations. The present paper works out such a theory, for the surface deformation under conditions of axial symmetry and stationarity. Good agreement is found with the experimental results of Casner and Delville [A. Casner and J. P. Delville, Phys. Rev. Lett. 87, 054503 (2001); Opt. Lett. 26, 1418 (2001); Phys. Rev. Lett. 90, 144503 (2003)], in the case of moderate power or a broad laser beam. In the case of large power and a narrow beam, corresponding to surface deformations of about 50 micrometers or higher, the theory is found to over-predict the deformation. Possible explanations of this discrepancy are discussed.

Adhesion phenomena in ferrofluids

One efficient way of determining the bond strength of adhesives is to measure the force or the work required to separate two surfaces bonded by a thin adhesive film. We consider the case in which the thin film is not a conventional adhesive material but a high viscosity ferrofluid confined between two narrowly spaced parallel flat plates subjected to an external magnetic field. Our theoretical results demonstrate that both the peak adhesive force and the separation energy are significantly influenced by the action and symmetry properties of the applied field. Specifically, we show that the adhesive strength of a ferrofluid is reduced if the applied magnetic field is perpendicular to the plates or if the applied field is in plane and exhibits azimuthal symmetry. Conversely, the adhesive strength can be either enhanced or reduced if the applied field is in plane and is directed radially outward. This establishes an interesting connection between adhesion and ferrohydrodynamic phenomena, allowing the control of important adhesive properties by magnetic means.

Nonlinear theory of pattern formation in ferrofluid films at high field strengths

When a magnetic field is applied to a thin layer of a suspension of magnetic nanoparticles (ferrofluid), the formation of labyrinthine and hexagonal patterns is observed. We introduce a theory to describe ferrofluid patterns at high field, where a nonlinear relationship between field and magnetization is expected. The computational difficulties due to the use of a nonlinear magnetization curve are solved by a reformulation of the magnetic energy equation. The evolution of the pattern size at intermediate and very high fields can be understood by an analysis of limiting cases of the magnetization curve. In particular, at a very high field the pattern size reaches a constant saturation value which has been recently confirmed by experiments. The field for the onset of a nonlinear behavior is shifted to higher field strength due to a demagnetization effect. This can partially explain the ability of linear approaches to reproduce experimental data even at a high field. Finally, the impact of the nonlinearity of the magnetization curve on the transition between hexagonal and labyrinthine patterns is discussed.

Laser-induced hydrodynamic instability of fluid interfaces

We report on a new class of electromagnetically driven fluid interface instability. Using the optical radiation pressure of a cw laser to bend a very soft near-critical liquid-liquid interface, we show that it becomes unstable for sufficiently large beam power P, leading to the formation of a stationary beam-centered liquid microjet. We explore the behavior of the instability onset by tuning the interface softness with temperature and varying the size of the exciting beam. The instability mechanism is experimentally demonstrated. It simply relies on total reflection of light at the deformed interface whose condition provides the universal scaling relation for the onset P(S) of the instability.

Theoretical study of the field-induced pattern formation in magnetic liquids

When a thin layer of magnetic fluid confined with an immiscible nonmagnetic liquid is subjected to a perpendicular field, the formation of hexagonal and labyrinthine patterns is observed experimentally. To develop a coherent theoretical description of this phenomenon, the free energy functionals of both types of magnetic structures are derived. Both energy functionals have the same form, which explains that the theoretical results found in this paper for hexagonal and labyrinthlike striped patterns are analogous. The size of the patterns is determined by minimizing the free energy. The influence of the method for computing the magnetic energy on the theoretical results is studied. An accurate computation of the magnetic energy proves important in predicting the experimental pattern size as a function of external field and of layer height. How the results change, when a constant magnetization is assumed during the pattern formation is also investigated. The transition between hexagonal and striped structures is studied by a comparison of their free energies. The ratio of the magnetic to the nonmagnetic liquid is found to be an important factor for the relative stability of the patterns. In agreement with experiments, striped structures are observed at large phase ratios, whereas at small phase ratios hexagonal patterns predominate.

Rayleigh-taylor instability with magnetic fluids: experiment and theory

We present experiments showing the Rayleigh-Taylor instability at the interface between a dense magnetic liquid and an immiscible less dense liquid. The liquids are confined in a Hele-Shaw cell and a magnetic field is applied perpendicular to the cell. We measure the wavelength and the growth rate at the onset of the instability as a function of the external magnetic field. The wavelength decreases as the field increases. The amplitude of the interface deformation grows exponentially with time in the early stage, and the growth rate is an increasing function of the field. These results are compared to theoretical predictions given in the framework of linear stability analysis.

Parallel flow in hele-shaw cells with ferrofluids

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 effects. However, the magnetic field does not affect the speed of wave propogation for a given wave number. We note that the magnetic field creates an effective interaction between the solitons.

Elongation of confined ferrofluid droplets under applied fields

Ferrofluids are strongly paramagnetic liquids. We study the behavior of ferrofluid droplets confined between two parallel plates with a weak applied field parallel to the plates. The droplets elongate under the applied field to reduce their demagnetizing energy and reach an equilibrium shape where the magnetic forces balance against the surface tension. This elongation varies logarithmically with aspect ratio of droplet thickness to its original radius, in contrast to the behavior of unconfined droplets. Experimental studies of a ferrofluid-water-surfactant emulsion confirm this prediction.