Static Magnetowetting of Ferrofluid Drops - Langmuir (ACS Publications)

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Static magnetowetting of ferrofluid drops Carlo Rigoni, Matteo Pierno, Giampaolo Mistura, Delphine Talbot, Rene Massart, Jean Claude Bacri, and Ali Abou-Hassan Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01934 • Publication Date (Web): 06 Jul 2016 Downloaded from http://pubs.acs.org on July 8, 2016

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Static magnetowetting of ferrofluid drops Carlo Rigonia, Matteo Piernoa, Giampaolo Misturaa,* Delphine Talbotb, René Massartb, Jean-Claude Bacric, Ali Abou-Hassanb,* a

Dipartimento di Fisica e Astronomia G.Galilei, Università di Padova, via Marzolo 8, 35131 Padova (Italy)

b

Sorbonne Universités, UPMC Univ Paris 06, UMR 8234 CNRS, Laboratoire Physico-chimie des Electrolytes et

Nanosystèmes InterfaciauX (PHENIX), 4 place Jussieu, 75005 Paris (France). c

Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057, CNRS and Université Paris Diderot, 75205 Paris

(France)

E–mail: [email protected] [email protected]

Abstract 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 subject to the action of permanent magnets of different size and strength. 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 due to 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, while the drop vertical elongation is

effectively expressed by a dimensionless number which compares the pressure jump at the ferrofluid interface due to the magnetization with the capillary pressure.

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Introduction Controlling the motion of liquid drops on solid surfaces is fundamental for droplet-based microfluidics.1 These nanoliter- to microliter-sized droplets, each serving as an isolated vessel for chemical processes, can be made to move, merge, split and dispense from reservoirs.2 To achieve this goal, a variety of different methods has been explored. Passive control is obtained by tailoring the surface with suitable patterns formed by hydrophilic/hydrophobic domains3- 6 or by altering the surface morphology.7,

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In particular, motion of drops on biomimetic superhydrophobic surfaces has been

extensively studied.9, 10 Active actuation of drops is realized with a spatial gradient of hydrophobicity,11 ultrasonic surface acoustic waves,12 vibrations of the substrate.13- 15 A more exotic method relies on the so-called Leidenfrost phenomenon, that is the levitation of drops on a cushion of vapor when they are brought in contact with a hot solid.16,

17

For polar liquids, electrowetting provides an efficient

mechanism to drive liquids with electric fields generated by arrays of electrodes integrated in the surface and covered with an insulating layer.2 Analogously, magnetic fields can be used to actuate ferrofluid drops.18-26 The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field has been investigated numerically.20 The droplet undergoes dramatic deformations owing to the presence of an external magnetic field gradient. Its shape is influenced by the magnetic Bond number, as well as inertia. The simulations show that the droplet velocity is mainly influenced by the competition between the magnetic force, which is proportional to the volume, and the viscous drag force, which is proportional to the radius. Hence, the larger the drop, the faster it is. The sliding of drops of ferrofluid aqueous solutions on a tilted hydrophobic surface is found to depend on the concentrations of surfactant and magnetic particles, the external field and the experimental assembly.19 Ferrofluid drops have been dragged on a horizontal substrate by a permanent magnet moving at a constant velocity. If the magnetic force is large enough to overcome the resistance of the friction and capillary forces, the drop can slide with the same linear ACS Paragon Plus Environment

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velocity as the magnet up to a critical velocity, beyond which the drop is not able to follow the moving magnet.22 The motion of ferrofluid drops on superhydrophobic surfaces in an external magnetic field has been studied and the interaction force between the magnetic water droplet and the surfaces is measured to be very low.18 It is observed that the threshold magnetic force necessary for the sliding of ferrofluid drops on superhydrophobic surfaces depends linearly on the drop radius, suggesting that the motion of the drop is defined by the processes occurring in the vicinity of the triple line only.21 A good understanding of the sliding of ferrofluid drops requires a prior knowledge of their static wetting properties under an external magnetic field. In general, the meniscus of a ferrofluid in the presence of a horizontal or vertical magnetic field has been extensively investigated.27-31 A waterbased ferrofluid drop surrounded by immiscible mineral oil is stretched by a uniform magnetic field parallel to the substrate surface.23 The results show that a rising magnetic field increases the drop width and decreases the droplet height. The apparent contact angle of stationary sessile ferrofluid drops under different magnetic field perpendicular to the substrate has been also measured.22 The top face of three permanent magnets of different size and strength is positioned at a fixed distance of 2 mm from the glass substrate coated with a Teflon layer. A stronger magnetic field is found to pull down and laterally stretch the ferrofluid droplet, increasing its base diameter, decreasing its height and its apparent contact angle, all variations being linear. The study of the shape of liquid oxygen drops subject to the magnetic field of a permanent magnet, whose distance from the substrate is varied, confirms the flattening of the drop, which can be accounted for by the modification of the capillary length due to the magnetic force.17 More important, it shows that the gradient of the magnetic field plays a key role in determining the drop shape. Recent results of density functional calculations of a nanodrop of an Ising fluid on a solid surface suggest a rich wetting scenario.32 In the nonuniform field generated by a permanent magnet, the contact angle first increases with increasing magnetic field and then decreases, with the decrease being almost linear for large values of the magnetic field. For the


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uniform magnetic field, the contact angle increases with increasing magnetic field, approaching an asymptotic value that depends on the strength of the fluid-fluid magnetic interactions. We have then decided to systematically explore the magnetowetting effect by measuring the morphology of ferrofluid drops subject to the action of 5 permanent magnets of different size and strength. By varying the magnets and their distance to the surface, it is possible to change both the amplitude and the gradient of the magnetic field. Magnetic forces up to 100 times the gravitational one and magnetic gradients up to 1 T/cm are achieved. In this way, we can observe flattened drops caused by the magnetic attraction to drops extended normally to the substrate due to the polarizing effect of the magnetic field and we find that the observed trends can be rationalized in terms of two dimensionless numbers.

Methods Ferrofluids. The ferrofluids used in this work are stable aqueous suspensions of maghemite (γFe2O3) nanoparticles. They are synthetized according to the Massart process.33 In brief, ammonium hydroxide (1L, 20% from VWR) is added to a mixture of ferric and ferrous chlorides (respectively 0.9 mol and 1.8 mol) to obtain magnetite nanoparticles that are oxidized to maghemite by adding an iron nitrate solution (800 mL, 1.3 mol) and heating at 80°C for 30 min followed by washing and suspension in a nitric acid solution (360 mL, 2 mol/L). These nanoparticles are positively charged with NO3- as counter ions. To obtain a higher concentration of the ferrofluid, the aqueous suspension is dialyzed (spectra pore membrane MWCO (Daltons): 12000) in a bath (1L) against nitric acid solution (0.1% wt) containing polyethylene glycol (PEG, MW 35000; 7% wt). After dialysis, the final concentration in iron as obtained from atomic absorption is 7.5 mol. L-1. The nanoparticles are rock like shape with a crystal diameter of about 8.5 nm, as determined from transmission electron microscopy. Figure 1 shows the magnetization curves of the seven ferrofluid solutions (denoted from F1 to F7) of different Fe concentrations used in this study and obtained using a vibrating sample ACS Paragon Plus Environment

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magnetometer (VSM). The magnitude of magnetization as a function of the field strength follows the Langevin law typical of superparamagnetism for diluted solutions,34) calculated for an assembly of nanoparticles with diameters fitted by a Log-normal distribution function of mean d0 = 8 nm and variance σ = 0.4 nm.

Figure 1. Magnetization curves at 285K of the different ferrofluids used in our experiments. The iron concentrations and the magnetic susceptibilities (χ ) of the different ferrofluids are: F1 = 0.2 mol/L, χF1 = 0.042; F2 = 0.4 mol/L, χF2 = 0.144; F3 = 0.8 mol/L, χF3 = 0.144; F4 = 1.5 mol/L, χF4 = 0.28; F5 = 2.0 mol/L, χF5 = 0.35; F6 = 3.0 mol/L, χF6 = 0.57; F7 = 4.0 mol/L, χF7 = 0.74

Magnets. Five different neodymium magnets are employed. Their main specs are listed in Table 1. The magnets have cylindrical shape and the diameter is always much larger than the maximum size of the ferrofluid drops. This guarantees that the magnetic field can be considered as homogeneous in the horizontal plane and only dependent on the vertical distance z between the magnet and the bottom of the drop.


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Magnet

t

d

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Type

Br

Bmax

(T)

(T)

(mm)

(mm)

M1

30.0±0.1

45.0±0.1

N40

1.25

0.48±0.05

M2

20.0±0.1

12.0±0.1

N35

1.17

0.50±0.05

M3

10.0±0.1

10.0±0.1

N45

1.32

0.55±0.05

M4

3.0±0.1

9.0±0.1

N35

1.17

0.33±0.03

M5

5.0±0.1

60.0±0.1

N42

1.29

0.10±0.01

Table 1. Main specs of the five neodymium magnets used in this work labelled M1 to M5 having thickness t, diameter d, grade of neodymium Type, residual magnetic field Br and maximum magnetic field measured at the center Bmax.

Figure 2 shows the magnetic fields measured with a Hall probe (LakeShore 460 3-Channel Gaussmeter with a 3-Axis Probe) along the axes of the five magnets. The continuous lines represent the spatial dependence of the axial component of the magnetic fields calculated from equation:35 =

+ − 2 +

2 + + 2

(1)

where Br is the residual magnetic field of the magnet, t is its thickness and d its diameter, whose values are listed in Table 1. The experimental data agree very well with the theoretical predictions. Accordingly, the gradient of the magnetic field is calculated from the spatial derivative of equation (1). In particular, we point out that the smallest (largest) magnet, M3 (M5), is that presenting the highest (lowest) gradient.


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Figure 2. Experimental (full symbols) and theoretical (continuous lines) values of the axial magnetic field as a function of the distance from the surface of the magnet. The curves are not fit to the data but are calculated from Eq. (1) using the parameters listed in Table 1.

Optical set-up. The experimental setup used in this study is described in Figure 3. To measure the deformation of ferrofluids, drops of known volume V are deposited on the substrate by using a syringe pump (World Precision Instruments Inc.). They are illuminated by a back-light collimated led and their profile is viewed by a CCD video camera (Manta G-146, Allied Vision Technologies) mounting a telecentric lens. Glass slides of thickness equal to 1 mm coated with different materials to span an ample wettability range are used as substrates. The coatings comprise a hydrophilic layer of a thiolenic adhesive36 (NOA 81 by Norland Products Inc., USA), a hydrophobic layer of Polydimethylsiloxane (PDMS) and a nearly superhydrophobic sol-gel layer. An automatic actuator varies the distance of the permanent magnet from the bottom of the glass slide in a controlled way. The acquired images and videos are analyzed off-line using a custom made program that calculates the apparent contact angle, the height and the lateral extension of the contact line of the ferrofluid drops.37


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Figure 3. Schematic drawing of the experimental set-up used to collect the profile of sessile drops in presence of a permanent magnet.

Results Figure 4 summarizes the overall phenomenology observed with ferrofluid drops deposited on a PDMS surface. The drops have all the same volume = 2.5 µL but different molar concentrations and are

placed at a distance of 1 mm from three different magnets. For each concentration, increasing the field gradient causes a flattening of the drop. A progressive flattening of the drop is also observed as the concentration of the drop is increased in presence of magnet M2. However, the middle sequence observed with magnet M1 and, above all, the top one with magnet M5 shows an opposite trend: increasing the magnetization elongates the drop profile along the field direction, which assumes the shape of a cusp as recently observed in a recent experiment on the self-assembly of ferrofluid drops.38 Next, we will discuss in more detail the various cases that we will show to be the result of a rich interplay between the strength of the magnetic field and its gradient.


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Figure 4. Images of ferrofluid drops with various concentrations placed at a distance of 1 mm from three permanent magnets having very different values of the axial gradient dB/dz. The value for magnet M5 is dB/dz = 1.34 ± 0.04 T/m , for magnet M1 dB/dz = 17.4 ± 0.4 T/m and for magnet M2 dB/dz = 86 ± 2 T/m.

The magnetic force per unit volume exerted by a magnet is:17 =

(2)

where is the ferrofluid magnetization corresponding to B and is the gradient of the magnetic field. The values of the magnetic force deduced from Eq. (2) for the three magnets mentioned above and for two different ferrofluid concentrations are reported in Figure 5. In the graph, the magnetic force is normalized to the volumic weight ρg, ρ being the mass density of the solution. Far

from the magnets (z ≳ 30 mm), the magnetic force is negligible compared to the volumic weight. For z ≈ 20 mm, these two forces are on the same order for most of the combinations magnet/solution and the ratio fm/ρg can go up to 80 at 1 mm from the magnet M2 for the solution 1.5 mol/L. This ratio can even

be higher for smaller magnets, for which the magnetic field gradient is stronger, and more concentrated solutions.


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Figure 5. Modulus of the magnetic force per unit volume fm, normalized by the volumic weight of the drop ρg, as a function of the distance z between the top face of the magnet and the bottom of the drop as sketched in the inset of figure 3. The curves refer to three different magnets and two different ferrofluidic solutions concentrations as indicated in the caption.

Since the magnetic force acts in the same direction as gravity, one can define a modified

capillary length a* corresponding to an effective gravitational acceleration ∗ : 17 ∗

" " =! ∗=! = # # +

1 +

#

(3)

where % is the surface tension of the ferrofluid solution. Its value, measured with a Krüss K10T ring tensiometer, is 71.4 mN/m at 20°C. It is very close to the surface tension of pure water (73.2 mN/m), in agreement with the fact that our ionic ferrofluid is free of surfactants. Equation (3) reduces to the standard capillary length representing the characteristic size below

which capillarity dominates gravity, in the absence of a magnetic field. The quantity &∗ can intuitively explain some of the shape changes displayed in Figure 4: placed at z = 1 mm above the magnet M5

where &∗ = 2.6 mm, practically coincident with the capillary length of pure water & = 2.7 mm, a ferrofluid drop of concentration 0.4 mol/L and volume V = 2.5 µL has a radius R = 0.9 mm much

smaller than &∗ and thus assumes the shape of an hemispherical cap with a contact angle θ = 110°. ACS Paragon Plus Environment

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Instead, if we place a drop of the same volume but with higher concentration, 3 mol/L, at 1 mm from M2, it looks flat due to the strong magnetic attraction and the thickness of the puddle t ~ 0.4 mm is twice the corresponding magnetic capillary length (~ 0.2 mm). Measuring this thickness as a function of z gives a direct evaluation of

∗

that can be compared to the value obtained from Eq. (3), where

fm is deduced from Figure 5. The results of such a comparison are shown in Figure 6 for puddles of two different molar concentrations deposited on a PDMS surface as the distance z from magnet M1 is varied. The agreement between the experimental data and the results of Eq. (3) is very good, suggesting that the demagnetization factor due to the drop shape is not very important in this case. The capillary length can therefore be varied continuously by a factor up to nearly five without practically changing either the surface tension, or the density of the liquid.

Figure 6. Variation of the thickness h of ferrofluid puddles of two different molar concentrations deposited on a PDMS surface as the distance z from the top face of magnet M1 is varied. The continuous lines are twice the values derived from Eq. (3).

The graph of Figure 7 shows the dependence of the key morphological parameters of ferrofluid drops of different concentration deposited on a PDMS coated glass surface kept at 1 mm distance from the five magnets. The contact angle θ remains practically constant except in presence of magnet M5, where it is found to decrease linearly with the drop concentration and a drop close to 60° is observed ACS Paragon Plus Environment

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for the 3 mol/L solution. The height of the drop h and the diameter of the contact line D show an even more complex behavior. For the magnets M1 to M4, a non-linear decrease in D is accompanied by a non-linear increase in h. These effects can be very pronounced: at the concentration 3 mol/L, the diameter doubles while the height becomes one third with respect to the corresponding values of a diluted solution. This behavior confirms what reported in previous studies, which was explained in terms of a strong magnetic attraction that enhances the effect of the gravitational field.17, 22, 24 Instead, for the magnet M5, D hardly changes while h increases with the drop magnetization, clearly suggesting that the normal traction due to a uniform magnetic field are dominant in this case.


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Figure 7. Contact angle (top graph), maximum height (middle graph) and diameter of the contact line (bottom graph) of ferrofluid drops of volume V = 2.5 µL and different concentrations deposited on a PDMS coated glass slide in contact with the various magnets.

The two contrasting effects, drop flattening due to the gradient of the magnetic field and drop elongation due to the magnetic field, can be easily observed by varying the distance from magnet and drop as reported in Figure 8, which shows the dependence of the key morphological parameters of ferrofluid drops of concentration 3 mol/L on the distance z from the three chosen magnets. With the largest magnet M5, which exhibits the smallest gradient, the maximum height h decreases by about 20% over a distance z ~ 60 mm while the diameter of the contact line D hardly changes. Mass ACS Paragon Plus Environment

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conservation then implies a progressive increase in the contact angle θ as displayed in the top graph: an increase of about 40° within 60 mm. With the magnet M2, characterized by the steepest magnetic field, the variations occur very close to it (z ≤ 20 mm) as expected. Within the first 10 mm, h increases sharply by a factor three while D decreases by 30%, a clear indication of a pronounced flattening effect. After reaching a peak (dip), h (D) slowly decreases (increases), suggesting that above 10 mm, the polarizing effect of the magnetic field becomes dominant. The contact angle θ trails h: after an initial peak there is a weak increase at larger distances. Switching to the magnet M1, whose field variation is between the previous two, widens the flattening region to about 40 mm. The not trivial behavior just reported cannot be simply classified in terms of the strength of the magnetic field experienced by the ferrofluid drops as done in refs. 22, 38


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Figure 8. Variation of the contact angle (top graph), maximum height (middle graph) and diameter of the contact line (bottom graph) of ferrofluidic drops of volume V = 2.5 µL and concentration 3 mol/L with the distance z from the three characteristic magnets used before. The drops are deposited on a PDMS coated glass slide.

In order to find a suitable scaling parameter to rationalize the role played by a magnet on the wetting properties of ferrofluid drops, we have plotted the main drop geometric data versus different dimensionless numbers. It turns out that the results for flattened ferrofluid drops are well described by the effective Bond number:39 '(∗ = # ∗ ⁄) " +,, which compares the effective attraction of a


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ferrofluid drop with the capillary force. Thus a* from Eq. (3) can be arranged as

∗

= 01

- .⁄/

2∗

.

Figure 9 shows the morphological data of ferrofluid drops of different concentrations and subject to the action of the five magnets placed at varying distances z in terms of '(∗ . The graphs show only the

data for '(∗ > 1. For a few selected points labelled with capital letters, the corresponding drop

profiles are shown as insets. Most of the data are found to exhibit very similar trends within the reproducibility level of these measurements estimated to be about ±5%: a nearly linear decrease (increase) in h (D), while θ hardly varies. The data corresponding to drops of concentration 3 mol/L interacting with the M1 magnet show a markedly distinct behavior. Inset D clearly shows that in this case the normal traction dominates the attraction due to the gradient of the magnetic field. This difference can be conveniently expressed in terms of the critical magnetization 4 , i.e. the lowest value of the magnetization at which the Rosenweig instability can be observed,33,

35, 36

which we

estimated from the formula valid for a flat slab of ferrofluid with constant permeability27 4 = 5 1 +

6

56 5

#∗ γ

,8

(4)

We have found that the drops of concentration 3 mol/L in presence of M1 are the only data points in figure 8 where the drop magnetization is bigger than 4 . In other words, for all other data points, such a threshold is never overcome regardless of the strength of the magnetic field.


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Figure 9. Contact angle (top), maximum height (middle) and diameter of the contact line (bottom) of ferrofluid drops of volume V=2.5 µL as a function of the effective Bond number. The symbols represent different concentrations of the ferrofluidic solutions: 0.2 mol/L, 0.4 mol/L, 0.8 mol/L, 1.5 mol/L, 2 mol/L, 3 mol/L , 4 mol/L. Different colors are associated to the magnets according to the following palette: magnet M1, magnet M2, magnet M3, magnet M4 and magnet M5, where the first (second) color corresponds to measurements done changing the distance of the magnet from the sample (with the magnet in contact with the substrate). The drops are deposited on a PDMS coated glass slide.

The points corresponding to '(∗ 9 1 represent elongated drops whose profile is mainly

affected by the normal traction due to the magnetic field. In this limit, we find that a convenient way to describe the drop morphology is in terms of the dimensionless number27,

40

= :;

,8 +, )" ,

which compares the pressure jump at the ferrofluid interface due to the magnetization vector that is


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normal to the drop surface with the capillary pressure. At the upper point of the sessile drop, where B is normal to the drop surface, there is a reduced pressure inside the drop as compared to the points in contact with the substrate, where the field component normal to the surface nearly vanishes. This pressure decrease can be balanced by an increase in the curvature at the upper point and a decrease at the contact points. As a result, the drop is stretched along the field. Figure 10 shows the main morphological quantities of elongated ferrofluid drops characterized by '(∗ 9 1 plotted in terms of S. Again, for a few selected points labelled with capital letters; the corresponding drop profiles are shown as insets. The data are found to nicely collapse on single curves: a linear decrease (increase) in θ (h), while D hardly varies suggesting that the apparent contact line remains pinned because the volume is conserved. We point out that all the data with > 1 have a magnetization bigger than 4 . The same

overall behavior has been observed with sessile ferrofluid drops deposited on NOA hydrophilic surfaces and on the nearly superhydrophobic surfaces, see Supplementary Information .


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Figure 10. Contact angle (top), maximum height (middle) and diameter of the contact line (bottom) of ferrofluid drops of volume V = 2.5 µL as a function of the S number. The symbols represent different concentrations of the ferrofluid solutions: 0.2 mol/L, 0.4 mol/L, 0.8 mol/L, 1.5 mol/L, 2 mol/L, 3 mol/L , 4 mol/L. Different colors are associated to the magnets according to the following palette: magnet M1, magnet M2, magnet M3, magnet M4 and magnet M5, where the first (second) color corresponds to measurements done changing the distance of the magnet from the sample (with the magnet in contact with the substrate). The drops are deposited on a PDMS coated glass slide.

In conclusion, we have studied the static magnetowetting behavior of sessile drops of ferrofluid water solutions at various concentrations deposited on a flat substrate and subject to the action of permanent magnets of different size and strength. A rich phenomenology is observed, ranging from flattened drops caused by the magnetic attraction to elongated drops due to the normal traction caused


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by a uniform magnetic field. We find that the former effect can be conveniently described in terms of the effective Bond number '(∗ = # ∗ ⁄) " +,, which compares the effective drop attraction with

the capillary force, while the drop vertical elongation is effectively expressed by the dimensionless number = :;

,8 +, )" ,

which compares the pressure jump at the ferrofluid interface due to the

magnetization with the capillary pressure. This phenomenology can be exploited to manipulate ferrofluid drops.38 Experiments are under way to study the sliding dynamics of flattened and elongated ferrofluid drops on chemically heterogeneous surfaces.

Acknowledgments We are particularly grateful to Alessandro Faggiani for support in the acquisition data and to Daniele Filippi and Enrico Chiarello for the assembling of the optical set-up.

References 1.

Seemann, R.; Brinkmann, M.; Pfohl, T.; Herminghaus, S. Droplet based microfluidics. Reports

on Progress in Physics 2012, 75, 016601. 2.

Choi, K.; Ng, A. H. C.; Fobel, R.; Wheeler, A. R. Digital Microfluidics. In Annual Review of

Analytical Chemistry, Vol 5, Cooks, R. G.; Yeung, E. S., Eds.; Annual Reviews: Palo Alto, 2012; Vol. 5, pp 413-440. 3.

Gau, H.; Herminghaus, S.; Lenz, P.; Lipowsky, R. Liquid morphologies on structured surfaces:

From microchannels to microchips. Science 1999, 283, 46-49. 4.

Ledesma-Aguilar, R.; Nistal, R.; Hernandez-Machado, A.; Pagonabarraga, I. Controlled drop

emission by wetting properties in driven liquid filaments. Nature Materials 2011, 10, 367-371.


20

Page 21 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

5.

Langmuir

Varagnolo, S.; Ferraro, D.; Fantinel, P.; Pierno, M.; Mistura, G.; Amati, G.; Biferale, L.;

Sbragaglia, M. Stick-Slip Sliding of Water Drops on Chemically Heterogeneous Surfaces. Physical Review Letters 2013, 111, 066101. 6.

Varagnolo, S.; Schiocchet, V.; Ferraro, D.; Pierno, M.; Mistura, G.; Sbragaglia, M.; Gupta, A.;

Amati, G. Tuning Drop Motion by Chemical Patterning of Surfaces. Langmuir 2014, 30, 2401-2409. 7.

Chen, Y.; He, B.; Lee, J. H.; Patankar, N. A. Anisotropy in the wetting of rough surfaces.

Journal of Colloid and Interface Science 2005, 281, 458-464. 8.

Semprebon, C.; Mistura, G.; Orlandini, E.; Bissacco, G.; Segato, A.; Yeomans, J. M.

Anisotropy of Water Droplets on Single Rectangular Posts. Langmuir 2009, 25, 5619-5625. 9.

Quere, D. Non-sticking drops. Reports on Progress in Physics 2005, 68, 2495-2532.

10.

Roach, P.; Shirtcliffe, N. J.; Newton, M. I. Progess in superhydrophobic surface development.

Soft Matter 2008, 4, 224-240. 11.

Chaudhury, M. K.; Whitesides, G. M. How to make water run uphill. Science 1992, 256, 1539-

1541. 12.

Yeo, L. Y.; Friend, J. R. Surface Acoustic Wave Microfluidics. Annual Review of Fluid

Mechanics, 2014, 46, 379-406. 13.

Brunet, P.; Eggers, J.; Deegan, R. D. Vibration-induced climbing of drops. Physical Review

Letters 2007, 99, 144501. 14.

Noblin, X.; Kofman, R.; Celestini, F. Ratchetlike Motion of a Shaken Drop. Physical Review

Letters 2009, 102, 194504. 15.

Sartori, P.; Quagliati, D.; Varagnolo, S.; Pierno, M.; Mistura, G.; Magaletti, F.; Casciola, C. M.

Drop motion induced by vertical vibrations. New Journal of Physics 2015, 17, 113017. 16.

Quere, D. Leidenfrost Dynamics. Annual Review of Fluid Mechanics, 2013, 45, 197-215.


21

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

17.

Page 22 of 25

Piroird, K.; Texier, B. D.; Clanet, C.; Quere, D. Reshaping and capturing Leidenfrost drops

with a magnet. Physics of Fluids 2013, 25, 032108. 18.

Guo, Z.-G.; Zhou, F.; Hao, J.-C.; Liang, Y.-M.; Liu, W.-M.; Huck, W. T. S. “Stick and slide”

ferrofluidic droplets on superhydrophobic surfaces. Applied Physics Letters 2006, 89, 081911. 19.

Asakura, H.; Nakajima, A.; Munetoshi, S.; Suzukia, S.; Kameshima, Y.; Okada, K.

Deformation and motion by gravity and magnetic field of a droplet of water-based magnetic fluid on a hydrophobic surface. Applied Surface science 2007, 253, 3098–3102. 20.

Afkhami, S.; Renardy, Y.; Renardy, M.; Riffle, J. S.; St. Pierre, T. Field-induced motion of

ferrofluid droplets through immiscible viscous media. Journal of Fluid Mechanics 2008, 610, 363 380. 21.

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, 12119 - 1212. 22.

Nguyen, N.-T.; Zhu, G.; Chua, Y.-C.; Phan, V.-N.; Tan, S.-H. Magnetowetting and sliding

motion of a sessile ferrofluid droplet in the presence of a permanent magnet. Langmuir 2010, 26, 12553-12559. 23.

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. 24.

Nam-Trung, N. Deformation of ferrofluid marbles in the presence of a permanent magnet.

Langmuir 2013, 29, 13982-13989. 25.

Katsikis, G.; Cybulski, J. S.; Prakash, M. Synchronous universal droplet logic and control.

Nature Physics 2015, 11, 588-596. 26.

Nam-Trung, N. Micro-magnetofluidics: interactions between magnetism and fluid flow on the

microscale. Microfluidics and Nanofluidics 2012, 12, 1-16.


22

Page 23 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

27.

Rosensweig, R. E. Ferrohydrodynamics; Dover Publications, Inc.: Mineola, New York, 2014.

28.

Flament, C.; Lacis, S.; Bacri, J. C.; Cebers, A.; Neveu, S.; Perzynski, R. Measurements of

ferrofluid surface tension in confined geometry. Physical Review E 1996, 53, 4801-4806. 29.

Rosensweig, R. E.; Elborai, S.; Lee, S. H.; Zahn, M. Ferrofluid meniscus in a horizontal or

vertical magnetic field. Journal of Magnetism and Magnetic Materials 2005, 289, 192-195. 30.

John, T.; May, K.; Stannarius, R. Meniscus of a ferrofluid around a vertical cylindrical wire

carrying electric current. Physical Review E 2011, 83, 056308. 31.

Eissmann, P. B.; Lange, A.; Odenbach, S. Meniscus of a magnetic fluid in the field of a current-

carrying wire: two-dimensional numerical simulations. Magnetohydrodynamics 2011, 47, 149-157. 32.

Berim, G. O.; Ruckenstein, E. Nanodrop of an ising magnetic fluid on a solid surface. Langmuir

2011, 27, 8753-8760. 33.

Massart, R. Preparation of aqueous magnetic liquids in alkaline and acidic media. IEEE

Transactions on Magnetics, 1981, 17,1247-1248. 34.

Meriguet, G.; Wandersman, E.; Dubois, E.; Cebers, A.; Gomes, J. D.; Demouchy, G.; Depeyrot,

J.; Robert, A.; Perzynski, R. Magnetic fluids with tunable interparticle interaction: monitoring the under-field local structure. Magnetohydrodynamics 2012, 48, 415-425. 35.

Camacho, J. M.; Sosa, V. Alternative method to calculate the magnetic field of permanent

magnets with azimuthal symmetry. Revista mexicana de física E 2013, 59, 8-17. 36.

Brigo, L.; Carofiglio, T.; Fregonese, C.; Meneguzzi, F.; Mistura, G.; Natali, M.; Tonellato, U.

An optical sensor for pH supported onto tentagel resin beads. Sensors and Actuators B-Chemical 2008, 130, 477-482. 37.

Ferraro, D.; Semprebon, C.; Toth, T.; Locatelli, E.; Pierno, M.; Mistura, G.; Brinkmann, M.

Morphological transitions of droplets wetting rectangular domains. Langmuir 2012, 28, 13919-13923.


23

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

38.

Page 24 of 25

Timonen, J. V. I.; Latikka, M.; Leibler, L.; Ras, R. H. A.; Ikkala, O. Switchable static and

dynamic self-assembly of magnetic droplets on superhydrophobic surfaces. Science 2013, 341, 253257. 39.

Seroguillaume, O. E.; Zouaoui, D.; Bernardin, D.; Brancher, J. P. The shape of a magnetic

liquid-drop. Journal of Fluid Mechanics 1992, 241, 215-232. 40.

Arkhipenko, V. I.; Barkov, D. Y.; Bashtovoi, V. G. Shape of a drop of magnetized fluid in a

homogeneous magnetic field. Magnitnaya Gidrodinamika 1978, 3, 131 - 134.


24

Page 25 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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