Article pubs.acs.org/Langmuir

Self-Assembling Array of Magnetoelectrostatic Jets from the Surface of a Superparamagnetic Ionic Liquid Lyon B. King,*,† Edmond Meyer,† Mark A. Hopkins,† Brian S. Hawkett,‡ and Nirmesh Jain‡ †

Department of Mechanical Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931, United States ‡ Key Centre for Polymers and Colloids, University of Sydney, NSW 2006, Sydney, Australia ABSTRACT: Electrospray is a versatile technology used, for example, to ionize biomolecules for mass spectrometry, create nanofibers and nanowires, and propel spacecraft in orbit. Traditionally, electrospray is achieved via microfabricated capillary needle electrodes that are used to create the fluid jets. Here we report on multiple parallel jetting instabilities realized through the application of simultaneous electric and magnetic fields to the surface of a superparamagnetic electrically conducting ionic liquid with no needle electrodes. The ionic liquid ferrofluid is synthesized by suspending magnetic nanoparticles in a room-temperature molten salt carrier liquid. Two ILFFs are reported: one based on ethylammonium nitrate (EAN) and the other based on EMIM-NTf2. The ILFFs display an electrical conductivity of 0.63 S/ m and a relative magnetic permeability as high as 10. When coincident electric and magnetic fields are applied to these liquids, the result is a self-assembling array of emitters that are composed entirely of the colloidal fluid. An analysis of the magnetic surface stress induced on the ILFF shows that the electric field required for transition to spray can be reduced by as much as 4.5 × 107 V/m compared to purely electrostatic spray. Ferrofluid mode studies in nonuniform magnetic fields show that it is feasible to realize arrays with up to 16 emitters/mm2.

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produce fine jets and monodisperse aerosols has been exploited for diverse applications such as the synthesis of nanofibers,8 production of pharmaceuticals,9 femtoliter-droplet direct writing onto surfaces,10 and microscale ion thrusters for spacecraft propulsion.11 Electrospray is an inherently microscale phenomenon. Regardless of the size of the fluid volume, the spray emits only from a micrometer-sized or even atomic-scale point that forms at the tip of the fluid Taylor cone. Because of this, the mass throughput of any single electrospray emitter is constrained to very small values. Many technological applications of electrospray could be improved by increasing the spray throughput, which can be achieved only by multiplexing many individual emitters in parallel. For instance, the thrust force from an electrospray micro ion thruster can be increased by fabricating on-chip arrays of multiple individual capillary emitters.12 Increased electrospray throughput could improve mass spectrometer sensitivity and increase the aerosol volume flow of industrial sprays.13,14 The Taylor cone instability of an electrified fluid has a magnetic analogue in the Rosensweig instability of a magnetized fluid. When a magnetic field is applied to a so-

INTRODUCTION A suitably strong electric field, applied at the free surface of a conducting or dielectric fluid, will exert electrostatic traction on the fluid surface that can stretch the meniscus into a pointed conical shape.1 Electrospray results when the field is strong enough to cause the tip of this Taylor cone to exhaust a jet of charged droplets or ions.2 By exact analogy to electrostatically stressed dielectric fluids, magnetic fields can distort magnetizable fluids into identical pointed geometries;3,4 however, magnetostatic jetting is never observed.5 It is believed yet not completely understood that electrostatic jetting is a result of finite charge conductivity, a phenomenon that has no parallel in the magnetic fluid. Electrospray occurs when an electrostatic surface traction exceeds a liquid’s surface tension. Because the field strength must be on the order of 109 V/m to overcome the surface tension of most fluids, electrospray is realized in practice by introducing the liquid through individual electrified hollow capillaries such that the spray emits from the high-field region at the tips of the sharp electrodes. Although fabrication details vary, all contemporary electrospray sources are purely electrostatic devices that are inherently identical in concept to the original apparatus of Zeleny.6 The most well-known contemporary application of electrospray is to produce intact ionized biomolecules for introduction into a mass spectrometer,7 but the ability of electrospray to © 2014 American Chemical Society

Received: August 20, 2014 Revised: November 4, 2014 Published: November 5, 2014 14143

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called ferrofluid, a static, regularly spaced pattern of fluid peaks can form on the fluid interface as first demonstrated by Cowley and Rosensweig15 and investigated extensively thereafter.16−20 Analytic models of magnetic pools, droplets, and jets have been studied since the first realization of ferrofluids in the 1960s.3,4,21−29 Electrohydronamically stressed conducting and polar liquids have received even more attention because of their wide technical utility in the field of electrospray.8,30−32 There has been some limited work on combined electric/magnetic fluids, mostly studies of equilibrium droplet shapes under combined field stress for instance by Tyatushkin,33 Dikansky,34,35 and Zakinyan.36 The flow of an electrically conductive and weakly magnetic fluid (magnetic susceptibility ∼10−6) was addressed by Tzirtzilakis in the context of biofluid dynamics.37 Ruo performed an analysis to determine the magnetic field effects on an electrospray jet; however, the fluid itself was nonmagnetic and the interaction was via the Lorentz force.38 Recently, in work paralleling that reported here, Mkrtchyan observed combined electrostatic and magnetostatic capillary instabilities from a single droplet of polar ferrofluid with low conductivity.39 The purpose of this article is to report on multiple parallel electromagnetostatic jets from a unique colloidal fluid that is both superparamagnetic and highly conductive.

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mole-for-mole basis, with N,N-dimethylacrylamide to prepare EMIMNTf2 based ILFF-2. In a typical reaction, DMAm (3.65 g, 36.8 mmol), V-501 (0.017 g, 0.061 mmol), and BuPAT (0.15 g, 0.61 mmol) were added to a 100 mL round-bottomed flask containing a mixture of dioxane (10 g) and water (10 g). The mixture was held at 70 °C for 3 h under a nitrogen atmosphere and then cooled to room temperature. MAEP (1.20 g, 6.1 mmol) and V-501 (0.017 g, 0.061 mmol) were added, and the reaction mixture was heated for another 12 h at 70 °C under nitrogen. At the end of this step, a block copolymer of nominal composition, poly(MAEP10-b-DMAm60), was obtained. Sterically stabilized iron oxide nanoparticles based on the Sirtex NPs were synthesized in water as reported previously.45 The ionic liquid ferrofluid based on EAN (ILFF-1) was prepared as previously reported.43 ILFF-2, based on EMIM-NTf2, was prepared by mixing a dispersion of sterically stabilized Sirtex magnetic nanoparticles in 50:50 (w/w) water and ethanol with EMIM-NTf2, followed by ultrasonication for 2 min. Water and ethanol were then removed by rotary evaporation, followed by nitrogen purging overnight. The magnetic properties of the ILFFs were measured in the liquid state at room temperature using a Lake Shore 7300 vibrating sample magnetometer (VSM) with a 2 T electromagnet. The magnetic moment was measured over a range of applied fields from −20 to +20 kOe with a sensitivity of 0.1 emu. An M−H curve of ILFF-2 is shown in Figure 1, showing zero hysteresis that is characteristic of

EXPERIMENTAL DETAILS

Experiment 1: Spray Emission Study. The motivation for our work was to produce multiple parallel electrospray emitters for eventual application to spacecraft micropropulsion systems. With this motivation, first we sought an electrically conductive ferrofluid that would be compatible with use in vacuum and thus display negligible vapor pressure near ambient temperature. Second, the ferrofluid must be stable so that it will not separate during long-term storage or when subjected to strong magnetic forces. Furthermore, we desire the ferrofluid to have low surface tension because this characteristic would maximize the tip-to-tip packing density of the magnetic Rosensweig instability and hence the areal mass throughput of the array. Finally, the ideal fluid would have low viscosity at room temperature and negligible viscoelasticity. These desired characteristics were best met by room-temperature molten salts or ionic liquids. Recently, there have been several efforts to synthesize ferrofluids from ionic liquids reported in the literature;40−42 however, only the ionic liquid ferrofluids (ILFFs) described in the work of Jain and Hawkett43 were of sufficient magnetic quality to demonstrate the hallmark Rosensweig instability. Initial testing was performed with Jain and Hawkett’s ethylammonium nitrate (EAN)-based ILFF, which we refer to here as ILFF-1. Although we report some results obtained with ILFF-1, the fluid was less than ideal for our application because it is hygroscopic and also because the viscosity of ILFF-1 was higher than we desired. Given the shortcomings of EAN-based ILFF-1, we sought to develop a custom ILFF. The second ionic liquid ferrofluid (ILFF-2) was prepared by sterically stabilizing an aqueous dispersion of magnetic nanoparticles in EMIM-NTf2. To prepare ILFF-2, we passed monoacryloxyethyl phosphate (MAEP, Aldrich) through an inhibitor removal column (Aldrich) prior to use. 1,4-Dioxane (Fluka) was distilled under reduced pressure. RAFT agent 2-[(butylsulfanyl)carbonothioyl]sulfanyl propanoic acid (BuPAT, DuluxGroup Australia), N,N-dimethylacrylamide (DMAm, Aldrich), 4,4′-azobis(4-cyanovaleric acid) (V-501, Wako), sodium hydroxide (NaOH, Aldrich), and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfphonyl)imide (EMIM-NTf2, Iolitec) were all used as received. The aqueous dispersion of iron oxide nanoparticles used in this work was obtained from Sirtex Medical Limited (Sirtex NPs). Poly(MAEP10-b-DMAm60) was prepared as reported previously.44 Monomer acrylamide in the reported synthesis was replaced, on a

Figure 1. M−H magnetization characteristic of ionic liquid ferrofluid ILFF-2. superparamagnetism, a remarkably high relative permeability of approximately μr = 10, and a saturation magnetization ∼1.2 × 105 A/m. Thermal gravimetric analysis demonstrated the thermal stability of ILFF-2 to 350 °C. The density of ILFF-2 was calculated on the basis of component densities to be ρ =1.84 g/mL, the electrical conductivity was measured to be σ = 0.63 S/m, and the surface tension was measured to be γ = 36.3 mN/m. The ILFF fluid holder/array was assembled as shown in Figure 2. A 2-mm-wide annular trench was milled into a block of aluminum; this trench was then filled with ILFF. A concentric annular extraction electrode was located 4.7 mm from the surface of the aluminum fluid holder. An electric field was created by biasing the fluid holder, and with it the conductive fluid, to high voltage while the extraction electrode was held at ground. Downstream of the extraction electrode was a planar glass slide coated on one side with conductive indium tin oxide; this layer was connected to an electrometer to measure the extracted spray current. A stack of three 3.2-mm-thick, 25.4-mm-diameter grade-N52 permanent magnets were placed below the fluid holder. This arrangement created a magnetic field directed normal to the unperturbed fluid free surface with a flux density of 340 G at the bottom of the fluid reservoir and 300 G at the free surface (measured 14144

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Figure 2. Magnetic electrospray jetting apparatus for experiment 1 was created by inducing a Rosensweig surface instability in an annular pool of ionic liquid ferrofluid. (A) Block diagram showing (1) an aluminum block and (2) an annular trench filled with ILFF. Below the trench is (3) a permanent magnet. (4) A coaxial extraction electrode was 4.7 mm downstream of the block, where (5) a glass slide coated with (6) indium tin oxide served as a current detector. (B) The magnetic field instability produced a five-tipped crown-shaped static Rosensweig pattern. (C) Assembled apparatus as viewed downstream of the ITO glass.

Figure 3. Electric field superimposed on the magnetic field causing the instability peaks to sharpen and emit current. (A) Profile image of the fivetipped array created in ILFF-2 under only a magnetic field. (B) Suitably strong electric field causing the tips to sharpen into current-emitting cones. (C−E) Magnetic features were incrementally strained and sharpened by the electric field, showing an abrupt onset of emission that in this case occurred at 2.6 kV to produce 2 μA of positively charged emission. Tests were conducted under vacuum with a pressure of 10−7 Torr.

Figure 4. Setup schematic for experiment 2 to determine how the peak-to-peak spacing of a magnetic surface instability depends upon the strength and gradient of the applied magnetic field. Experiment 2: Emitter Density Investigation. Each of the five tips in the Rosenswieg surface pattern of experiment 1 serves as an individual electrospray emitter. In principle, it would be straightforward to scale this design to many more emitters simply by using a pool with a larger surface area and a broader magnet. From a practical standpoint, it would be advantageous to maximize the emitter areal density, that is, pack as many emitter tips as possible into a given surface area to realize high-density broad electrospray beams. To determine the maximum practical emitter density, it is necessary to

with no fluid in the reservoir). As a result of the magnetic field, the ILFF in the concentric trench displayed a Rosensweig surface instability consisting of five symmetric fluid tips in a crown-type configuration as shown in Figures 2B and 3A. The width of the trench was intentionally chosen to be less than the ILFF capillary length in order to constrain the Rosensweig pattern geometrically to a single tip in the radial direction. The shark’s-tooth-shaped tips were then conveniently aligned with the downstream aperture in the concentric extraction electrode. 14145

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Figure 5. Current−voltage characteristics of the five-tipped emitter arrays in (A) ILFF-1 and (B) ILFF-2. Error bars show the standard deviation in current fluctuations recorded during 1 s of emission at the given voltage.

Figure 6. Comparison of varied emission geometries noted during spray operation. (A) Quiet conelike emission, (B) extended jet, (C) double apex, and (D) triple apex. understand how the tip-to-tip spacing in a ferrofluid surface instability depends upon fluid and field characteristics. In a classical Rosenswieg instability, a uniform, gradient-free magnetic field, such as that produced in the bore of a Helmholtz pair, is applied in the vertical direction to a pool of ferrofluid. In this configuration, the peak-to-peak spacing does not depend upon the strength of the magnetic field. As long as the fluid magnetization is greater than a critical value given by Mcrit2 = 2/μ0(1 + 1/μr)(ρgγ)1/2, then the peak-to-peak spacing is equal to the capillary length, λ = 2π(γ/ρg)1/2.15 The pattern of surface peaks induced in a ferrofluid excited by a permanent magnet is different from the classical Rosensweig instability in one important way: the permanent magnet creates a field with an intrinsic gradient, and this gradient strongly influences the shape of the surface instability. Surprisingly, a relationship quantifying the instability peak spacing in a nonuniform magnetic field is absent in the literature, despite the fact that countless undergraduate physics students have their first exposure to ferrofluids by placing a permanent magnet under a vial of fascinating black fluid. The astute student would notice that the peak-to-peak spacing caused by the permanent magnet can be more than an order-of-magnitude smaller than predicted by classical Rosenswieg instability theory for the same strength magnetic field. Rupp proposed an expression to estimate the peak-to-peak spacing of ferrofluid surface instabilities incited by a nonuniform magnetic field, but the derivation was not rigorous and the expression was never validated.46 To this end, we designed an experiment to measure the peak-to-peak spacing in a magnetic field with a nonzero spatial gradient with the goal of testing Rupp’s hypothesis. The setup is shown in Figure 4. The field above an assembly of permanent magnets was mapped with a spatial resolution of 0.5 mm using a Gauss probe mounted to micrometer translation stages. Two magnet assemblies were used separately. Magnet assembly 1 was a stack of three 152 mm × 3.18 mm × 7.84 mm rectangular-prism-grade N42 neodymium magnets. The magnetization direction of each bar was aligned in the 7.84 mm direction, and the bars were stacked so that their fields were additive. Magnet assembly 2 consisted of seven 3.18 mm × 3.18 mm × 25.4 mm rectangular-prism-grade N42 neodymium magnets arranged

as a Hallbach array. A Hallbach array is a linear assembly of magnets wherein each sequential magnet’s polarization is rotated 90° from its neighbor. The result is a magnetic field having a strength of 2× that of an individual bar magnet on one side of the array and negligible strength on the opposite side. For magnet assembly 2, the field measured at a location 0.52 mm from the surface of the high-field side was approximately 6200 G, and the field on the low-field side was 800 G. The Hallbach field also possesses a high spatial gradient. By using the two magnet assemblies, it was possible to subject the ferrofluid to a range of M∇B values that spanned three orders of magnitude. After mapping the magnetic field with the Gauss probe, a dish of ferrofluid was placed above the magnet assembly. Because the peak-topeak spacing does not depend on the electrical properties of the fluid and also because of the large volume of fluid required for these tests, a commercial ferrofluid, Ferrotec EFH-1, was used instead of ILFF. EFH-1 has a surface tension of γ =29 mN/m, a density of ρ =1210 kg/ m3, a relative permeability of μr = 2.6, and a magnetic saturation of Msat = 3.5 × 104 A/m. The position of the fluid pool and thus the strength and gradient of the magnetic field at the location of the fluid surface were adjusted by translating the dish vertically via a micrometer stage. A camera with a macrolens was positioned above the pool and used to image the resulting pattern of peaks. Software image processing was then used to locate the apex of each peak and register its spatial location.

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RESULTS AND DISCUSSION Experiment 1: Spray Emission Study. The fluid pool and electrode apparatus was placed in vacuum of 10−7 Torr. A voltage applied between the aluminum block holding the fluid pool and the extraction electrode stressed the ILFF, causing the peaks to grow taller with a decreasing apex radius of curvature as shown in Figure 3. Once a critical threshold voltage was reached, the curved peaks abruptly transitioned to sharp points, signaling the onset of spray emission. The electrospray current was measured on a collection electrode downstream, and current versus voltage (I−V) traces were recorded over a period 14146

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of a few minutes. Although the current from each of the five peaks in the array was not measured separately, postexperiment analysis of the collection electrode showed evidence of spray impingement above each peak, so we infer that all five peaks were emitting in parallel. Only limited data are available for ILFF-1 and only for bias polarity wherein negatively charged spray was emitted. The onset of this negative emission occurred when the extraction voltage reached −3250 V with an initial spray current of 1.6 μA. ILFF-2 was operated in both polarities with the magnitude of onset voltage between 2100 and 2500 V. The positively charged emission from ILFF-2 was seen to be significantly lower than the emission of negative spray for the same magnitude of extraction voltage. Results for ILFF-1 and ILFF-2 are shown in Figure 5. For voltages just slightly greater than the onset voltage, both ILFF-1 and ILFF-2 displayed quiescent spraythe visual appearance of the apex and the measured emission current were stable. As the voltage was increased beyond the onset values, both liquids demonstrated transients with ILFF-2 being generally less stable than ILFF-1. These transients in measured current were accompanied by fluctuations in the geometry of the apex. Quiet emission corresponded to a single sharp point in the apex as shown in Figure 6A. When the current was increased, the transients included sudden filamentary extensions (Figure 6B) that grew from the tip before collapsing and also temporary bifurcation and trifurcation (Figure 6C,D) of the emitter into multiple emission sites. Because of the high viscosity, ILFF-1 was more resistant to transient deformation in the tip structure, and we believe that this is the reason that ILFF-1 emission was more stable than that of ILFF-2. ILFF-1 displays a marked increase in current at an extraction voltage greater than 3540 V. The reason for this behavior is unknown, but the increase in current is also associated with an increase in fluctuation magnitude and likely indicates a different operating regime. The nonmonotonic behavior at the highest voltage in Figure 5A is likely an artifact of the erratic emission behavior for high electric fields. The magnetostatic Rosensweig surface features created in the ILFF serve the same role as the electrified capillaries in conventional electrospray. Namely, they are a means to realize a pointed fluid meniscus that can be further stressed by application of an electric field to result in eventual spray from the cone tip. However, whereas conventional electrospray is exclusively an electrostatic process, the current-emitting instabilities observed here are simultaneously electrostatic and magnetostatic manifestations. Both the electric and magnetic fields act in concert to stress and elongate the fluid meniscus in a way that neither field could accomplish alone. The behavior of the system is best described by analyzing the potential energy of the fields and their interaction with the fluid volume. Let the surface of a pool of ILFF be described by the function z = z(x, y), where z denotes the vertical location of the fluid interface in the presence of gravity. In the absence of applied fields, the pool of ILFF lies quiescent and planar with z = 0; this configuration simultaneously minimizes the gravitational and surface tension potential energy. When the pool of ILFF is then placed within electric and magnetic fields, the change in potential energy of the system due to the presence of the magnetized and conductive fluid is expressed as the sum of the gravitational, surface tension, magnetic, and electric potential energies as U = Ug + Uγ + UM + UE

where the contributions of gravitational, surface tension, magnetic, and electric energies are Ug =

1 ρg 2

Uγ = γ

∬ z 2(x , y) dx dy

∬

1 + (∇z)2 dx dy

UM =

∭ ∫ H dB dx dy dz

UE =

∭ ∫ E dD dx dy dz

(2)

The fluid is treated as a linear magnetic material having susceptibility χM such that M = χMH = (μr − 1)H and ∫ H dB = 1 /2HB. The magnetic energy can then be expressed as the sum of the vacuum magnetic field energy plus the additional energy contribution attributable to the presence of the ILFF in the field region UM =

1 2

∭volume μ0H02 dx dy dz

−

1 2

∭fluid μ0MH0 dx dy dz

(3)

where H0 is the value of the vacuum magnetic field (i.e., before the fluid was introduced), the first integral is taken over the entire volume (fluid and vacuum), the second integral is taken only over the fluid volume, and it is assumed that the magnetic charges responsible for creation of the vacuum field are held constant while the fluid is introduced into the field volume. The term ΔUM ≡ −

1 2

∭fluid μ0MH0 dx dy dz

(4)

is the energy change in the system associated with the presence of the magnetic fluid volume. The dependence of ΔUM on the shape and orientation of the fluid volume can be understood by invoking the concept of a demagnetizing field within the fluid: the magnetization of the fluid will reduce the intensity of the field internal to the fluid according to H = H0 − NM, where N is the shape-dependent demagnetizing factor. The magnetization within the fluid can then be written M=

(μr − 1) 1 + N (μr − 1)

H0

(5)

so that now ΔUM ≡ −

1 2

⎡

(μ − 1)

⎤

∭fluid μ0⎢⎢⎣ 1 + Nr (μ − 1) ⎥⎥⎦H02 dx dy dz r

(6)

An analogous derivation can be used to express the change in system energy attributable to the introduction of an electrically responsive fluid volume into a region of electric field E0 by replacing M with P, H with E, and μ with ε. The factor N, although usually referred to as the depolarization factor in the electrical context, is in fact the same shape-dependent function as that used to express the demagnetization. The electric energy associated with the fluid takes on a slightly different form for an electrically conductive fluid. In this case, the depolarization field within the fluid is complete such that the internal electric field is exactly zero or ε0E = ε0E0 − NP

(1) 14147

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stress is limited by the saturation magnetization of the fluid, which for ILFF-2 is Msat = 1.2 × 105 A/m. The maximum achievable magnetic surface stress for ILFF-2 is then 9 × 103 N/m. This stress is equivalent to the electrostatic stress produced by an electric field of En = 4.5 × 107 V/m. Compared to the electric stress, the magnetic stress is clearly an appreciable effect that significantly reduces the critical electric field required to cause the meniscus to snap over into a jetting instability. Experiment 2: Emitter Density Investigation. The pool of ferrofluid described in Figure 4 was translated vertically above each of the two magnet assemblies, and images of the surface instability were recorded at 0.5 mm increments. In each image, the x and y locations for each peak were registered, and for each peak, the nearest neighbors were identified. For this analysis, nearest neighbors were defined as any peaks that were within 135% of the closest peak. The peak-to-peak spacing for that peak was then defined as the average distance to all nearest neighbors, and the magnetic field strength and gradient for that peak were assigned from the Gauss probe data maps. In the vicinity of a permanent magnet, a pool of ferrofluid will experience a Kelvin body force that attracts the fluid as a whole to the high-field region at the magnet surface. Rupp proposed that, in the context of magnetic surface instabilities, the Kelvin force has an effect analogous to a gravity force, and thus it is reasonable to simply replace the gravity force term, fg = ρg, with the Kelvin magnetic force, f B = M∇B0/μr, in the classical Rosensweig dispersion relation for surface instabilities.46 Under this model, the peak-to-peak spacing then is not the capillary length but instead is

= 0, meaning that the polarization can be written as P = ε0E0/N and the change in system energy attributable to the fluid becomes ΔUE = −

1 2

∭fluid ε0 N1 E02 dx dy dz

(7)

When the pool of ILFF is then placed within electric and magnetic fields, the change in potential energy of the system due to the presence of the magnetized and conductive fluid is expressed as the sum ΔU =

1 ρg 2

∬surface z 2(x , y) dx dy

+γ

∬surface

− ...

1 2

1 − 2

1 + (∇z)2 dx dy ⎡

(μ − 1)

⎤

∭fluid μ0⎢⎢⎣ 1 + Nr (μ − 1) ⎥⎥⎦H02 dx dy dz r

1 ε0 E0 2 dx dy dz fluid N

∭

(8)

The equilibrium shape assumed by the fluid under these combined effects is such that the net energy of the system is minimized.17 Thus, whereas a curved fluid surface having protrusions extending in the vertical direction increases the gravitational and surface tension potential energy over a flat pool, the elongated fluid features aligned with the electric and magnetic field concomitantly decrease the magnetic and electric potential energy until a balance is struck. Demagnetizing/depolarizing factor N is a number less than or equal to unity that can be analytically determined only for simple shapes such as planar slabs (N = 1), spheres (N = 1/3), and spheroids;47 however, it is true that for a general arbitrary shape the value of N is reduced as that shape is stretched or made more prolate along the direction of the applied field.48 This behavior is exemplified by the well-documented distortion of discrete magnetic fluid droplets subjected to a field H.3,4,28,29 When E and H are aligned, both the magnetic and electric potential energies favor fluid configurations that are elongated in the common field direction so that N is reduced in magnitude.32,33 As N decreases so too does the system energy associated with the electric and magnetic fields. The magnetic field thus does more than simply create a pointed fluid meniscus from which a purely electrostatic spray is induced. Instead, when an electric field is applied to a preformed Rosensweig instability the distortion of the fluid peaks is greater than can be described by the electrostatic stress alone. The result is an ever-sharpening fluid meniscus that displays breakdown to spray emission at a lower electric field than would be expected in a purely electrostatic configuration. A purely electrostatic spray is modeled by considering the competing effects of electrostatic traction and surface tension at a curved liquid meniscus. The electrostatic traction applied normal to the liquid surface, σE = ε0En2/2, stretches the liquid toward the downstream electrode. The surface tension stress σγ = 2γ/rs, where rs is the surface radius of curvature, resists this deformation. The electric field strength where the electrostatic traction exceeds the surface tension is known as the critical field, and when σE ≥ σγ, the meniscus will begin to emit electrospray. The magnetic stress exerted on the surface of the ILFF introduces an additional force that acts together with the electrostatic traction to deform the meniscus. The magnetic stress normal to the surface is given by σM = μ0En2/2. This

λRUPP = 2π

γ M ∇B0

(9)

The peak-to-peak measurements recorded in experiment 2 are plotted versus M∇B0 in Figure 7, where B0 is the Gauss-probemeasured value of the field with no ferrofluid present. The fluid magnetization was taken to be the smaller value of M = (1 −

Figure 7. Measured peak-to-peak spacing from experiment 2. The inset photograph shows a sample image where individual peaks in the surface instability created by magnet assembly 1 have been identified with green markers. The solid line is λRUPP from eq 9.46 Vertical dashed lines indicate where the Kelvin body force is equal to 1× and 10× the gravitational force on the fluid. 14148

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(1/μr))/μ0B0 or Msat = 3.5 × 104 A/m (the saturation magnetization of EHF-1). In experiment 2, the Kelvin force was applied in the same direction as gravity, so the forces act together. When the parameter M∇B0 is greater than 105 A T/m2, the Kelvin force is more than 10× the gravity force and thus should dominate the instability dynamics when compared to gravity. In this regime, it is apparent from Figure 7 that Rupp’s model provides a very good description of the peak-to-peak spacing. Agreement is not very good when Kelvin and gravity forces are comparable, but this behavior is not unexpected given the simple assumption of the model. At small values of M∇B0, the peak spacing is seen to approach the capillary length, which is approximately 1 cm for EHF-1. When M∇B0 is very large, as was the case for magnet assembly 2, the peak spacing was as small as 0.4 mm. Given the surface tension and saturation magnetization of ILFF-2, the data in Figure 7 and Rupp’s model predict that the peak spacing of ILFF-2 subject to magnet assembly 2 would be 0.24 mm; arranged in a rectangular pattern, this implies an achievable emitter density of 16 tips/mm2.

Research, the U.S. Air Force Asian Office of Aerospace Research and Development, and Sirtex Medical.

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(1) Taylor, G. I. The stability of a horizontal fluid interface in a vertical electric field. J. Fluid Mech. 1965, 2, 1−15. (2) de la Mora, J. F.; Loscertales, I. G. The current emitted by highly conducting Taylor cones. J. Fluid Mech. 1994, 260, 155−184. (3) Brancher, J. P.; Zouaoui, D. Equilibrium of a magnetic liquid drop. J. Magn. Magn. Mater. 987, 65, 311−314. (4) Afkhami, S.; Tyler, A. J.; Renardy, Y.; Renardy, M.; St. Pierre, T. G.; Woodward, R. C.; Riffle, J. S. Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields. J. Fluid Mech. 2010, 663, 358−384. (5) Stone, H. A.; Lister, J. R.; Brenner, M. P. Drops with conical ends in electric and magnetic fields. Proc. R. Soc. London, Ser. A 1999, 455, 329−347. (6) Zeleny, J. The electrical discharge from liquid points, and a hydrostatic method of measuring the electric intensity at their surfaces. Phys. Rev. 1914, 3, 69−91. (7) Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. F.; Whitehouse, C. M. Electrospray ionization for mass spectrometry of large biomolecules. Science 1989, 246, 64−71. (8) Yarin, A. L.; Koombhongse, S.; Reneker, D. H. Taylor cone and jetting from liquid droplets in electrospinning of nanofibers. J. Appl. Phys. 2001, 90, 4836−4846. (9) Duong, A. D. Electrospray encapsulation of Toll-like receptor agonist resiquimod in polymer microparticles for the treatment of viscral leishmaniasis. Mol. Pharmaceutics 2013, 10, 1045−1055. (10) Paine, M. D.; Alexander, M. S.; Smith, K. L.; Wang, M.; Stark, J. P. W. Controlled electrospray pulsation for deposition of femtoliter fluid droplets onto surfaces. J. Aerosol Sci. 2007, 38, 315−324. (11) Gamero-Castano, M.; Hruby, V. Electrospray as a source of nanoparticles for efficient colloid thrusters. J. Propul. Power 2001, 17, 977−987. (12) Velasquez-Garcia, L. F.; Akinwande, A. I.; Martinez-Sanchez, M. A planar array of micro-fabricated electrospray emitters for thruster applications. J. Microelectromech. Syst. 2006, 15, 1272−1280. (13) Deng, W.; Klemic, J. F.; Li, X.; Reed, M. A.; Gomez, A. Increase of electrospray throughput using multiplexed microfabricated sources for the scalable generation of monodisperse droplets. J. Aerosol Sci. 2006, 37, 696−714. (14) Tang, K.; Lin, Y.; Matson, D. W.; Kim, T.; Smith, R. D. Generation of multiple electrosprays using microfabricated emitter arrays for improved mass spectrometric sensitivity. Anal. Chem. 2001, 73, 1658−1663. (15) Cowley, M. D.; Rosensweig, R. E. The interfacial stability of a ferromagnetic fluid. J. Fluid Mech. 1967, 30, 671−688. (16) Boudouvis, A. G.; Puchalla, J. L.; Scirven, L. E.; Rosensweig, R. E. Normal field instability and patterns in pools of ferrofluid. J. Magn. Magn. Mater. 1987, 65, 307−310. (17) Gailitis, A. Formation of the hexagonal pattern on the surface of a ferromagnetic fluid in an applied magnetic field. J. Fluid Mech. 1977, 82, 401−413. (18) Rosensweig, R. E. Magnetic fluids. Annu. Rev. Fluid Mech. 1987, 19, 437−463. (19) Richter, R.; Lange, A. Surface Instabilities of Ferrofluids. In Colloidal Magnetic Fluids: Basics, Development, and Application of Ferrofluids; Odenbach, S., Ed.; Lecture Notes in Physics 763; SpringerVerlag: Berlin, 2010; pp 157−248. (20) Rosensweig, R. E. Ferrohydrodynamics; Cambridge University Press: New York, 1985; pp 177−236. (21) Taktarov, N. G. Disintegration of streams of magnetic fluid. Magnetohydrodynamics 1975, 11, 156−158. (22) Berkovsky, B.; Bashtovoi, V. Instabilities of magnetic fluids leading to a rupture of continuity. IEEE Trans. Magn. 1980, 16, 288− 297. (23) Malik, S. K.; Singh, M. Stability of a magnetic fluid jet. Int. J. Eng. Sci. 1991, 29, 1493−1500.

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CONCLUSIONS A unique colloid has been developed by dispersing magnetic nanoparticles in an ionic liquid. Fluid ILFF-1 has nearly zero vapor pressure at room temperature and is superparamagnetic with a relative permeability of μr ≈ 10, saturation magnetization Msat = 1.2 × 105 A/m, and electrical conductivity σ = 0.63 S/m. When subjected to a magnetic field, this fluid displays a static Rosensweig instability with regularly spaced conical protrusions in the free surface. When the surface is further stressed with an electric field, the tip of each protrusion emits a jet of electrospray. A potential energy analysis of the fluid and field shows that the electric and magnetic effects act in concert to stretch the meniscus, ultimately resulting in fluid jetting. The onset of this jetting is expected to occur at a significantly lower value of extraction voltage than for a strictly electrostatic spray emitter; however, this has not been verified. An experiment measuring the shape of ferrofluid surface instabilities in the presence of strong magnetic fields with large spatial gradients shows that it should be possible to create electrospray sources with up to 16 emission sites/mm2 in ILFF-1.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

M.A.H motivated the work with ferrofluids and provided research input. L.B.K. and E.M. designed the research. E.M. conducted the experiments. B.S.H. and N.J. synthesized the ionic liquid ferrofluids. L.B.K. wrote, and all authors commented on the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge support from Dr. Mitat Birkan of the Air Force Office of Scientific Research, Dr. Ingrid Wysong from the Air Force Asian Office of Aerospace Research and Development, and Drs. James Haas and Dan Brown of the Michigan/ AFRL Center of Excellence in Electric Propulsion. Funding for this work was provided by the U.S. Air Force Office of Scientific 14149

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Article

(24) Sikora, M.; Sabados, T.; Svikova, M.; Timko, M. Flowing of magnetic fluid with free surface and drop formation. Phys. Procedia 2010, 9, 194−198. (25) Arkhipenko, V. I.; Barkov, Y. D.; Bashtovoi, V. G. Shape of a drop of magnetized fluid in a homogeneous magnetic field. Magnetohydrodynamics 1979, 14, 373−375. (26) Bacri, J. C.; Salin, D. Instability of ferrofluid magnetic drops under magnetic field. J. Phys. Lett. 1982, 43, 649−654. (27) Bacri, J. C.; Salin, D. Dynamics of the shape transition of a magnetic ferrofluid drop. J. Phys. Lett. 1983, 44, 415−420. (28) Zhu, G.-P.; Nguyen, N.-T.; Ramanujan, R. V.; Huang, X.-Y. Nonlinear deformation of a ferrofluid droplet in a uniform magnetic field. Langmuir 2011, 27, 14834−14841. (29) Lee, C.-P.; Yang, S.-T.; Wei, Z.-H. Field dependent shape variation of magnetic fluid droplets on magnetic dots. J. Magn. Magn. Mater. 2012, 324, 4133−4135. (30) Artana, G.; Romat, H.; Touchard, G. Theoretical analysis of linear stability of electrified jets flowing at high velocity inside a coaxial electrode. J. Electrost. 1998, 43, 83−100. (31) Ozgen, S.; Uzol, O. Investigation of the linear stability problem of electrified jets, inviscid analysis. J. Fluids Eng. 2012, 134, 091201. (32) Sherwood, J. D. The deformation of a fluid drop in an electric field: a slender-body analysis. J. Phys. A: Math Gen. 1991, 24, 4047− 4053. (33) Tyatyushkin, A. N.; Velarde, M. G. On the interfacial deformation of a magnetic liquid drop under the simultaneous action of electric and magnetic fields. J. Colloid Interface Sci. 2001, 235, 46− 58. (34) Dikansky, Y.; Nechaeva, O. A. Electrohydrodynamical instability of microdrops shapes in a magnetic fluid. J. Magn. Magn. Mater. 2005, 289, 90−92. (35) Dikansky, Y.; Nechaeva, O. A.; Zakinyan, A. R. Deformation of magnetosensitive emulsion microdroplets in magnetic and electric fields. Colloid J. 2006, 68, 137−141. (36) Zakinyan, A.; Tkacheva, E.; Dikansky, Y. Dynamics of a dielectric droplet suspended in a magnetic fluid in electric and magnetic fields. J. Electrost. 2012, 70, 225−232. (37) Tzirtzilakis, E. E. A mathematical model for blood flow in magnetic field. Phys. Fluids 2005, 17, 077103. (38) Ruo, A.-C.; Chang, M.-N.; Chen, F. Electrohydrodynamic instability of a charged liquid jet in the presence of an axial magnetic field. Phys. Fluids 2010, 22, 044102. (39) Mkrtchyan, L.; Zakinyan, A.; Dikansky, Y. Electrocapillary instability of magnetic fluid peak. Langmuir 2013, 29, 9098−9103. (40) Rodriquez-Arco, L.; Lopez-Lopez, M. T.; Gonzalez-Caballero, F.; Duran, J. D. G. Steric repulsion as a way to achieve the required stability for the preparation of ionic liquid-based ferrofluids. J. Colloid Interface Sci. 2011, 357, 252−254. (41) Pensado, A.; Padua, A. H. Solvation and stabilization of metallic nanoparticles in ionic liquids. Angew. Chem. 2011, 123, 8842−8846. (42) Huang, W.; Wang, X. Study on the properties and stability of ionic liquid-based ferrofluids. Colloid Polym. Sci. 2012, 290, 1695− 1702. (43) Jain, N.; Zhang, X.; Hawkett, B. S.; Warr, G. G. Stable and water-tolerant ionic liquid ferrofluids. ACS Appl. Mater. Interfaces 2011, 3, 662−667. (44) Bryce, N. S.; Pham, B. T. T.; Fong, N. W. S.; Jain, N.; Pan, E. H.; Whan, R. M.; Hamble, T. W.; Hawkett, B. S. The composition and end-group functionality of sterically stabilized nanoparticles enhances the effectiveness of co-administered cytotoxins. Biomater. Sci. 2013, 1, 1260−1272. (45) Jain, N.; Wang, Y.; Jones, S. K.; Hawkett, B. S.; Warr, G. G. Optimized steric stabilization of aqueous ferrofluids and magnetic nanoparticles. Langmuir 2010, 26, 4465−4472. (46) Rupp, P. Spatio-Temporal Phenomena in a Ring of Ferrofluid Spikes. Ph.D. Dissertation, University of Bayreuth, Bayreuth, Germany, 2003. (47) Osborn, J. A. Demagnetizing factors of the general ellipsoid. Phys. Rev. 1945, 67, 351−357.

(48) Aharoni, A. Demagnetizing factors for rectangular ferromagnetic prisms. J. Appl. Phys. 1998, 83, 3432−3434.

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