RSC Advances
View Article Online

Open Access Article. Published on 29 March 2019. Downloaded on 10/20/2024 1:40:10 AM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

PAPER

View Journal | View Issue

Cite this: RSC Adv., 2019, 9, 10030

Eﬀect of moderate magnetic ﬁelds on the surface
tension of aqueous liquids: a reliable assessment†
Masayuki Hayakawa,ab Jacopo Vialetto,a Manos Anyfantakis, ac
Masahiro Takinoue, b Sergii Rudiuk, a Mathieu Morel a and Damien Baigl*a

Received 31st January 2019
Accepted 23rd March 2019

We precisely measure the eﬀect of moderate magnetic ﬁeld intensity on the surface tension of liquids, by

DOI: 10.1039/c9ra00849g

tension of water is unaﬀected while that of paramagnetic salt solutions slightly decreases with increasing

rsc.li/rsc-advancesﬁeld strength.

placing pendant drops inside uniform ﬁelds where bulk forces due to gradients are eliminated. The surface

Controlling the properties of uids in a contactless manner,
through the use of external stimuli, oﬀers great advantages ina variety of applications where liquid solutions are involved.
Especially, the on-demand variation of their surface/interfacial
tension has been proved to be a very eﬃcient method fortheir handling and manipulation, both in microuidic channels, or on open surfaces.1 For this purpose, various stimulations have been used, such as thermal,2 electrical3 or optical.4–9
In addition, magnetic control has been proved to be suitable formany practical operations, thanks to its various advantages,10,11
such as: (i) dropping the need of specic substrate modication, (ii) its relative insensitivity to the variation of solution
properties (e.g. pH, temperature, ionic concentration, turbidity),(iii) its non-invasive and remote character, and (iv) the good
spatio-temporal control. On one hand, uid manipulation
using magnetic elds has been typically performed by adding
magnetic particles into the liquids.12–17 Despite being a powerful
technique, the use of magnetic particles decreases its applicability, increases costs, and causes sample contamination. On
the other hand, for complex uid handling in microuidic
devices, building up surface tension gradients has already been
proved to be suitable in controlling various uidic operations.
Even though intense research eﬀort has been put on studying
the magnetic eﬀect on the properties and behaviour of water orother liquids,18–21 only a few studies on their surface tension
were reported.22–25 This is true especially for relatively low
magnetic elds,26,27 as the one that can be produced with small
permanent magnets used inside microuidic chips (100 mT).

a

PASTEUR, Department of Chemistry, École Normale Supérieure, PSL University,
Sorbonne Université, CNRS, 75005 Paris, France. E-mail: damien.baigl@ens.frb

Department of Computer Science, Tokyo Institute of Technology, Kanagawa 226-8502,
Japanc
University of Luxembourg, Physics & Materials Science Research Unit, 162a Avenue dela Faiencerie, Luxembourg L-1511, Luxembourg† Electronic supplementary
10.1039/c9ra00849g

information

10030 | RSC Adv., 2019, 9, 10030–10033(ESI)

available.

See

DOI:

Up to now, surface tension measurements have always been
performed using the pendant drop method, with drops placedin a non-homogeneous magnetic eld. The pendant drop is themost 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, anddeducing the surface tension value with a mathematical model
which considers that the drop shape is dictated by the interplayof 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 isparamagnetic (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 notconsidered by the soware used for analysis. In these conditions, tting the drop shape does not allow to distinguishbetween 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 dropsthat 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 onlyand 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 thependant drop technique. Fig. 1A shows a sketch of theThis journal is © The Royal Society of Chemistry 2019

View Article Online

Open Access Article. Published on 29 March 2019. Downloaded on 10/20/2024 1:40:10 AM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Paper

RSC AdvancesFig. 1 Experimental setups and measured maps of the magnetic ﬁeld around a pendant drop. (A) Sketch of a pendant drop in a non-homogeneous magnetic ﬁeld generated by a small permanent magnet placed below the drop. The distance between the magnet surface and thecentre of the drop was d ¼ 10 mm. (B) Map of the measured magnetic ﬁeld norm (|B|) around the drop in (A). (C) Sketch of a pendant drop ina homogeneous magnetic ﬁeld generated by two permanent magnets placed parallel to each other, each at a distance d ¼ 5 cm from the drop
centre. (D) Map of the measured magnetic ﬁeld norm (|B|) around the drop in (C). The indicated x, y, z coordinates refer to all (A–D) panels.
Drawings of the drop contours (to scale) are shown in (B) and (D) for helping visualizing the drop position in the magnetic ﬁeld.

conguration used to measure the apparent surface tension ofdrops in a non-homogeneous magnetic eld generated bya 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 withpublished results, and with the surface tension of the same
solutions as measured in a homogeneous magnetic eld ofsimilar intensity. Fig. 1B shows the measured map of themagnetic eld norm (|B|) around a drop in this conguration.
Both the components of the magnetic eld perpendicular andparallel to the magnet surface were highly non-homogeneous at
the drop level (Fig. S1A and B†), resulting in a variation in |B| ofaround 70 mT from the drop neck to its bottom. In order toobtain 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, whenfacing each other at relatively short distances (in the order ofcentimetres) exert a very strong attractive force. Therefore,a rigid scaﬀold was constructed in order to keep the twomagnets at a controlled distance. This set-up was conceived tobe compatible with a KRÜSS tensiometer for surface tension
measurements. All components used (e.g., syringes and pipettetips) were non-metallic in order to avoid interactions with thestrong magnets. In this way, a drop could be produced in thecentre of the two parallel magnet surfaces, where both theperpendicular and parallel components of the magnetic eld

This journal is © The Royal Society of Chemistry 2019were highly homogeneous (Fig. S1C and D†). Fig. 1D shows themeasured 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  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  0.4  C; relative humidity¼ 31.4  5.8%). For each sample, the air/water surface tension
values were obtained by averaging measurements over at leastten 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 purewater, having a volumic magnetic susceptibility c ¼ 9.5  0.4
 106; the paramagnetic sample is an aqueous HoCl3 solution
at a concentration of 100 mM, with c ¼ 45  1.7  106
(Fig. S3†). The actual surface tension (g) of those liquids, in theabsence of the magnetic eld, is reported on the le side of thegraph. We note that the addition of HoCl3 induced a weaksurface tension decrease of the aqueous solution. Approachinga 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), whereasa paramagnetic one was attracted (elongated).

RSC Adv., 2019, 9, 10030–10033 | 10031

View Article Online

Open Access Article. Published on 29 March 2019. Downloaded on 10/20/2024 1:40:10 AM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

RSC AdvancesFig. 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) anda solution of 100 mM HoCl3 (blue triangles) in the absence ofa magnetic ﬁeld (left), with a small permanent magnet approachedfrom the bottom (centre) at a distance d ¼ 10 mm (see Fig. 1 for a mapof 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 ¼g*). (B) Surface tension (g) measurements for water (violet circles) andsolutions of increasing HoCl3 concentration as a function of the normof 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  SD from 10 individual experiments.

Upon tting of the drop proles, the soware of the instrument detected an apparent surface tension variation that wasquantied as Dg* ¼ 0.5 mN m1 for pure water (violet circles,
Fig. 2A), and Dg* ¼ 1.2 mN m1 for 100 mM HoCl3 (blue10032 | RSC Adv., 2019, 9, 10030–10033

Paper

triangles). Similar Dg* values in a non-homogeneous magnetic
eld were reported in ref 27 both for water and a paramagnetic
solution (in their case 200 mM aqueous solution of FeCl3).
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 propertiesof 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 theright side of the drop. As a result, the drop was repelled (purewater) or attracted (100 mM HoCl3 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 dropis 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 ofvaried intensities. We quantied the maximum surface tension
variation as Dg ¼ g0  g140, where g0 and g140 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 0.1 mNm1, 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 twoorders of magnitude stronger than ours, (10 T) was employed.
A similar result, Dg ¼ 0.1 mN m1, was also obtained fordiamagnetic aqueous solutions composed of 1 mM and 10 mM
HoCl3 (c ¼ 8.4  106 and c ¼ 3.4  106, respectively, seeFig. S3†). When a paramagnetic drop composed of 100 mM
HoCl3 was placed inside the homogeneous magnetic eld, themaximum surface tension diﬀerence measured was Dg ¼ 0.46
mN m1. Such amplitude is of similar order of magnitude tothat caused by small temperature changes. For instance, thesurface tension of water typically varies as Dg ¼ 0.1 mN m1
K1.33 We can therefore conclude that a 100 mM HoCl3 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 ofgeneral interest in characterizing the eﬀect of the magnetic eldon 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

This journal is © The Royal Society of Chemistry 2019

View Article Online

Open Access Article. Published on 29 March 2019. Downloaded on 10/20/2024 1:40:10 AM.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.

Paper

in microuidic devices and/or for the magnetic handling ofdrops. We note that, even though not showed, the liquid/liquidinterfacial tension of pendant drops immersed in an outerliquid 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, andcompared 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 themoderate magnetic eld intensities explored.

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

Acknowledgements
This work was supported by the Mairie de Paris [Emergence(s)2012], the Institut de France (Subvention Scientique Del
Duca), and the Labex IPGG (ANR-10-LABX-31).

References
1 D. Baigl, Lab Chip, 2012, 12, 3637–3653.
2 J. B. Brzoska, F. Brochard-Wyart and F. Rondelez, Langmuir,
1993, 9, 2220–2224.
3 F. Mugele and J.-C. Baret, J. Phys.: Condens. Matter, 2005, 17,
R705–R774.
4 K. Ichimura, S.-K. Oh and M. Nakagawa, Science, 2000, 288,
1624–1626.
5 J. Berná, D. A. Leigh, M. Lubomska, S. M. Mendoza,
E. M. Pérez, P. Rudolf, G. Teobaldi and F. Zerbetto, Nat.
Mater., 2005, 4, 704–710.
6 A. Diguet, R. M. Guillermic, N. Magome, A. Saint-Jalmes,
Y. Chen, K. Yoshikawa and D. Baigl, Angew. Chem., Int. Ed.,
2009, 48, 9281–9284.
7 A. Diguet, H. Li, N. Queyriaux, Y. Chen and D. Baigl, Lab
Chip, 2011, 11, 2666.
8 A. Venancio-Marques, F. Barbaud and D. Baigl, J. Am. Chem.
Soc., 2013, 135, 3218–3223.
9 C. Gao, L. Wang, Y. Lin, J. Li, Y. Liu, X. Li, S. Feng and
Y. Zheng, Adv. Funct. Mater., 2018, 28, 1803072.

This journal is © The Royal Society of Chemistry 2019

RSC Advances

10 N. Pamme, Lab Chip, 2006, 6, 24–38.
11 Y. Zhang and N.-T. Nguyen, Lab Chip, 2017, 17, 994–1008.
12 Z. Long, A. M. Shetty, M. J. Solomon and R. G. Larson, Lab
Chip, 2009, 9, 1567.
13 N. T. Nguyen, Microuid. Nanouid., 2012, 12, 1–16.
14 J. Pipper, M. Inoue, L. F.-P. Ng, P. Neuzil, Y. Zhang and
L. Novak, Nat. Med., 2007, 13, 1259–1263.
15 L. Zhang, D. Cha and P. Wang, Adv. Mater., 2012, 24, 4756–
4760.
16 E. Bormashenko, R. Pogreb, Y. Bormashenko, A. Musin and
T. Stein, Langmuir, 2008, 24, 12119–12122.
17 M. K. Khaw, C. H. Ooi, F. Mohd-Yasin, R. Vadivelu, J. S. John
and N.-T. Nguyen, Lab Chip, 2016, 16, 2211–2218.
18 E. Beaugnon and R. Tournier, Nature, 1991, 349, 470.
19 M. Sueda, A. Katsuki, M. Nonomura, R. Kobayashi and
Y. Tanimoto, J. Phys. Chem. C, 2007, 111, 14389–14393.
20 J. Vialetto, M. Hayakawa, N. Kavokine, M. Takinoue,
S. N. Varanakkottu, S. Rudiuk, M. Anyfantakis, M. Moreland D. Baigl, Angew. Chem., Int. Ed., 2017, 56, 16565–16570.
21 M. Frenkel, V. Danchuk, V. Multanen, I. Legchenkova,
Y. Bormashenko, O. Gendelman and E. Bormashenko,
Langmuir, 2018, 34, 6388–6395.
22 X.-F. Pang and B. Deng, Phys. B, 2008, 403, 3571–3577.
23 Y. Fujimura and M. Iino, J. Appl. Phys., 2008, 103, 124903.
24 C. Li, L. Chen and Z. Ren, J. Mol. Liq., 2013, 181, 51–54.
25 L. Chen, C. J. Li and Z. M. Ren, Adv. Mater. Res., 2013, 750–
752, 2279–2282.
26 P. Brown, A. Bushmelev, C. P. Butts, J. Cheng, J. Eastoe,
I. Grillo, R. K. Heenan and A. M. Schmidt, Angew. Chem.,
Int. Ed., 2012, 51, 2414–2416.
27 P. Degen, E. Zwar, M. Paulus, M. Tolan and H. Rehage,
Langmuir, 2014, 30, 11563–11566.
28 P.-G. de Gennes, F. Brochard-Wyart and D. Quéré, Capillarity
and Wetting Phenomena, Springer New York, New York, NY,
2004.
29 C. R. Reisin and S. G. Lipson, Appl. Opt., 1996, 35, 1120.
30 A. Katsuki, K. Kaji, M. Sueda and Y. Tanimoto, Chem. Lett.,
2007, 36, 306–307.
31 G. P. Zhu, N. T. Nguyen, R. V. Ramanujan and X. Y. Huang,
Langmuir, 2011, 27, 14834–14841.
32 P. Brown, T. Alan Hatton and J. Eastoe, Curr. Opin. Colloid
Interface Sci., 2015, 20, 140–150.
33 N. B. Vargaik, B. N. Volkov and L. D. Voljak, J. Phys. Chem.
Ref. Data, 1983, 12, 817–820.

RSC Adv., 2019, 9, 10030–10033 | 10033