The field instability of the free surface of ferrofluid was investigated under microgravity and hypergravity environments conducted by parabolic flight. It is observed that the perturbation was suppressed under hypergravity, whereas at the microgravity condition, it appeared to have only slight increase in the amplitude of the perturbation peaks compared to the case of ground condition. Besides, an observation of peak-trough distance showed that not only the peak, but the trough was also very much dependent on the applied magnetic field. The difference of magnetic pole (north and south) had shown to be a factor to the perturbation as well.

A suspension of magnetic nanoparticle, carrier liquid and surfactant form a magnetic liquid called as ferrofluid. Ferrofluid has been widely implemented in various industries, such as biomedical, sensor etc.1–4 The free surface of the ferrofluid gained much interest in investigation of several relevant technology fields due to its interesting behavior under the influence of external magnetic field. Depending on the strength of external magnetic field, ferrofluid could change phase5,6 into anisotropic ordering of labyrinthe or hexagonal structure,7 bent-wall,8 or lamellar-like patterns.9 

The magnetic field effect on ferrofluid also leads to a classical theory proposed by Cowley and Rosensweig, namely the normal field instability theory. The theory implies that, the interface of two fluids, with at least one of them being ferromagnetic, may be unstable when there is an applied magnetic field perpendicular to the surface.10 The instability would lead to surface perturbation and peaks and troughs may be presence. The surface equilibrium is determined by the surface tension and gravitational force. Cowley and Rosensweig showed that the perturbation is influenced by several parameters including the type of fluids, density difference between the two interfacing fluids, surface tension, gravitational force etc.

In the same work, Cowley and Rosensweig had shown the influence of density difference towards the surface instability with two type of fluid interface.10 Besides, several works have been reported on the normal field instability behaviour of the magnetic fluid.11–13 Nevertheless, there are only few studies on the gravity effect. Odenbach had conducted some experiments with drop tower and parabolic flight simulated microgravity environment on the field stability of magnetic fluid, but the scope of study were on the non-Newtonian Weissenberg effect14 and particle volume concentration.15 Hence, a study of gravity acceleration effect on the normal field instability of magnetic fluid was carried on in this work by comparing the perturbation of the ferrofluid under the ground condition (1G) with the simulated microgravity (μG) and hypergravity (1.8G) conditions by parabolic flight.

An experimental rack was setup as shown in Fig. 1(a). The rack consisted of two camcorders and a sample kit. The two camcorders, namely CamF and CamT, captured the top and front view of ferrofluid samples, respectively, which placed in the sample kit. The camcorders were turned on for the entire parabolic flight. The sample kit consisted of two layers with four cubical cells with edge length of 4 cm. A magnet holder consisted of four magnets (dimension of 1 cm x 1 cm x 1 cm) was placed in between the layers, as shown in Fig. 1(b). The magnets were positioned carefully to be centered at each cells, this configuration minimised the magnetic interaction with neighbouring ferrofluids. This can be confirmed by the magnetic field profile shown in Fig. 2, with P50 used magnet M1 and W40 used M2. ‘S’ and ‘N’ denote south and north pole respectively. Distance between magnet and adjacent fluids was more than 3 cm, this means that the magnets had minimal, if not no effect on the adjacent fluids. The effective distance between magnet and fluid, taking into consideration the thickness of the holder and kit, was measured to be 0.8 cm. The top and bottom layer of each cell were placed with same ferrofluid.

FIG. 1.

Schematic illustration of (a) experimental rack which consisted of two camcorders (CamT and CamF) for top and front view respectively, and a sample holder for placement of ferrofluid, enlarged at (b).

FIG. 1.

Schematic illustration of (a) experimental rack which consisted of two camcorders (CamT and CamF) for top and front view respectively, and a sample holder for placement of ferrofluid, enlarged at (b).

Close modal
FIG. 2.

Magnetic strength profile of magnets used in the experiment. M1 used for sample P50, M2 used for sample W40. ‘S’ and ‘N’ denote south and north pole respectively. Inset shows the larger scale at 0.8cm.

FIG. 2.

Magnetic strength profile of magnets used in the experiment. M1 used for sample P50, M2 used for sample W40. ‘S’ and ‘N’ denote south and north pole respectively. Inset shows the larger scale at 0.8cm.

Close modal

Two types of ferrofluid, Taiho W40 (water based) and Ferrotec P50 (oil based) were used. Each type of fluid was placed with volume of 0.1 ml and 0.5 ml respectively. The properties of the two ferrofluid are shown in table I.

Table I.

Properties of W40 (water based) and P50 (oil based) ferrofluid used in this experiment.

 W40P50
Density (g/ml) 1.40 ± 2 1.25 
Viscosity (cp) 25 ± 7 <40 
Surface Tension (dyne/cm) 28 ± 2 32 
Magnetization (gauss) 380 ± 30 500 
 W40P50
Density (g/ml) 1.40 ± 2 1.25 
Viscosity (cp) 25 ± 7 <40 
Surface Tension (dyne/cm) 28 ± 2 32 
Magnetization (gauss) 380 ± 30 500 

The experiment was conducted on a parabolic flight simulated environment. The special feature of parabolic flight enables us to make use of both microgravity and hypergravity on our experiment. The changes in G-force start with a fluctuating G before entering into hyper-G of 1.8G. Then, microgravity is experienced, before getting into 1.5G. The detail flow is as shown in Fig. 3. There existed a turbulence force during the parabolic flight, which was treated as a constant in this study.

FIG. 3.

Figure shows the gravity profile of the parabolic flight. A and B are the points where dynamic transition is shown on Fig. 4.

FIG. 3.

Figure shows the gravity profile of the parabolic flight. A and B are the points where dynamic transition is shown on Fig. 4.

Close modal

The 1G data was obtained at ground whereas the 1.8G and μG data were obtained during the parabolic flight. The cut frames of the camcorders were extracted for analysis. The side view results of 0.5ml P50 sample and top view results of W40 will be discussed here.

Fig. 4 shows the dynamic behavior of 0.5ml P50 sample, seen from side view. The frames were sampled at one second interval. With the aid of grid lines, the transition of peak amplitude was observed. For the top set sample, lower amplitude was observed for the 1.8G case and it increased as it went into μG. Whereas when gravity transited from μG to 1.5G, the peak amplitude was suppressed. For the bottom set sample, the peak profiles were of opposite of the top set sample.

FIG. 4.

Video cut frames of the 0.5ml P50 sample. A and B each corresponds to the position labeled at Fig. 3. The frames are sampled at one second interval. Grid lines are for reference.

FIG. 4.

Video cut frames of the 0.5ml P50 sample. A and B each corresponds to the position labeled at Fig. 3. The frames are sampled at one second interval. Grid lines are for reference.

Close modal

The side view cut frames of the sample is shown in Fig. 5. With the aid of the two reference lines, can be seen that, for the top set sample, which is the south pole side, 1.8G sample was having lowest peak amplitude, followed by 1G, then μG with slightly higher amplitude. This can be explained by the normal field instability theory mentioned before. The theory states that there exist a critical magnetic field strength that will cause the instability to the surface of the fluid, and the critical field, H* is given by16 

\begin{equation}H^* = \frac{1}{\chi }\left[ {\frac{2}{{\mu _o }}\left( {\frac{{2 + \chi }}{{1 + \chi }}} \right)} \right]^{1/2} \left( {\rho g\sigma } \right)^{1/4}\end{equation}
H*=1χ2μo2+χ1+χ1/2ρgσ1/4
(1)

where χ is susceptibility of the fluid, ρ is its density, σ is its surface tension, μo is the vacuum permeability and g is the gravitational acceleration. The experiment by Cowley and Rosensweig also showed that the surface perturbation starts when the applied normal field, Happlied, exceeds H*. Further increase of Happlied, would lead to a more violent perturbation, i.e. bigger amplitude of peaks and more peaks are formed.

FIG. 5.

Video cut frames (CamF) of 0.5ml P50 ferrofluid under different G-conditions. ‘M1’ represents the magnet used for this sample, with south and north poles labeled. Horizontal reference lines are for easy comparison.

FIG. 5.

Video cut frames (CamF) of 0.5ml P50 ferrofluid under different G-conditions. ‘M1’ represents the magnet used for this sample, with south and north poles labeled. Horizontal reference lines are for easy comparison.

Close modal

The equation shows the dependency of gravity towards the critical field, a reduction in gravitational force causes the H* to decrease. The decrease in H* equals to a larger magnitude difference between Happlied and H*, which will increase the surface perturbation. This explains the increase of amplitude of peaks as observed in the case of μG. The same explanation goes to the case of 1.8G, where heavy gravity leads to raise in H*, then reduction in |Happlied-H*|, hence decrease in surface perturbation. It was observed that the increase in amplitude of peak in μG was small as compared to the decrease in 1.8G. It is worth to note that the surface tension of ferrofluid can be related to gravitational force as well, where a larger gravitational acceleration leads to a larger surface tension.11 

Besides the amplitude of peaks, another observation can be seen was on the trough. The term “peak-trough” is defined as the distance from the tip of the peak till the valley of the trough, as illustrate in Fig. 6. 1G showed the largest peak-trough distance, followed by 1.8G, then μG.

FIG. 6.

Schematic diagram for the definition of “peak-trough” distance.

FIG. 6.

Schematic diagram for the definition of “peak-trough” distance.

Close modal

It is suspected that the increase in |Happlied-H*| not only gave rise to the amplitude of the peaks, it also elevated the trough of the fluid, which explains the small peak-trough distance in μG. Whereas for the 1.8G case, the trough showed slight reduction as compared to the peak, mainly because of the reduction in peak led to the excessive volume which shifted up the horizon surface level, hence the trough of the fluid.

As mentioned, the surface perturbation would lead to the changes in number of peaks as shown in Fig. 7. For north pole sample, the number of peaks at μG was 29, 1G was about 28, and reduced to 25 at 1.8G. For south pole sample, the numbers of peaks were 25, 19, 17 for case of μG, 1G and 1.8G respectively. The results were tally with the theory where at a reduced gravity condition, |Happlied-H*| increased and more violent perturbation happened which leads to more peaks appeared. Whereas for hypergravity case, the reduction in |Happlied-H*| caused the number of peaks to decrease. By controlling the Happlied, the work by Cowley and Rosensweig had shown similar observation on the number of peaks.10 

FIG. 7.

The relationship between number of peaks and gravitational force.

FIG. 7.

The relationship between number of peaks and gravitational force.

Close modal

Cowley and Rosensweig had only discussed on the case where light fluid on top and heavy fluid on bottom, with gravity is acting in the direction from light fluid to heavy fluid. Our experiment setup allowed us to study on the opposite case where gravity force is acting from heavy fluid to light fluid. It was observed that the amplitude profile of bottom set samples was exactly of opposite of the top set samples. The reverse oriented fluid samples were actually being attracted by the magnetic force, rather than gravitational force in the case of normal oriented samples. Instead of stabilizing the fluid down to the horizon surface, the gravitational force further attracted the reversed fluids away from the horizon surface. The surface equilibrium was achieved under the influence of both magnetic and gravitational force.

The north and south poles of magnet resulted in different flux experienced by the top and bottom sample. In our setup, the magnet was placed with south pole facing up (as illustrated in Fig. 5). As shown in Fig. 7, the differences in pattern between south and north pole sample prove that magnetic pole does have effect on the perturbation shape. Nevertheless, it is worth to note that there was some difference in magnetic strength between the south and north pole of the magnets, which might be another factor on affecting the perturbation. Note that the images for both samples were shot in the normal oriented way, with gravity acting in the direction from light fluid to heavy fluid.

A study of gravitational influence on the field instability of ferrofluid had been conducted under various G-conditions simulated by parabolic flight. It was observed that the peak amplitude of ferrofluid increased with the decrease in G-force, which is tally with the mathematical equation by Cowley and Rosensweig. Besides, increase in number of peaks of the perturbed surface supports the theory as well. The observation on the peak-trough distance suggested that not only peak, but trough might also be influenced by the magnetic field. In contrast with the setup reported by Cowley and Rosensweig, reversed oriented observation had been made as well. The results showed that gravitational force further attracted the reversed fluid downwards, results in higher peak amplitude with greater gravitational force and vice versa. Magnetic flux from north and south poles influenced the surface perturbation differently.

We would like to thank ANGKASA, JAXA, JSF and DAS for giving us the chance to conduct this experiment in Nagoya, Japan. Appreciation is given towards Professor Toshio Suzuki for providing us the W40 ferrofluid, Taiho Industries Co. Ltd., Japan for the data sheet of the ferrofluid and Ferrotech Japan for providing us the P50 ferrofluid.

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