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Dynamics of ferrofluid drops on magnetically patterned surfaces Carlo Rigoni, Davide Ferraro, Matteo Carlassara, Daniele Filippi, Silvia Varagnolo, Matteo Pierno, Delphine Talbot, Ali Abou-Hassan, and GIAMPAOLO MISTURA Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01520 • Publication Date (Web): 03 Jul 2018 Downloaded from http://pubs.acs.org on July 6, 2018

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Dynamics of ferrofluid drops on magnetically patterned surfaces C. Rigoni a, D. Ferraro a, M. Carlassara a, D. Filippi a, S. Varagnolo*a, M. Pierno a, D. Talbotb, A. Abou-Hassan b and G. Misturaa

a

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

Italy, bSorbonne Université, CNRS, Laboratoire PHysico-chimie des Electrolytes et Nanosystèmes, PHENIX, F-75005 Paris, France.

Corresponding author: [email protected] *present address: Department of Chemistry, University of Warwick, United Kingdom CV4 7AL.

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Abstract The motion of liquid drops on solid surfaces is attracting a lot of attention because of its fundamental implications and wide technological applications. In this article, we present a comprehensive experimental study of the interaction between gravity driven ferrofluid drops on very slippery oil impregnated surfaces and a patterned magnetic field. The drop speed can be accurately tuned by the magnetic interaction and, more interestingly, drops are found to undergo a stick-slip motion whose contrast and phase can be easily tuned by changing either the strength of the magnetic field or the ferrofluid concentration. This motion is the result of the periodic modulation of the external magnetic field and can be accurately analyzed because the intrinsic pinning due to chemical defects is negligible on oil impregnated surfaces.

Keywords Ferrofluid drops. Liquid impregnated surfaces. Wetting of ferrofluid drops on modulated magnetic fields. Gravity driven sessile drops. Stick-slip motion. Friction of ferrofluid drops.


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Introduction Controlling and predicting the mobility of drops in contact with a solid surface is a major scientific challenge,1 relevant for fundamental research2 and crucial for an ample variety of applications including self-cleaning coatings,3 microfluidics,4 dropwise condensation5 and fog collection.6 In order for a drop to slide on a tilted surface, it must both advance (on the downhill side) and recede (on the uphill side). This implies that the frontal contact angle must be larger than the advancing contact angle , while the rear contact angle must be smaller than the receding contact angle . The difference ∆ = − , known as contact angle hysteresis, is characteristic of the surface chemistry and topography and is the key macroscopic parameter governing drop dynamics.7,

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Suitable chemically heterogeneous surfaces

can then be tailored to passively control drop motion. For instance, water drops sliding on alternating stripes of different wettability introduce an anisotropic behavior: drops slide more easily along the alternating stripes than across them9,

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and periodic variations in the contact angles, possibly

accompanied by fluctuations in the drop velocity, take place along this latter direction.10 More interestingly, if the wettability contrast between adjacent stripes is high, drops undergo a stick-slip motion whose average speed can be an order of magnitude smaller than that measured on a homogeneous surface having the same apparent contact angle.11 In fact, this motion is the result of the periodic deformations of the drop interface when crossing the stripes. Lattice Boltzmann simulations reproduce the stick-slip motion and indicate that the slowdown is the result of the pinning-depinning transition of the contact line, which causes energy dissipation to be localized in time and a large part of the driving energy to be stored in the periodic deformations of the contact line when crossing the stripes.11,

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More recent numerical studies have analyzed further features of the stick-slip motion of

drops on chemically patterned surfaces.13-16 On the other hand, active control of drop motion can be achieved with different approaches.1 Oscillations of the substrate couple to the drop inertia and thus provide, in principle, a universal actuation method for all types of liquids. For instance, vertical vibrations can make drops climb against ACS Paragon Plus Environment

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gravity on an inclined plane17 and merge them together.18 Electric fields generated by arrays of electrodes integrated in the surface and covered with an insulating layer are widely used as a tool to control shape, motion and generation of conductive drops.19,

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Electric fields combined with

temperature can also tune the wettability of graphene sponges for accurate liquid handling.21 Similarly, magnetic fields are extensively employed in microfluidics22 to handle drops,23-25 carry out continuous flow cell separation,26,

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perform chemical ferrofluid synthesis28 and study the drop breakup

dynamics.29 They are also used to modify the shape of ferrofluid sessile drops and to drag them along a surface.30-34 If ferrofluid drops move on superhydrophobic surfaces in an external magnetic field, their interaction force with the substrate is measured to be very low35 and is defined by the processes occurring in the vicinity of the triple line only.36 In this article we present the first experimental evidence of the role played by a patterned magnetic field on the dynamics of ferrofluid drops. A continuous evolution from uniform to stick-slip motion is observed, which can be tuned by increasing the ferrofluid concentration and/or the magnetic field. More interestingly, the delay between the depinning of the front and rear contact lines is found to depend on the mean speed of the drop. In order to concentrate only on the intrinsic pinning effects caused by inhomogeneous magnetic fields, a rough surface is impregnated with oil. Since the oil surface is intrinsically smooth and free from chemical and morphological defects typical of solid surfaces, these so called liquid-impregnated surfaces (LIS) are recognized to hardly pin sessile drops.1, 37, 38

Methods Ferrofluid-impregnated surfaces have been studied for active manipulation of water droplets39, 40. In this study, instead, we use ferrofluid drops on conventional, non-magnetic LIS produced following the recipe described in:41 a film of silicone oil is spread on the surface of a coverglass and heated at 300°C for 10 minutes; after cooling down the glass at room temperature, the oil in excess is washed away with acetone. Because of the thermal process, the thin solidified silicone layer (≈200 nm of thickness) presents pores that can be easily impregnated by liquid silicone oils.41 The resulting LIS are 4 ACS Paragon Plus Environment

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characterized by performing static and dynamic tests using drops of distilled water and impregnating the solid matrix with three silicone oils of different viscosity (5 cSt, 100 cSt and 1000 cSt). Regardless of the viscosity, the apparent contact angle of sessile water drops is 107°±2° and the contact angle hysteresis is a few degrees (3.1°±0.5°). Similar values are exhibited by ferrofluid drops at different concentrations (see Section 1 in Supporting Information). Furthermore, the downward velocity of water drops of volume Ω=20 µL measured at different inclination angles α and oil viscosities scales as expected42 (see Section 2 in Supporting Information). Based on these preliminary results, the 100 cSt silicone oil is chosen as lubricant for this work because it allows to easily explore an ample interval of velocities with suitable inclinations. Its viscosity (≈100 times that of the ferrofluids) avoids drainage of the impregnated oil by the moving drops and, at the same time, yields very low roll off angles, well below 5°. The ferrofluid drops are stable aqueous colloidal suspensions of maghemite (γ-Fe2O3) nanoparticles in aqueous acidic solutions at pH ∼2 with NO3‾ counterions synthesized following the Massart process,43 which guarantees stable suspensions over long time intervals. The nanoparticles have a rock like shape with a crystal diameter of about 8.5 nm (more details about their synthesis and characterization can be found in our previous work.34) To explore the influence of the magnetic interaction on the dynamics of ferrofluid drops, eight different concentrations are used. The experimental setup allows acquiring images of a drop on an inclined surface.44 As shown in Fig. 1, it is composed by a permanent magnet that can be tilted at a desired angle α by a motor. A white LED back-light source and a high-speed camera are used for illuminating and acquiring the images, respectively. During a typical experiment, a drop (Ω ≈ 10 − 40 µL) is gently placed on the already tilted surface and its motion is recorded. Every image sequence is then processed off-line by a customized LabVIEW program that provides the time evolution of the frontal and rear positions of the drop contact line.44 Side views show that drops are quasi-hemispherical and surrounded by a small oil meniscus as shown in Fig. 1. This circular meniscus,


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pulled from the oil film by the surface tension of water,45 is found to persist in dynamical conditions, which impacts the friction opposing the moving drop.46 The permanent magnet is made of neodymium and has a cylindrical shape (diameter 18 cm, height 3 cm). The ample surface guarantees that a drop moving on its central part experiences a uniform magnetic field whose strength depends only on the vertical distance z from the face of the magnet (see Section 3 in Supporting Information). For this study, the distance of the sliding surface from the permanent magnet is 15 mm and the corresponding value of the uniform magnetic field is 148± 2mT. A comb-shape iron sheet (thickness 2 mm) placed on the permanent magnet modulates the magnetic field along the drop sliding direction (x axis), as reported in Fig. 1. The teeth have width of 0.5 mm and period of 1.7 mm. The drop is deposited on the LIS sample placed on the iron comb. By increasing the distance of the sample from the magnet, the modulation of the magnetic field decreases as shown in Fig. 1. The profile of the patterned magnetic field used in this study is that one corresponding to the distance 0.2 mm. The droplet interaction with the magnetic field can be characterized by the effective gravitational acceleration ∗ = + with the acceleration of gravity and = ∇ the magnetic force per unit volume exerted by the magnet, being the ferrofluid magnetization corresponding to B and ∇ the gradient of the magnetic field. For the uniform magnetic field ∗ ~10 m/s2, while on the patterned magnetic field, ∗ locally can be as high as 1300 m/s2 (for further details on the magnetic field see Section 3 of Supporting Information).


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Figure 1. a) Experimental set-up: a ferrofluid drop of known volume is deposited on a silicone oil impregnated surface tilted by an angle α placed above a permanent magnet. Its stationary speed is denoted as v. To modulate the magnetic field, an iron comb is placed between the magnet and the impregnated surface. b) Spatial modulation of the magnetic field at different distances from the magnet. c) Ferrofluid drop (volume 20 µL, concentration 0.8 mol/L) going down the surface tilted by 5° and d) enlargement of the oil front meniscus pushed by the drop.

Results The left graph of Fig. 2 shows the time evolution of the drop frontal position of ferrofluid drops deposited on lubricant impregnated surfaces inclined by an angle α=25°, in the presence of either a uniform or a modulated magnetic field. The drops subject to a uniform magnetic field slide at a constant ACS Paragon Plus Environment

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speed that decreases with ferrofluid concentration. Since no apparent variation in the drop shape and oil meniscus is observed, we ascribe this loss to magnetoviscous effects.47 Actually, the viscosity of maghemite ferrofluids is found to increase with concentration and the application of a magnetic field further enhances this effect48,49 (see Section 4 of Supplemental Information for more details). On a patterned magnetic field, the speed decreases and a pronounced stick-slip motion appears, similar to what reported for water drops sliding on stripes of alternating wettability.11,

44

Selected snapshots

indicate the position of the contact line (CL) with respect to the underlying comb. Between instants a and b, the rear CL is pinned at the edge of a tooth comb while the frontal CL is slowly moving down; at instant c, the frontal CL gets pinned at the edge of a tooth comb and the rear starts moving till in d it gets pinned at the edge of the following tooth comb and the system recovers the initial configuration translated by one pattern periodic distance. This periodic alternation of pinning and depinning between the frontal and rear CL implies an oscillation in the instantaneous length L of the sliding drop. Additionally, the oscillation ∆L, evaluated as the difference between the maximum and minimum measured L, increases with the ferrofluid concentration, as shown in the right graph of Fig 2. Again, the amplitude of these oscillations can be continuously changed from a “rigid” drop moving at constant speed to an oscillating drop undergoing stick-slip motion by varying either the ferrofluid concentration, as done here, or, more generally, the magnetic strength. This tuning is a significant advantage with respect to the passive control provided by chemically heterogeneous surfaces, whose effects on the drop dynamics can only be modified by varying the nature or shape of the different chemical domains.1


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Figure 2. Left graph: time evolution of the frontal point of ferrofluid drops at different concentrations (Volume = 20 µL) moving on liquid impregnated surfaces inclined by an angle α=25°, in the presence of either a uniform or a patterned magnetic field. The snapshots show the position of the drop with respect to the underlying magnetic pattern at specified instants. The orange lines indicate the contact angles. Right graph: percentage variation of the drop length ∆L during stickslip as a function of ferrofluid concentration. The inset underlines the drop length oscillation (L) during the motion for three particular concentrations.

We exploit this advantage to systematically characterize the phase shift φ of the stick-slip motion by varying both the drop volume and ferrofluid concentration. The phase shift is calculated from the ratio = 360°

∆

, where ∆ is the time interval between the consecutive instants of maximum acceleration of

the frontal and rear contact points, and T is the time interval between two consecutive instants of maximum acceleration of the frontal contact point. Therefore, of the drop, while when

= 0° corresponds to a rigid translation

= 180° the front and rear contact points move in counter-phase. The graph of

Fig. 3 shows the dependence of φ on the drop speed v. A clear linear trend is seen up to v=60 mm/s. The largest drops (Ω=40 µL) reach

= 360° at around 80 mm/s. Above this speed,

keeps on increasing

linearly. Furthermore, two distinct regimes are observed during drop motion. At low speed (shaded area of the graph), only the contours near the front and rear contact lines change during a stick-slip motion as shown by the images (aj) taken at the instant of maximum (minimum) elongation of the moving drop (see also Movie S1 in Supporting Information). At higher speed, the entire drop profile oscillates as indicated by the images b and Movie S2 in Supporting Information. As the speed is further increased, this oscillation becomes more pronounced (see images ci,j and Movie S3 in Supporting Information). If ACS Paragon Plus Environment

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we analyze in more detail the data at high ferrofluid concentration where the stick-slip motion is more marked, we find that

does not depend on the ferrofluid concentration and thus the magnetic force.

Figure 3. Left: sliding phase as a function of the drop speed, varying the ferrofluid concentration (different colors), drop volumes (◑=10 µL, ●=20 µL, ◒=30 µL, ○=40 µL). The colored gray background represents conventional stick-slip, while the white part indicates where the vertical oscillations of the drop profile appear. Right: frames at the maximum (i) and minimum (j) elongation instants of drops (40 µL, 0.8 mol/L) moving at three different speeds. The two points b in the graph display the same motion described in the snapshots bi and bj.

To shed more light on the interplay between drop dynamics and magnetic field, systematic measurements are performed at a constant drop volume (Ω=20 µL) by varying the ferrofluid concentration and the angle α. For each combination, the mean drop speed is determined by the slope of least square linear fits of the time evolution of the frontal points, for either uniform (vu) or patterned (vp) magnetic fields. The left graph of Fig. 4 summarizes all speed data plotted in terms of the ferrofluid concentration for increasing inclination angles. It clearly shows that the drop speed decreases with the ferrofluid concentration as already discussed. At high concentrations (> 0.4 mol/L), the presence of the comb significantly slows down the drops as compared with the uniform field, indicating the presence of an extra dissipation due to deformation of the drop undergoing stick-slip. This decrease is larger at higher concentrations where the stick-slip motion is more pronounced, as displayed in the inset of Fig. 4, where the relative velocity decrease ∆" =

#$ %#& #$

is plotted as a function of α. The comb reduces the

drop speed by about 35% for a ferrofluid concentration of 0.8 mol/L, and it is barely observable at the ACS Paragon Plus Environment

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concentration 0.1 mol/L. Interestingly, this decrease does not seem to depend on the inclination angle, at least in the explored range. Finally, as a result of the weak pinning LIS, we notice that this decrease is much smaller than the factor of ten reported for water drops sliding on chemically heterogeneous surfaces.11, 44 The right graph of Fig. 4 displays the velocity in a log scale as a function of the sine of the tilt angle for ferrofluid drops having Ω = 20 mL and different molar concentrations, in the presence of either uniform or patterned magnetic fields. On this compressed scale, the differences in drop velocity observed between the uniform and patterned magnetic fields disappear and the data show that v is not linear in driving force but rather exhibits a power law behavior. For this system where the silicone oil is more viscous than the ferrofluid, dissipation is expected to mainly occur in the oil, that is, in the underlying film and in the surrounding meniscus. A recent study46 shows that, contrary to what one could think a priori, the dominant contribution is not in the subjacent film. The analysis of the viscous effects in the front edge of the moving meniscus yields nonlinear friction and estimates that "~'()*⁄+ -.46 As the driving force is increased, the wedge dissipation is suddenly suppressed, which leads to a different dynamical regime that seems to arise from the self-lubrication of the drop where "~'()* -, explained assuming that oil is constantly extracted from the texture by water surface tension before being reinjected below the drop.46 Our results indicate a superlinear behavior which, at the highest inclinations and in the presence of a uniform magnetic field (full symbols), is consistent with a power law with exponent 3. As sin - decreases, the exponent becomes smaller and there may be a cross-over to the '()*⁄+ - regime at a critical velocity "~1 cm/s. Finally, as expected, the data on the patterned surface show a distinct behavior, a clear indication that the modulation of the magnetic field contributes to friction.


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Figure 4. Left graph: mean velocity of ferrofluid drops (Ω=20 µL) of different concentrations moving on LIS at increasing inclination angles in the presence either of a uniform (U, open symbols) or a patterned (P, full symbols) magnetic field. The inset compares the relative velocity decrease at two ferrofluid concentrations (the points enclosed in the two dashed boxes) on the same patterned surface at increasing -. Right graph: the same data plotted in terms of sin - proportional to the in plane component of the gravitational driving force.

In summary, we have characterized, for the first time, the influence of a magnetic field on the motion of ferrofluid drops on very slippery surfaces. The application of a uniform magnetic field slows down gravity driven ferrofluid drops. The presence of magnetic heterogeneities significantly enriches the drop dynamics. In particular, a linear modulation in the magnetic field causes stick-slip whose contrast and phase can be easily tuned. In particular, the phase shift between the moving frontal and rear contact points change continuously with the drop velocity from 0 to 2π. These observations are possible because the intrinsic pinning due to chemical defects is negligible on oil impregnated surfaces. More precisely, these effects could be seen also with a standard solid surface, but the data reproducibility would be much lower and to construct a graph of the phase variation like that of figure 3 would be practically impossible. A specific feature of LIS is the nonlinear friction of moving drops, which we have measured and found to be consistent with a recent specific study46 where it is attributed to the dissipation taking place in the oil meniscus surrounding the drop. These experimental results suggest that ferrofluid drops moving in the presence of heterogeneous magnetic fields represent an ideal playground for fundamental studies on drop dynamics and provide useful strategies for passive and active control of the drop ACS Paragon Plus Environment

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motion. Surprisingly, there is very little in the literature on the dynamics of ferrofluid drops in the presence of magnetic fields. It is our hope that this preliminary work be a stimulus for further studies, both experimental and theoretical.

SUPPORTING INFORMATION Wetting characterization of ferrofluid drops. Motion of water droplets on LIS. Characterization of the permanent magnet. Magnetorheology of the ferrofluid solution. Three movies showing the motion of ferrofluid drops on patterned magnetic fields.

ACKNOWLEDGEMENTS We thank Prof. Régine Perzynski from PHENIX laboratory, Sorbonne Université and Prof. Jean-Claude Bacri from MSC laboratory, Paris 7 for discussions and Giorgio Delfitto for assistance in the assembly of the experimental set-up.


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