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Controlling the motion of ferrofluid droplets using surface tension gradients and magnetoviscous pinning Tyler J Ody, Mohan Panth, Andrew D. Sommers, and Khalid F. Eid Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01030 • Publication Date (Web): 08 Jun 2016 Downloaded from http://pubs.acs.org on June 17, 2016
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Controlling the motion of ferrofluid droplets using surface tension gradients and magnetoviscous pinning T. Ody1, M. Panth1, A.D. Sommers2, and K.F. Eid1 1 2
Department of Physics, Miami University, Oxford, Ohio 45056 Department of Mechanical and Manufacturing Engineering, Miami University, Oxford, Ohio 45056
Abstract This work demonstrates the controlled motion and stopping of individual ferrofluid droplets due to a surface tension gradient and a uniform magnetic field. The surface tension gradients are created by patterning hydrophilic aluminum regions, shaped as wedges, on a hydrophobic copper surface. This pattern facilitates the spontaneous motion of water-based ferrofluid droplets down the length of the wedge towards the more hydrophilic aluminum end due to a net capillarity force created by the underlying surface wettability gradient. We observed that applying a magnetic field parallel to the surface tension gradient direction has little or no effect on the droplet’s motion, while a moderate perpendicular magnetic field can stop the motion altogether effectively “pinning” the droplet. In the absence of the surface tension gradient, droplets elongate in the presence of a parallel field but do not travel. This control of the motion of individual droplets might lend itself to some biomedical and lab-on-a-chip applications. The directional dependence of the magnetoviscosity observed in this work is believed to be the consequence of the formation of nanoparticle chains in the fluid due to the existence of a minority of relatively larger magnetic particles.
Introduction The control of the flow of small amounts of fluid (in the microliter to nanoliter range) continues to attract considerable research interest due to the unique problems encountered and the many potential applications like DNA amplification1, DNA sequencing2, cell separation and detection3,4, ultrafast inkjet printers5, and micro-chemical reactors6. Micro-scale surface tension gradients offer a unique way to control the flow of fluid droplets on smooth metal or semiconductor surfaces.7 Ferrofluids however offer additional manipulation ability over water droplets since they can be impacted by uniform as well as varying magnetic fields. Ferrofluids are colloidal suspensions of single domain magnetic particles having typical diameters of a few to a few tens of nanometers in a carrier liquid.8 Brownian motion keeps the nanoparticles from settling under gravity and a surfactant usually provides the steric repulsion between particles to prevent them from agglomerating.9,10 Ferrofluids are used in dynamic sealing as well as heat dissipation and can also be used in different biomedical applications like hyperthermia, image contrast-enhancing, magnetic drug targeting, etc.11 A slightly different kind of ferrofluid is magnetorheological fluid (MRF), which is composed of micron-sized particles.
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Magnetorheological fluids are used in brakes, clutches and shock absorbers, among other mechanical devices, owing to their tunable viscosity that can become very high in moderate magnetic fields.12,13,14 The strong magnetoviscosity associated with MRFs is due to the formation of particle chains in the presence of relatively small magnetic fields. Such chains resist the shearing of the fluid, giving rise to magnetoviscosity. Ferrofluids, which have small nanoparticles on the other hand, are predicted not to form particle chains due to the much smaller interparticle interactions; as a result, they typically have a much smaller magnetoviscosity.15 To date, significant research efforts have been focused on the behavior of ferrofluid droplets in magnetic fields and field gradients, where understanding their flow characteristics is of special importance.16,17 For example, transverse forces (i.e. the Magnus effect) have been used to explain the motion of ferrofluid droplets in a rotating magnetic field.18 When a sufficiently large magnetic field gradient is applied, ferrofluids will flow toward regions of stronger magnetic field, and the hydrodynamic properties of the fluid such as viscosity can be significantly altered.19,20,21 Magnetic fields have also been used to control the surface tension (i.e. contact angle) of fluids on specialized surfaces22 and to directly change the shape and behavior of ferrofluid droplets.23,24,25 The behavior of ferrofluid droplets placed on a surface tension gradient in the presence of a uniform magnetic field however needs more study. In this research, we study the behavior of ferrofluid droplets placed on surfaces that either contain a surface tension gradient or are uniformly hydrophilic or hydrophobic in the presence of various uniform magnetic fields. Of special interest is the case where the uniform magnetic field is either parallel or perpendicular to the surface tension gradient direction. While magnetic fields can influence the behavior of fluid droplets in different ways, this work is focused on the field-dependent magnetoviscosity of individual ferrofluid droplets placed on a surface tension gradient.
Materials and Methods Surface Preparation: Mirror-finish aluminum plates (Alloy 6061) with dimensions 2” × 2” × 0.1” (50.8 mm × 50.8 mm × 2.54 mm) were used to study the motion of ferrofluid droplets on a surface tension gradient. To prepare the gradient, the aluminum surface was first cleaned in Alconox immediately after peeling off the protective coating. The surface was gently rubbed with a Kimwipe during the Alconox soaking followed by a rinsing in acetone, isopropyl alcohol (IPA) and deionized water separately. A gentle oxygen plasma etching was then performed for two minutes to remove any organic residue left on the surface. Next, a wedge-shaped shadow mask made out of aluminum was used to cover the surface during the deposition of copper on the surface. The thermal deposition of 80 nm of copper was done in a background pressure of approximately 2×10-7 Torr (2.67×10-5 Pa) resulting in a final sample as shown in Fig. 1. After copper deposition, the surface was immersed in a 0.1M heptadecafluoro-1-decanethiol (HDFT) solution for six minutes to create a self-assembled monolayer (SAM) on the copper surface. The SAM was observed to selectively adsorb on the copper but not on the aluminum, possibly due to
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the formation of a strong oxide layer on the aluminum which served as a barrier.7 This rendered the copper regions of the surface hydrophobic, while the aluminum regions remained hydrophilic or even super-hydrophilic. These wedges and their associated wettability contrast thus formed a surface tension gradient (in the direction of increasing aluminum contact area) when a fluid droplet was placed at the vertex of the wedge. The angles of the various wedges that were examined in this work are shown in Table 1. To measure the contact angles of these different surface regions, copper was thermally deposited on a second aluminum block on half of the surface to form two distinct regions each with an area of 1” × 2” (25.4 mm × 50.8 mm) using the same protocol as described above. This enabled the contact angle of individual ferrofluid droplets to be studied independently on both the Cu and Al regions in the presence of a uniform external magnetic field without the gradient.
Experimental Setup Figure 2 shows the experimental setup used in this study, where an electromagnet was used to produce a uniform magnetic field of up to 2000 Gauss. A 14 MP Pentax camera with a wideangle 5× optical zoom lens (28-140mm equivalent) was used to take both the still images and videos of the ferrofluid droplets in magnetic fields of different magnitudes and directions relative to the wedges. The camera was capable of capturing video at a rate of 30 frames per second. For an experiment, the camera was either placed on the top of the pole pieces of the magnet for getting top-view images, or placed on a tripod outside of the magnet's frame to get side images thus allowing the contact angles to be measured at the two points closest to the poles (i.e. where the droplet’s contact line is perpendicular to the magnetic field direction). A third position (i.e. droplet end view) involved placing the camera above the sample and using a mirror tilted at 45o in order to get the contact angles at the two points where the droplet contact line is parallel to the magnetic field. The droplets are injected on the surface horizontally between the poles of the magnet to eliminate the effect of gravity. The magnetic field direction can be either parallel or perpendicular to the surface tension gradient, but is always kept in the plane of the metal surface (see Fig. 3). Two different magnetic particle concentrations of a commercially available water-based ferrofluid from Ferrotec Corp. were studied in this work—namely, EMG 700 (5.8% vol.) and EMG 705 (3.9% vol.). The nominal average particle diameter in both cases was 10 nm. The EMG 700 ferrofluid had a saturation magnetization at 25°C of 357.5 Gauss (±10%), and the EMG 705 ferrofluid had a saturation magnetization of 220 Gauss (±10%). Ferrofluid droplets were dispensed/injected on the surface using an adjustable micropipette with a typical droplet volume of 15 µL. The micropipette was capable of dispensing droplets in the volume range of 2 to 20 µL. To begin an experiment, the camera was positioned in one of the three locations indicated above. A ferrofluid droplet was then placed at the vertex of a wedge, and video of the droplet travel was recorded. Next, an open-source software package called Free Studio was used to splice the videos into a sequence of still images showing the time-elapsed motion of the droplet. These images were then used to calculate the velocity and acceleration of the droplet
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down the gradient. After each test, the surface was cleaned and ‘re-energized’ through a soak and gentle rinse in Alconox.
Results and Discussion Figure 4 shows pictures of ferrofluid droplets on the Cu/HDFT and Al surfaces in zero external magnetic field. Top-view pictures of droplets on Cu and on Al are shown in Fig. 4a) and 4d) respectively, where the contact lines are relatively smooth circles, with small deformations due to imperfections on each surface that act as pinning sites to the contact line. The side-view pictures show much more contrast between the shape of droplets on the HDFT-coated Cu and the bare Al. It is seen from Figs. 4b) and 4c) that the contact angles on the Cu are about 90o. On the other hand, Figs. 4e) and 4f) show extremely small contact angles of less than 15o confirming that the Al surface is strongly hydrophilic and may be characterized as super-hydrophilic. Both droplets are isotropic in shape and not elongated in any direction, showing that there is no residual magnetic field in the electromagnet. It should also be noted that the droplet placed on the Cu is significantly ‘thicker’ than the one placed on the Al, and yet the total volume is the same for both droplets since the one on the Al spreads out more. Figure 5 shows pictures of two ferrofluid droplets on the Cu/HDFT and Al in an external magnetic field of 1000 Gauss. Apart from the expected elongation of the droplets in the direction of the magnetic field and a reduction in the apparent contact angle on both the Cu and Al23,26, the overall behavior is quite similar to that in zero external magnetic field as shown in Fig. 4. The most important observation about these droplets is that despite the expected change in the droplet shape, there is no net translational motion of the droplets (i.e. the center-of-mass of the droplet never moves with the application of a uniform magnetic field). Moreover, a uniform magnetic field is not expected to cause a net ‘translational’ motion of a ferrofluid because it does not give rise to any net force. This is best seen when considering the net force on a magnetic fluid placed (. ), where = = is the magnetic moment, M0 is the in a magnetic field: = ∇ magnetization of the material, V is the volume of the nanoparticle (assumed to be spherical), d is the particle diameter, and B is the magnetic field. The formula simplifies to the so-called Kelvin ) in a uniformly magnetized ferrofluid. 27,28 This shows that a body force given by: = ( ∙ ∇ uniform magnetic field (i.e. with no field gradient) exerts no net force on a ferrofluid. A magnetic field gradient, on the other hand, causes a net force on the ferrofluid, which is why ferrofluids move to areas with stronger magnetic fields. This force is sometimes utilized in the process of filtering larger nanoparticles from the fluid in order to have a relatively monodisperse particle size distribution. 29,30 Placing a ferrofluid droplet on the wedge-shaped hydrophilic Al pattern surrounded by the hydrophobic Cu results in a net capillary force on the droplet towards the base of the Al wedge. Figure 6(a) is a schematic diagram showing the three-phase contact line of a circular droplet placed on the wedge. In a simplified model that assumes there to be only two different contact angles around its perimeter, the net force on the droplet can be found by integrating around the three-phase contact line which yields the following expression7:
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= 2 ! − #$ ! %['()* − '()+ ] Here Fsx is the net surface tension (i.e. capillary) force, γ is the surface tension of the fluid, R is the radius of the droplet, θ phobic and θ philic are the contact angles on the hydrophobic Cu and the hydrophilic Al respectively, and ϕB and ϕF are angles related to the geometry as shown in Fig. 6(a). The triangular shape serves a crucial role. Since the front of the droplet in contact with the Al is longer than the rear part, which is also in contact with Al, a net capillary force forward is produced. It should be noted that the part of the droplet in contact with the hydrophobic surface also gives rise to a net force in the same direction. This latter force would be zero if the triangle was replaced with a simple rectangular shape instead with parallel sides. The effect of the wedge angle ψ on the net capillary force is shown in Fig. 6(b). It is evident from the figure that there is a linear relationship between the angle and the net force divided by the surface tension parameter, which is in good agreement with our observations as well as other published experimental and theoretical reports.31,32,33 Figure 7 shows time-elapsed images of a droplet placed on a wedge-shaped surface tension gradient both in the absence of an external magnetic field and in the presence of 200 G parallel and perpendicular fields. In the case of zero field, the large difference in contact angles between the parts of the droplet on the Al and on the Cu leads to a net capillary force that pulls the droplet towards the Al end. This force leads to a spreading motion of the droplet. This behavior was observed previously with water droplets7, which was the reason behind the choice of a waterbased ferrofluid for this study in order to offer a direct comparison thereby enabling better isolation of the effect of the magnetic field on the droplets. When a magnetic field is applied, on the other hand, a completely different behavior emerges, which depends on the orientation and strength of the magnetic field relative to the surface tension gradient direction. In the case of the 200 G field, the droplet is observed to travel approximately the same distance independent of the field orientation; however, the shape associated with the advancing front of the droplet is observed to be flatter in the perpendicular field, whereas it is more rounded and raised up in the parallel field. Droplet movement also proceeded more slowly in the perpendicular field. In both zero field and the parallel field, the droplet stopped moving after approximately 2-3 seconds, whereas for the perpendicular field, the droplet continued moving for more than 10 seconds. The movement of the droplet front proceeded even slower when the perpendicular magnetic field was just below the critical stopping field. In this case a precursor (i.e. hemi-wicking) film first extends outward followed by more flow from the main droplet. This is consistent with earlier observations involving water droplet behavior.7, 31 Figure 8 contains two panels of spliced pictures showing a moving droplet in a parallel magnetic field and a stopped droplet in a perpendicular magnetic field. Although the uniform external magnetic field exerts no net force on a ferrofluid droplet, it induces a highly anisotropic change in the viscosity of the fluid (i.e. magnetoviscous effect) which in turn affects the behavior and flow of the droplet. While the ability to stop the motion or allow it in a magnetic field can have many potential biomedical applications, the details of the behavior are also important from a basic science point of view. Magnetoviscosity was first discovered more than four decades ago34, and the underlying microscopic behavior of the ferrofluid was also modeled successfully soon
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after that by M.I. Shliomis.35, 29 The Shliomis model assumes that the ferromagnetic particles will rotate within a flowing ferrofluid under shear flow. In the absence of a magnetic field, the magnetic nanoparticles can rotate freely and only have to overcome the inherent viscosity of the ferrofluid. When a magnetic field is applied, however, it will tend to align the dipole moment of . This magnetic torque in turn can the particles in its direction due to the torque: - = . increase the magnetoviscosity when the magnetic field is not in the same direction as the ‘vorticity’ of the flowing fluid, since the field will prevent the particles from rotating in a way that misaligns their moments with the field direction. A magnetic field parallel to the vorticity will have no effect on the flow, since the magnetic nanoparticles can rotate with their magnetic moment still aligned with the field. Thus, the Shliomis model suggests that the magnetoviscosity is highest when the magnetic field is perpendicular to the vorticity and is zero when it is parallel. Since the fluid in our experiment flows down the wedge in the surface tension gradient direction, the vorticity vector is expected to be perpendicular to the flow direction. So, when the magnetic field is parallel to the surface tension gradient, it is assumed to be perpendicular to the vorticity vector, and when the field is perpendicular to the flow, it is assumed to be parallel to the vorticity vector. Following this line of reasoning then, one might expect the magnetoviscous effect to be highest when the magnetic field is parallel to the motion. This is in sharp contrast however with what we observed—namely, that the magnetoviscosity was apparently higher when the field was perpendicular to the flow and did not seem to change much when the field was oriented parallel to the flow. In fact, for moderate magnetic fields, droplet pinning was observed when the field was perpendicular to the flow direction, while no pinning was observed in the parallel orientation. It is important to point out that the Shliomis model assumes no interaction of particles (i.e. a highly diluted suspension). The commercial ferrofluid that was primarily used in this work had a volume concentration of magnetic material of 5.8 vol.%. While this is likely considered dilute, it is important to note that the thickness of the surfactant layer can effectively increase the particle diameter leading to a larger apparent concentration of suspended material. 15 It should also be pointed out that due to the low droplet speeds involved in this work and the presence of an adjoining solid surface, the vorticity of the fluid is likely to be quite small. Figure 9 shows a histogram of the speed of propagation of the moving front of the ferrofluid droplet down the surface tension gradient in different applied magnetic fields. The histogram shows clearly that a relatively small or moderate uniform magnetic field is sufficient to prevent ferrofluid droplets from moving even in a strong surface tension gradient. At the same time an order-of-magnitude larger magnetic field applied parallel to the surface tension gradient does not even slow the flow of the droplets down the surface tension gradient. Next, the “critical field” for droplet pinning in the perpendicular orientation was determined. Although small variations were observed experimentally when trying to quantify the “critical field,” a magnetic field of 250 Gauss was observed to pin the droplet and prevent motion on multiple wedges. (Note: Due to small differences attributed to the coating and/or the cleaning process between tests, droplet motion was observed during one set of tests at 275 Gauss; however, at higher magnetic field, droplet pinning was once again observed.) Figure 10 shows the instantaneous droplet velocity as a function of time for Wedge 1 and Wedge 4 in both parallel and perpendicular fields. On Wedge 1 at 200 G, the droplet is seen to move
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more slowly in the perpendicular field than the parallel field (i.e. 0.4 cm/s vs. 1.7 cm/s); however, droplet motion is detected for a longer period of time (i.e. 13.3 sec vs. 2.3 sec). On Wedge 4 at 250 G, however, the droplet is pinned (after initial placement on the wedge) in the perpendicular field but is observed to still move along the gradient in the parallel field. These plots also reveal that the droplet traveled for a longer period of time on Wedge 4 versus Wedge 1 in the parallel field. This could be explained both in terms of the smaller angle associated with Wedge 4 and the increased field strength used here. As mentioned earlier, the Shliomis model attributes the moderate magnetoviscosity observed in dilute ferrofluids to the hindrance of rotational motion of the nanoparticles due to the magnetic field torque. This model however makes at least one major assumption—namely, that the ferromagnetic particles are non-interacting. The more likely cause of the directional dependence of the magnetoviscosity in our study is the formation of nanoparticle chains within the ferrofluid. The formation of such chains was earlier thought to not be possible, due to the very small coupling between low concentrations of magnetite particles with an average diameter of 10 nm. It can be shown that a magnetic particle (i.e. magnetic dipole) creates a field / = 01 4 [(3/ . 6̂ )6̂ − ], / and the force between two such particles having a diameter d and 23 interparticle spacing r depends on the strength of the magnetic field B1 at the location of particle (9 . / ), which is always 2 (with magnetic moment µ 2) through the relation: /,9 = ∇ proportional to
0: 0; 3
1; ?@ 3
