Article pubs.acs.org/Langmuir
Experimental Investigation of Wetting with Magnetic Fluids Selin Manukyan*,† and Marius Schneider‡ †
Merck KGaA, Frankfurter Str. 250, 64283 Darmstadt, Germany Institute of Gas Turbines and Aerospace Propulsion, Technische Universität Darmstadt, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany
‡
S Supporting Information *
ABSTRACT: Here we report the experimental results of the general wetting behavior of an oil-based ferrofluid and a water-based magnetic paint droplet on a hydrophobic surface under the effect of an external magnetic field. By increasing the magnetic field in the vertical direction, the height of the oil-based ferrofluid droplet increases while the width decreases; on the contrary, under the same circumstances, the height of the water-based magnetic paint droplet decreases whereas the width increases. The wetting behavior of the oil-based ferrofluid and the waterbased magnetic paint droplets is evaluated as a function of the contact angle, contact line diameter, and hysteresis curve alterations. Conclusively, a general explanation is given for the contrary behavior of both liquids, and some application processes for future implementations are introduced.
magnetic field strength. Moreover, Hong et al., Malouin et al., and Büscher et al. used the magnetic field and water-based ferrofluids for no-loss transport processes on capillary surfaces or thin separations.12−14 Zhu et al. reported an experimental and numerical study on the deformation of water-based ferrofluid droplets on hydrophobic surfaces under a uniform horizontal magnetic field.15 Tan et al. published a study on the formation and manipulation of ferrofluid droplets at microfluidic Tjunctions. They archived their control of the size of ferrofluid droplets in a microfluidic device by changing the magnetic field strength.16 A numerical study on the time-independent interactions between magnetic fields and ferrofluids with free surfaces was conducted by Lavrova et al.17 They achieved a simulation of the transition between shapes with rounded and conical ends of equilibrium drops numerically. Two years later, Chen and Cheng conducted an experimental investigation on Rosensweig instabilities on ferrofluid droplets. They measured the breakups of the initial droplet into numerous subscale droplets and showed a relationship between the magnetic Bond number and the volume of droplets.18 However, a detailed experimental investigation on the contact angle and contact angle hysteresis of magnetorheological fluids under various magnetic fields has not yet been conducted. In this article, we compared the wetting characteristics of an oil-based ferrofluid and a water-based magnetic paint on a hydrophobic flat surface. The contact angle, contact line diameter, droplet height, and magnetic hysteresis curves are measured as a function of the varying magnetic field strengths on
1. INTRODUCTION Ferrofluids are colloidal suspensions of ferromagnetic particles with a mean diameter of 10 nm that float in a carrier liquid. The particles are coated with a stabilizing dispersing agent to prevent particle agglomeration under strong magnetic field gradients. Ferrofluids are mainly used in mechanical components such as seals, bearings, and dampers and electronic components such as loudspeakers, stepper motors, and sensors because of their magnetic properties, broad working temperature range (−55 to 200 °C depending on the carrier fluid), and heat-transfer capacities under reduced gravity. Magnetic paint is a mixture of iron particles with a mean diameter of 35 μm, spread in a special lacquer. Because of the size and weight of the particles, floating in the carrier fluid is not possible. The iron particles precipitate in lacquer over time. Magnetic paints are starting to be used for 3D printing.1 The 3D effect is produced by the action of a permanent magnet or electromagnet on the freshly printed liquid printing ink. The lamellar pigments are oriented along the field lines of the magnet and thereby create the 3D image. To avoid the color and weakening of the magnetic alignment, the ink is dried immediately to freeze the 3D image. In the literature, we face a number of deep investigations devoted to the wetting of magnetic liquids.2−6 Moving and controlling water drops with fractions of paramagnetic particles are observed by Garcia et al., Egatz-Gomez et al., and Gou et al.7−9 With permanent magnets, they guide and control the microsized water drops mixed with various magnetic particles (such as spherical, paramagnetic magnetizable carbonyl iron particles) on superhydrophobic surfaces. Furthermore, Bormashenko et al. and Nguyen et al. replicated the same observation using water-based ferrofluidic drops.10,11 The kinematic behavior of the droplets is investigated as a function of the drop radius and © XXXX American Chemical Society
Received: December 29, 2015 Revised: April 17, 2016
A
DOI: 10.1021/acs.langmuir.5b04737 Langmuir XXXX, XXX, XXX−XXX
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cold light source (LED) is preferred to eliminate the heat effect of light. The images are stored in BMP format, and image processing is done with a customized MATLAB code. A Ni−Cu−Ni plated cylindrical NdFeB permanent magnet (purchased from Webcraft GmbH) is used for the experiments. The magnetic field strength and gradient are varied by moving the magnet up and down on the lifting table. A Hall-effect solid-state sensor (GaussMeter type 181002 from ThyssenKrupp with 2% overall accuracy) is used to measure the magnetic field (B, magnetic flux density) of the magnet on the test surface. The distance from the surface versus the magnetic flux density plot for the magnet is given in Figure 1b. All experiments are done at 24−26 °C and 35−40% RH. A drop of the fluid to be investigated is placed on the particular surface in front of the camera. The droplets are disposed of by using syringes with different kinds of needles, and the volume of the droplets in the initial state is calculated with an image-processing tool (Matlab) by assuming that the contact line has circular propagation. The initial parameters (i.e., the initial distance from the permanent magnet to the fluid, the temperature, and the air humidity) are recorded. As the video capture is started, the magnetic field is simultaneously and steadily increased/decreased by elevating/lowering the magnet until a specified number of images are recorded. On the flat hydrophobic surface, the change in the contact angle, height, contact line diameter, and magnetic hysteresis of the droplets is measured in time. In the experiments, oilbased ferrofluid and water-based magnetic paint are compared. These two liquids differ in viscosity, magnetic particle concentration, magnetic particle size, and susceptibility (Table 1). The surface tension and density of both liquids are very similar despite the dissimilar carrier fluids, but both liquids have a distinguishing initial contact angle on the hydrophobic surface as a result of the carrier liquids. The aim of the experiments is to characterize the wetting features of the oil-based ferrofluid droplets and the water-based magnetic paint droplets under various magnetic field strengths on a hydrophobic surface. The fundamental data might be used for future industrial applications such as coating, homogeneous painting on rough surfaces, and microfluidic tool design.
a planar hydrophobic surface. We also used a theoretical formulation for the differences and similarities of both liquids and their states under increasing/decreasing magnetic field strength.
2. MATERIALS AND METHODS The features of the test liquids are given in Table 1. The oil-based ferrofluid (EFH1-type ferrofluid purchased from Ferrotec GmbH) is a
Table 1. Characteristic Features of the Ferrofluid and Magnetic Paint ferrofluid
magnetic paint
carrier fluid viscosity μ
light hydrocarbon 6 mPa·s @27 °C (Newtonian)
nominal particle diameter density ρ magnetic particle concentration surface tension σ capillarity length l = (σ/ρg)1/2 magnetic particles
l0 nm
water 500 mPa·s @23 °C (nonNewtonian/shear thinning) ∼35 μm
1.21 g/cm3 7.9 vol %
1.16 g/cm3 10 vol %
29 mN/m 2.44 mm
30 mN/m 2.64 mm
spherical Fe3O4 particles
FC3O4 coated flake pigments shape anisotropy due to flake pigments
anisotropy interaction energy between particles magnetic susceptibility of carrier fluid
magnetocrystalline anisotropy due to spherical particles low paramagnetic
high diamagnetic
colloidal suspension of spherical Fe3O4 particles (7.9%) in light hydrocarbon oil (92.1%). However, the water-based magnetic paint (magnetic effect screen printing ink 750 purchased from Pröll KG) is a mixture of water (50%), Fe3O4-coated flake pigments (10%), color pigments (10%), and additives and dispersion polymers (30%). The hydrophobic surfaces used in the experiments are prepared by spray coating clean microscope slides with Tegotop210 (Evonik Industries), which is not soluble either in oil-based ferrofluid or water-based magnetic paint. The arrangement of the components is given in Figure 1a. Image capture is accomplished by the HCC 1000 Vosskuehler camera with a maximum dynamic range of 8 bits (256 gray levels) and a resolution of 1024 pixels × 1024 pixels. The spatial resolution is 100 pixels per mm. A
3. RESULTS We first investigated the effect of an increasing magnetic field on the shape of the oil-based ferrofluid and water-based magnetic paint on a hydrophobic surface. The arrows in Figure 2 show the deformation direction of the sessile droplet of each fluid under increasing magnetic field strength. As the magnetic flux density increases on the vertical axis, the water-based magnetic paint droplet lowers its height along the direction of the magnetic field and becomes flattened upon enlarging its contact line diameter; on the other hand, the sessile ferrofluid droplet is elongated along
Figure 1. (a) Side-view sketch of the experimental setup (not to scale). (b) Magnetic flux density versus distance from the magnet’s surface measured using a Hall sensor. A power law fitting is used. The measurement error is 2%. B
DOI: 10.1021/acs.langmuir.5b04737 Langmuir XXXX, XXX, XXX−XXX
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more or less constant and the contact angle decreases until the turning point is reached. Above the threshold magnetic field strength, the contact line moves, resulting in an increasing contact angle and a decreasing diameter. For the magnetic paint, the contact line diameter and height of the droplet stay constant up to the threshold magnetic field strength value as the contact angle increases. Up to the specific threshold value, the contact line diameter starts to increase as the height and contact angle of the droplet decrease. The slope of the normalized height and normalized contact line diameter of ferrofluid are steeper compared to the slope of the normalized height and the normalized contact line diameter of the magnetic paint (Figure 4). It is due to the inertia of the magnetic paint. Having a higher viscosity, magnetic paint does not react upon magnetic field changes as much as the ferrofluid does. The experiments are done with various drop volumes to evaluate the relationship between the volume dependence on the contact angle turning points at the optimum magnetic field strength. It is concluded that the volume alteration plays a role only in the initial contact angle, initial height, and initial contact line diameter but not on the general attitude of the droplets. The higher values of the contact angles of the water-based magnetic paint compared to those of the ferrofluid on a hydrophobic surface can be explained by the different carrier liquids of both suspensions. Because the ferrofluid carrier liquid is oil, it has a rather low contact angle on the hydrophobic surfaces. The magnetic paint suspension is based on water; therefore, its contact angle is remarkably higher. To measure the magnetic hysteresis of the droplets, one initially nonmagnetized droplet was exposed to a magnetic field whose strength increased first and then decreased to the initial state. In Figures 5 and 6, the hysteresis curves of the contact angle, droplet height, and contact line diameter are given. The contact angles show their typical V shape (as in Figure 3) in both curves, but the bottom/peak of the curves is shifted to smaller magnetic field strengths. Both curves have the same value of the advancing and receding contact angles, respectively. The hysteresis curves of droplet height and contact line diameter show also a similar regime as contact line hysteresis. As the magnetic field decreases, the magnetic particles need a trigger magnetic field value to regulate their magnetic dipoles to react. As soon as the stimulation is achieved, the variation with respect to the height and contact line diameter begins.
Figure 2. (a) Ferrofluid droplet (10.3 μL) on a Tegotop201-coated microscope slide with an applied magnetic field. (b) Magnetic paint (15.5 μL) on a Tegotop201-coated microscope slide without any applied magnetic field compared to an oil-based ferrofluid, (a) raising its apex (H) and shrinking its contact line diameter (D) under an increasing magnetic field strength, contrary to a water-based magnetic paint droplet (b), which lowers it apex (H) and enlarges its contact line diameter (D). White horizontal dashed lines symbolize the contact line, and black dashed arrows show the movement direction of the drops with increasing magnetic field strength.
the direction of the magnetic field by elevating its apex and reducing its contact line diameter. Figures 3 and 4 show the measured parameters (contact angle, normalized height, and normalized contact line diameter as a function of magnetic field strength) for both droplets. The experimental results show that the contact angle change in the ferrofluid droplet has a minimum turning point independent of the volumetric size of the droplet. Similar behavior is observed for the magnetic paint with a maximum turning point. As can be seen in the plotted data (Figures 3 and 4), when the magnetic field strength is increased, the contact angle of the magnetic paint droplet increases and that of the ferrofluid droplet decreases without the movement of the triple line until a threshold value is reached. As soon as the turning point is reached, the contact line starts to move, the contact angle of the magnetic paint droplet decreases, and the ferrofluid droplet increases. Furthermore, the plots (Figures 3 and 4) show that the height of the ferrofluid droplet begins to increase before the contact line diameter begins to fall rapidly. Up to the threshold magnetic field strength, the contact line diameter of the ferrofluid droplet is
Figure 3. Measurements of the contact angle as a function of magnetic field strength for sessile ferrofluid and magnetic paint droplets in three different volumetric sizes. The contact line is pinned until the minimum (and, respectively, maximum) contact angle is reached. The turning point on the contact angle shows that at a specific magnetic field strength the pinned contact line starts to loosen itself and slides on the substrate. C
DOI: 10.1021/acs.langmuir.5b04737 Langmuir XXXX, XXX, XXX−XXX
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Figure 4. Plots of normalized height and normalized contact line diameter as a function of magnetic field strength for sessile ferrofluid and magnetic paint droplets in three different volumetric sizes.
Figure 5. Hysteresis plots of contact angle (a) and normalized height and normalized contact line diameter (b) as a function of magnetic field strength for a sessile ferrofluid droplet with a volume of 4.7 μL.
Figure 6. Hysteresis plots of contact angle (a) and normalized height and normalized contact line diameter (b) as a function of magnetic field strength for a sessile magnetic paint droplet with a volume of 21.4 μL.
drops under magnetic field alterations. Moreover the size, shape, concentration, and distribution of the magnetite particles play important roles in the attitude of the droplets (Supporting Information). This can be explained theoretically by applying the well-known Bernoulli equation explained in Appendix A. The height difference between the initial and final position for each
4. DISCUSSION The ferrofluid has a paramagnetic carrier fluid (oil) compared to magnetic paint’s diamagnetic carrier fluid, namely, water. Because of this fact, ferrofluid has a positive magnetic susceptibility and magnetic paint has a negative magnetic susceptibility, which explains the opposite attitude of the two D
DOI: 10.1021/acs.langmuir.5b04737 Langmuir XXXX, XXX, XXX−XXX
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Figure 7. Summary sketch of Figures 3 and 4. (Left) The contact angle and droplet height/contact line behavior of the ferrofluid droplet on a hydrophobic surface with increasing magnetic field strength. (Right) The contact angle and droplet height/contact line behavior of the magnetic paint droplet on a hydrophobic surface with increasing magnetic field strength.
drop can be estimated using eq 1a, where the average magnetization M̅ contains the susceptibility variable h2 − h1 =
M̅ =
1 H
mass × acceleration
μ0 HM̅
∫0
ρg H
M dH =
∫0
force due to gravity
dH + μ0 M a ds ds (A.1)
force due to magnetism
H
χH dH
where ρ is the density, a is the flow area, ν is the velocity, s is the flow length, g is the gravitational constant, μ0 is the permeability of free space, M is the magnetization, H is the magnetic field strength, and α is the angle of applied force on the horizontal axis. The augmented Bernoulli equation for magnetic fluids after some calculations is shown in eq A.2.
(1b)
where h2 − h1 is the height difference, ρ is the density, g is the gravitational constant, μ0 is the permeability of free space, M is the magnetization, H is the magnetic field strength, M̅ is the average magnetization, and χ is the magnetic susceptibility.
H1 ν12 + ρgh1 − μ0 M dH 0 2 H2 ν2 = p2 + ρ 2 + ρgh2 − μ0 M dH 0 2
5. CONCLUSIONS
∫
p1 + ρ
We investigated the wetting properties of the oil-based ferrofluid droplets compared to those of the water-based magnetic paint droplets in various volumetric sizes on a hydrophobic flat surface. We observed that with increasing magnetic field strength the ferrofluid droplet gets a pointy shape with the decreasing and then increasing contact angle change and magnetic paint gets a clenched shape with an increasing and then decreasing contact angle change (Figure 7). The analysis of the ferrofluidic and magnetic paint droplets on plain surfaces is carried out with the aim of providing a theoretical basis for the description of their general behavior and the parameters affecting it. This basic information might construct a basis for future technical applications such as industrial magnetic coatings. A colloidal suspension of magnetic paint might be an alternative for the homogeneous uniform coating of structured surfaces, which shall be spread on a structured surface and preserve the surface shape of the structure in the best way possible under exposure of a magnetic field while drying. The points that should be considered are the homogeneity of the magnetic field, the magnetic field strength, and the fluid volume. The applied magnetic field should be larger than the coated/wetted area, and the magnetic field strength should not be increase spontaneously but gradually to avoid instabilities.
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− ρa ds g sin α
net force due to pressure
(1a)
1 H
dp −a ds ds
dv ρ a ds v = s d
∫
(A.2)
In our case, the drop is stationary, where ν = 0 and p1 = p2, so the equation becomes h2 − h1 =
M̅ =
1 H
μ0 HM̅ ρg
∫0
H
M dH =
(A.3a)
1 H
∫0
H
χH dH
(A.3b)
where M̅ is the average magnetization and χ is the magnetic susceptibility. Equation A.3a is a function of the magnetic susceptibility χ and magnetic field strength H. In our case, the magnetic field strength is equal for both liquids, but the magnetic susceptibility χ is negative for the ferrofluid and positive for the magnetic paint, which explains the ascent/descent of the two liquids. We calculated a reduced magnetic susceptibility value for magnetic paint due to amorous water content, which is a diamagnetic material χreduced =
χ1 A% × χ2 B% χ1 A% + χ2 B%
(A.4)
where χ is the magnetic susceptibility and A and B are the percentages of the substrates. The water content in magnetic paint maintains the negative pole sign of the magnetic susceptibility, which causes a decrease in droplet height with increasing magnetic field. We also defined a magnetic-fieldstrength-dependent contact angle given below
APPENDIX A. MAGNETIC BERNOULLI EQUATION
To be able to explain the ascent of the ferrofluid and the descent of magnetic paint under an increasing magnetic field, an augmented magnetic Bernoulli equation has been implemented. The equation of motion is given below E
DOI: 10.1021/acs.langmuir.5b04737 Langmuir XXXX, XXX, XXX−XXX
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χ a|B − Bt | + θi |χ |
(4) Zhao, Y.; Fang, J.; Wang, H.; Wang, X.; Lin, T. Magnetic Liquid Marbles: Manipulation of Liquid Droplets Using Highly Hydrophobic Fe3O4 Nanoparticles. Adv. Mater. 2010, 22 (6), 707−710. (5) Xue, Y.; Wang, H.; Zhao, Y.; Dai, L.; Feng, L.; Wang, X.; Lin, T. Magnetic Liquid Marbles: A “Precise” Miniature Reactor. Adv. Mater. 2010, 22 (43), 4814−4818. (6) Rosensweig, R. E. Ferrohydrodynamics; Cambridge University Press, 1985. (7) Egatz-Gomez, A.; et al. Discrete magnetic microfluidics. Appl. Phys. Lett. 2006, 89, 034106. (8) Garcia, A.; et al. Magnetic movement of biological fluid droplets. J. Magn. Magn. Mater. 2007, 311, 238−243. (9) Guo, Z.; Zhou, F.; Hao, J.; Liang, Y.; Liua, W.; Huck, W. ”Stick and slide” ferrofluidic droplets on superhydrophobic surfaces. Appl. Phys. Lett. 2006, 89, 081911. (10) Bormashenko, E.; Pogreb, R.; Bormashenko, Y.; Musin, A.; Stein, T. New Investigations on Ferrofluidics: Ferrofluidic Marbles and Magnetic-Field-Driven Drops on Superhydrophobic Surfaces. Langmuir 2008, 24 (21), 12119−12122. (11) Nguyen, N.; Zhu, G.; Chua, Y.; Phan, V.; Tan, S. Magnetowetting and Sliding Motion of a Sessile Ferrofluid Droplet in the Presence of a Permanent Magnet. Langmuir 2010, 26 (15), 12553−12559. (12) Hong, X.; Gao, X.; Jiang, L. Application of Superhydrophobic Surface with High Adhesive Force in No Lost Transport of Superparamagnetic Microdroplet. J. Am. Chem. Soc. 2007, 129 (6), 1478−1479. (13) Malouin, B.; Vogel, M.; Hirsa, A. Electromagnetic control of coupled droplets. Appl. Phys. Lett. 2010, 96, 214104. (14) Buescher, K.; Helm, C.; Gross, C.; Gloeckl, G.; Romanus, E.; Weitschies, W. Nanoparticle Composition of a Ferrofluid and Its Effects on the Magnetic Properties. Langmuir 2004, 20, 2435−2444. (15) Zhu, G.; Nguyen, N.; Ramanujan, R.; Huang, X. Nonlinear Deformation of a Ferrofluid Droplet in a Uniform Magnetic Field. Langmuir 2011, 27, 14834−14841. (16) Tan, S.; Nguyen, N.; Yobas, L.; Kang, T. Formation and manipulation of ferrofluid droplets at a microfluidic T-junction. J. Micromech. Microeng. 2010, 20, 045004. (17) Lavrova, O.; Matthies, G.; Mitkova, T.; Polevikov, V.; Tobiska, L. Numerical treatment of free surface problems in ferrohydrodynamics. J. Phys.: Condens. Matter 2006, 18, 2657−2669. (18) Chen, C.; Cheng, Z. An experimental study on Rosensweig instability of ferrofluid droplet. Phys. Fluids 2008, 20, 054105. (19) Papathanasiou, A.; Boudouvis, A. Three-dimensional magnetohydrostatic instabilities of rotating ferrofluid drops. J. Magn. Magn. Mater. 1999, 201, 290. (20) Bormashenko, E.; Whyman, G. Variational approach to wetting problems. Chem. Phys. Lett. 2008, 463, 103−105. (21) Bormashenko, E. Yount, Boruvka-Neumann, Wenzel and CassieBaxter equations as the transversality conditions for the variational problem of wetting. Colloids Surf., A 2009, 345, 163−165.
(A.5)
where θc(B) is the contact angle, a is a constant, Bt is the magnetic field strength at the turning point, and θi is the initial contact angle. The χ/|χ| parameter gives us the direction of movement of the drop being a ferrofluid or a water-based magnetic fluid. This equation is applicable for wetting or coating applications. (Except eqs A.4 and A.5, all equations are cited from ref 6.)
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APPENDIX B. SHAPE OF THE DROPLET UNDER AN APPLIED MAGNETIC FIELD Papathanasiou et al.19 and Bormashenko et al.20,21 conducted a number of in-depth theoretical studies on the equilibrium shape of the magnetic sessile droplets under an applied magnetic field. Papathanasiou et al.19 solved the magnetohydrostatic equilibrium by using Young−Laplace eq B.1 with magnetic terms.
where (ρ2 − ρ1) is the difference between the magnetic fluid and air density, g is the gravitational acceleration, R0 is the radius of a sphere of volume equal to that of the drop, σ is the surface tension, μ0 is the magnetic permeability, χ is the susceptibility of the magnetic liquid, H0 is the applied field strength, u is the magnetostatic potential, is the local mean curvature, and P is the constant reference pressure. Moreover, Bormashenko et al.20,21 analyzed the shape of a pinned droplet exposed to an external potential as a 3D wetting problem. They replaced the potential energy term in the freeenergy equation of the droplet with an external potential (e.g., magnetic potential) and solved it to define the shape of the droplet. These studies can be taken to investigate the wetting phenomena of magnetic liquids with varying carrier fluids and magnetic particles more in detail.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.5b04737. Effect of magnetic particle size on the characterization of the magnetic liquid, free body diagrams of the ferrofluid and magnetic paint drops, relationship of the force components on the magnetic liquids, and accumulation structure of the spherical and magnetic flake particles in a ferrofluid and in magnetic paint under a magnetic field (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Pröll, K. G. www.proell.de. (2) Tadmor, R.; Rosensweig, R. E.; Frey, J.; Klein, J. Resolving the Puzzle of Ferrofluid Dispersants. Langmuir 2000, 16 (24), 9117−9120. (3) Rosensweig, R. E. Annu. Rev. Fluid Mech. 1987, 19, 437−461. F
DOI: 10.1021/acs.langmuir.5b04737 Langmuir XXXX, XXX, XXX−XXX
