Effect of moderate magnetic fields on the surface tension of aqueous liquids: a reliable assessment

We precisely measure the effect of moderate magnetic field intensity on the surface tension of liquids, by placing pendant drops inside uniform fields where bulk forces due to gradients are eliminated. The surface tension of water is unaffected while that of paramagnetic salt solutions slightly decreases with increasing field strength.

Up to now, surface tension measurements have always been performed using the pendant drop method, with drops placed in a non-homogeneous magnetic eld. The pendant drop is the most commonly used method to determine the interfacial tension of liquid/liquid or liquid/gas interfaces. 28 It is based on analysing the shape of drops hanging from a capillary, and deducing the surface tension value with a mathematical model which considers that the drop shape is dictated by the interplay of the forces acting on the drop (surface tension and gravity). However, a non-homogeneous magnetic eld exerts an additional bulk force on the liquid drop that causes its deformation. 20,29 Such magnetic force will be attractive if the liquid is paramagnetic (having a magnetic susceptibility c > 0), while it will be repulsive if the liquid is diamagnetic (c < 0). This interaction can deform the pendant drop in a way that is not considered by the soware used for analysis. In these conditions, tting the drop shape does not allow to distinguish between the bulk and the eventual surface effects. With such an approach, only an apparent surface tension can be detected by the instrument. 27,30 In order to suppress the bulk component, which arises in the presence of a magnetic gradient, we constructed an experimental setup where surface tension measurements were performed using the pendant drop method inside highly uniform magnetic elds. Unlike ferrouid drops that can elongate along eld lines due to their strong magnetic response, 31 most common liquid drops maintain their shape under uniform elds. Therefore, with our experimental setup, the drop deformation was essentially due to surface effects only and tting its shape allowed us to accurately extract its surface tension. By varying the eld intensity, we could reliably establish the effect of magnetic eld on the evolution of surface tension of various diamagnetic and paramagnetic solutions (water and aqueous solutions containing dissolved paramagnetic salts). Fig. 1 shows the two experimental setups used to measure the surface tension of aqueous solutions by means of the pendant drop technique. Fig. 1A shows a sketch of the conguration used to measure the apparent surface tension of drops in a non-homogeneous magnetic eld generated by a small permanent magnet placed below the drop. This geometry is similar to the one commonly reported in literature. 26,27,32 It has been used in order to compare our experiments with published results, and with the surface tension of the same solutions as measured in a homogeneous magnetic eld of similar intensity. Fig. 1B shows the measured map of the magnetic eld norm (|B|) around a drop in this conguration. Both the components of the magnetic eld perpendicular and parallel to the magnet surface were highly non-homogeneous at the drop level ( Fig. S1A and B †), resulting in a variation in |B| of around 70 mT from the drop neck to its bottom. In order to obtain a magnetic eld that is homogeneous over the whole drop volume, a novel setup was developed (Fig. 1C). We placed the drop at a precisely controlled distance between two largesized parallel magnetic plates facing their opposite poles. It is important to note that permanent magnets of this size, when facing each other at relatively short distances (in the order of centimetres) exert a very strong attractive force. Therefore, a rigid scaffold was constructed in order to keep the two magnets at a controlled distance. This set-up was conceived to be compatible with a KRÜSS tensiometer for surface tension measurements. All components used (e.g., syringes and pipette tips) were non-metallic in order to avoid interactions with the strong magnets. In this way, a drop could be produced in the centre of the two parallel magnet surfaces, where both the perpendicular and parallel components of the magnetic eld were highly homogeneous ( Fig. S1C and D †). Fig. 1D shows the measured map of |B| when the distance between the magnet surfaces and the centre of the drop was d ¼ 5 cm. In that case, the |B| value around the drop was equal to 141 AE 0.5 mT. Varying d allowed us to tune the magnetic eld intensity while keeping the eld highly homogeneous at the drop region ( Fig. S2 †).
All experiments were conducted at controlled room temperature and humidity (T ¼ 22.3 AE 0.4 C; relative humidity ¼ 31.4 AE 5.8%). For each sample, the air/water surface tension values were obtained by averaging measurements over at least ten different drops. The apparent surface tension (g*) calculated by the tensiometer soware of a diamagnetic and a paramagnetic liquid measured in a non-homogeneous magnetic eld are reported in Fig. 2A. The diamagnetic liquid is pure water, having a volumic magnetic susceptibility c ¼ À9.5 AE 0.4 Â 10 À6 ; the paramagnetic sample is an aqueous HoCl 3 solution at a concentration of 100 mM, with c ¼ 45 AE 1.7 Â 10 À6 (Fig. S3 †). The actual surface tension (g) of those liquids, in the absence of the magnetic eld, is reported on the le side of the graph. We note that the addition of HoCl 3 induced a weak surface tension decrease of the aqueous solution. Approaching a small permanent magnet from the bottom ( Fig. 2A, middle) up to a distance d ¼ 10 mm (corresponding magnetic eld map in Fig. 1B) caused a deformation of the drop as outlined above: a diamagnetic drop was repelled (compressed), whereas a paramagnetic one was attracted (elongated). Upon tting of the drop proles, the soware of the instrument detected an apparent surface tension variation that was quantied as Dg* ¼ 0.5 mN m À1 for pure water (violet circles, Fig. 2A To show that the change in the apparent surface tension, detected for compressed and elongated drops, was due to a bulk magnetic effect and not to a variation of the surface properties of the solutions in the presence of the magnetic eld, we placed the magnet at the same distance from the drop, but on its side, so that the magnetic eld gradient pointed from the le to the right side of the drop. As a result, the drop was repelled (pure water) or attracted (100 mM HoCl 3 solution), but no compression or elongation occurred. Consequently, the apparent surface tension detected in this conguration ( Fig. 2A, right) was the same as without the magnetic stimulation for both solutions. We thus conclude that a setup where a pendant drop is placed in a non-homogeneous magnetic eld is not appropriate for measuring the actual effect of the magnetic eld on the surface tension.
To rule out bulk effects that interfere with the measurements, and to quantify the effect of the magnetic eld intensity on surface tension, we performed measurements using the setup depicted in Fig. 1C. Fig. 2B shows the surface tension measured when a drop of a diamagnetic or paramagnetic solution is placed inside a homogeneous magnetic eld of varied intensities. We quantied the maximum surface tension variation as Dg ¼ g 0 À g 140 , where g 0 and g 140 were the surface tension without magnetic stimulation, and at the maximum magnetic eld intensity used (|B| ¼ 140 mT), respectively. For pure water (violet circles in Fig. 2B) we obtained Dg ¼ À0.1 mN m À1 , a decrease that was smaller than our experimental error. We can therefore conclude that, under moderate magnetic elds up to 140 mT, no magnetic effect on the surface tension was detected. We do not exclude that signicant surface tension variation can occur at higher magnetic eld intensities, as reported, for example, in ref. 23 and 25 where a magnetic eld two orders of magnitude stronger than ours, (10 T) was employed.
A similar result, Dg ¼ À0.1 mN m À1 , was also obtained for diamagnetic aqueous solutions composed of 1 mM and 10 mM HoCl 3 (c ¼ À8.4 Â 10 À6 and c ¼ À3.4 Â 10 À6 , respectively, see Fig. S3 †). When a paramagnetic drop composed of 100 mM HoCl 3 was placed inside the homogeneous magnetic eld, the maximum surface tension difference measured was Dg ¼ À0.46 mN m À1 . Such amplitude is of similar order of magnitude to that caused by small temperature changes. For instance, the surface tension of water typically varies as Dg ¼ À0.1 mN m À1 K À1 . 33 We can therefore conclude that a 100 mM HoCl 3 paramagnetic solution shows only a very small decrease of its surface tension in a moderate, homogeneous, magnetic eld.

Conclusions
This communication reports a custom-built setup that can be of general interest in characterizing the effect of the magnetic eld on the surface/interfacial tension of liquids. The setup allowed us to precisely measure the surface tension of pendant drops placed into a homogeneous magnetic eld of moderate intensities, whose strength is comparable to the one commonly used Fig. 2 Apparent surface tension (g*) and surface tension (g) measurements for diamagnetic and paramagnetic liquids. (A) Apparent surface tension (g*) measurements for water (violet circles) and a solution of 100 mM HoCl 3 (blue triangles) in the absence of a magnetic field (left), with a small permanent magnet approached from the bottom (centre) at a distance d ¼ 10 mm (see Fig. 1 for a map of the corresponding magnetic field), and with a small magnet approached from the side at a distance d ¼ 10 mm. Note that g* in (A) without the magnet (left side), is an actual surface tension value (g ¼ g*). (B) Surface tension (g) measurements for water (violet circles) and solutions of increasing HoCl 3 concentration as a function of the norm of the magnetic field at the drop level. The map of the magnetic field in Fig. 1 corresponds to the points at |B| ¼ 140 mT. Symbols and error bars show mean AE SD from 10 individual experiments.
in microuidic devices and/or for the magnetic handling of drops. We note that, even though not showed, the liquid/liquid interfacial tension of pendant drops immersed in an outer liquid could be measured as well with our conguration. The surface tension of diamagnetic and paramagnetic solutions could be analysed for various magnetic eld intensities, and compared to previously reported experiments where the drops were placed in non-homogeneous magnetic elds. Being unaffected by bulk effects, our measurement in homogeneous elds offers a correct and more reliable value. We established that, while pure water was unaffected, only a small negative variation has been detected for the paramagnetic solution tested (holmium chloride dissolved in water) in the range of the moderate magnetic eld intensities explored.

Conflicts of interest
There are no conicts to declare.