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Article

Formation and Behaviour of Active Droplets and Bubbles in a Magnetic Fluid in an Inhomogeneous Magnetic Field

by
Evgeniy Sokolov
,
Dariya Kaluzhnaya
,
Elena Shel’deshova
and
Petr Ryapolov
*
Faculty of Natural Sciences, Department of Nanotechnology, Microelectronics, General and Applied Physics, Southwest State University, 50 Let Oktyabrya Street, 94, 305040 Kursk, Russia
*
Author to whom correspondence should be addressed.
Fluids 2023, 8(1), 2; https://doi.org/10.3390/fluids8010002
Submission received: 25 November 2022 / Revised: 13 December 2022 / Accepted: 18 December 2022 / Published: 21 December 2022
(This article belongs to the Special Issue Recent Advances in Hydrodynamics and Magnetised Fluids)
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Versions Notes

Abstract

:
This work proposes a new technique for creating active bubbles and droplets with a non-magnetic core and a coating formed by a magnetic fluid. The procedure consists of the injection of a non-magnetic phase into a magnetic one that is supported by the presence of an inhomogeneous magnetic field from the source, which combines an annular magnet and an electromagnet. We explored various modes leading to different active bubbles and drops as well as the influence of the magnetic field on the size, velocity, and acceleration of the formed active droplets. It is shown that active bubbles change their trajectory under the action of a constant magnetic field and also disintegrate under the action of a pulsed one. This provides a new mechanism for controlling the absorption of droplets and bubbles using a magnetic field. Therefore, these results can be applied to create droplet-based microfluidics systems, in which an inhomogeneous magnetic field can be used for focusing droplet and bubble flows in a magnetic fluid.

1. Introduction

Active or smart materials have unique features and are becoming more common due to the possibility to control their dynamics and physical properties by external stimuli. A magnetic field makes it possible to exert the greatest non-contact impact on an object [1]. This feature makes magnetic materials popular for organizing active systems among which magnetic soft composites [2], multifunctional emulsions [3], magnetorheological fluids [4], and magnetic fluids [5,6,7,8,9] can be listed. A magnetic fluid, which was the first proposed example of such composite media [10,11], is a colloidal solution of magnetic nanoparticles coated with a surfactant dispersed in a carrier liquid [12,13,14].
Magnetic fluids, soft magnetic systems, and magnetic nanoparticles are so popular for such active-systems applications due to the possibility to implement an external control of the physical parameters and dynamics of such systems with external magnetic fields [15,16,17,18]. As a rule, in such systems, magnetic particles are modified using specific surfactants which are extremely difficult to synthesize and which can interact and be combined only with certain types of biological objects (cells, proteins, viruses, etc.) or organic compounds [19,20,21,22,23,24]. Further, such systems are subjected to separation according to magnetic parameters [25,26,27].
Another popular phenomenon is the self-assembly of non-magnetic inclusions in liquid magnetic media under the influence of both inhomogeneous and homogeneous magnetic fields [28]. During the past few years, a number of works describing various approaches to influencing magnetic multiphase systems by applying spatially inhomogeneous magnetic fields have been published [29,30,31]. Among various topologies of external magnetic fields, the configuration, which contains a region with zero magnetic field intensity (the region of ‘magnetic vacuum’, in which the magnetic field gradient changes its direction), is of particular interest. This unique region makes it possible to control the dynamics of non-magnetic inclusions in a magnetic fluid by an external inhomogeneous magnetic field [32,33,34].
In recent reviews on magnetically active materials [9,35,36,37,38,39], more and more attention is paid to active droplets that contain non-magnetic fluid and magnetic particles. Active droplets can be used as magnetic liquid robots for magnetically controlled medicine delivery [40]. The dynamical regimes of magnetic fluid droplets in oil in a flow-focusing channel were considered in [41] for non-magnetic phase feed rates varied from 0.1 mL/h to 1.0 mL/h. It has been found that the droplet modes change from squeezing to dripping. In addition to visual observation, using a Sensor microscope based on giant magnetoresistance has been proposed for droplet detection. A system comprised of a droplet of liquid metal, which, due to surface tension forces, adheres to a fluid non-magnetic drop of a much larger size was explored in the work [42]. Due to the external magnetic field control, this system can move through channels of various configurations. However, gallium-based alloys used are toxic and cannot be used for biological applications. The work [43] describes a technique for the production of active magnetic droplets by injecting a surfactant containing magnetic nanoparticles into water. However, this method is only suitable for hydrophobic droplets. The oil droplets were coated with nanoparticles by mixing; as a result, not all droplets had a magnetic shell, and clusters formed, which adversely affected the possibility of external control of such systems.
Thus, the approaches mentioned above have certain drawbacks, which demand developing new experimental techniques aimed at the formation of controlled active bubbles and magnetically coated droplets. An inhomogeneous magnetic field of a special configuration, created by an annular permanent magnet, can act as a tool for focusing droplets and bubble flows in a magnetic fluid. In addition, such an experimental technique will contribute to solving several tasks: ensuring the formation of active bubbles and droplets without a significant concentration of surfactants; creating an additional mechanism for controlling the size of bubbles and droplets, as well as their magnetic shell thickness and strength.

2. Materials and Methods

To study the dynamics of droplets and bubbles flow in magnetic fluids, an experimental setup was developed. Its construction is shown in Figure 1.
A flat glass channel 1 (2 mm thick), installed vertically using a non-magnetic fastener system, is filled with an MF sample. The top of it is filled with a layer of non-magnetic phase with the help of a syringe. An annular permanent magnet 2 (NdFeB 60 × 24 × 10 mm) placed on top of electromagnet 3 is used as a source of an inhomogeneous magnetic field. Taken together, they form a combined magnetic field source, which is located coaxially with the channel axis and connected to a power source 4 to change the magnetic field’s intensity. A syringe pump tube 5 is used to supply gas or fluid to the ‘magnetic vacuum’ region [33,34]. A permanent magnet 6 can be moved towards this region to study the impact of an external magnetic field on the dynamics of bubbles or droplets covered with a magnetic shell. A controlled LED light source 7 is used for illumination. Recording of the dynamics of non-magnetic inclusions is carried out in the transmitted light mode using the high-speed camera 8 (Nikon 1, Tokyo, Japan) connected to computer 9.
To process the obtained video and photo images, a special set of programs based on machine vision algorithms has been developed in the National Instruments LabView environment.
Figure 2 provides plots representing the axial component of the magnetic field intensity H created by a combined source comprised of a permanent annular magnet and an electromagnet as a function of the z coordinate. The middle of the annular magnet is taken as z = 0. Different markers correspond to different values of current in electromagnet I.
The following technology of channel preparation was applied: two optically transparent glass plates were glued together at a distance of 2 mm using a two-component epoxy resin. To feed the non-magnetic phase to the region of the magnetic vacuum, an inlet tube was glued to the bottom of the channel.
In this work, we studied the samples of magnetic fluids obtained by chemical condensation. The particles of nanosized magnetite Fe3O4 stabilized with oleic acid were used as a magnetic fraction. Water, kerosene, mineral oil, and synthetic oil were used as carrier liquids. The water-based MF1.1 sample was obtained at Southwest State University. MF1.2, MF1.3, and MF1.4 were produced by diluting MF1.1 with water in certain proportions. MF2.1 and MF2.2 samples are kerosene-based, MF3.1 and MF3.2 samples use mineral oil as a carrier liquid, and the MF4.1 sample is synthetic oil-based; they were obtained at Ivanovo State Power Engineering University. All measurements of the studied magnetic fluids samples’ physical parameters, namely, the solid phase volume concentration, the fluid density, the MF viscosity, and saturation magnetization, were carried out according to the techniques and using the setups developed in the laboratory of nanoscale acoustics of the Southwest State University. The physical parameters of the samples under study are presented in Table 1, where ρ is the MF sample’s density, φ is the concentration, Ms is the saturation magnetization, and η is the viscosity.
Such fluids as polymethylsiloxane-5 (PMS-5), polymethylsiloxane-100 (PMS-100), mineral oil VDL100 (oil), Kerosene TS-1, Water were used as a non-magnetic phase fed to the magnetic vacuum region. The physical parameters of these fluids are presented in Table 2.

3. Results

In the studies on the dynamics of the droplet flow formation of various combinations of fluid non-magnetic phases, glass channel No.1 was used. Magnetic fluid samples (MF1.1 and MF2.1) were the dispersion medium in the experiment. Such fluid samples as PMS 5, PMS 100, oil, kerosene, and water were used as the fed dispersed phase. The results of experiment No.1 are presented in Table 3.
During the experiments, a droplet flow did not occur. In all given combinations of “MF-non-magnetic fluid”, the formation of a layer of a non-magnetic phase on the surface of the MF column was observed.
A distinctive feature of the next experiment is an addition of a liquid non-magnetic phase to both the magnetic vacuum region and the MF surface. Samples of magnetic fluids (MF1.1-MF1.3, MF2.1, MF4.1) were used as the bulk phase. Air, water, or oil were in the form of a dispersed phase fed to the magnetic vacuum region. The results of Experiment No. 2 are presented in Table 4.
From the presented table it can be seen that a bubble flow formation is observed when air is fed to the cavity filled with non-magnetic fluid PMS 5, PMS 100, oil, or water. The emerging air bubble, flying through the MF column, is covered with a magnetic shell and continues its movement through the non-magnetic phase already in the form of an active bubble covered with a magnetic fluid layer.
When water is fed to the channel with MF4.1, the formation of droplets separated by a magnetic bridge is observed on the surface of the MF layer. Further, the dynamics of the droplet flow were studied with the combination of “MF1.3-oil-oil”. It can be seen that the droplet formation does not occur, but the formation of a jet flow is observed in the MF layer. When oil is fed to the cavity with water in MF2.1, one can see how a jet flow of oil in water is formed above the MF surface.
The next stage of our work was to study the dynamics of bubble flow in the ‘MF-oil’ multiphase system. The two-phase system consisted of a magnetic medium (samples MF1.1–MF1.4) and a nonmagnetic (oil) phase.
The oil was on the top of the MF column. A permanent magnet was used to study the influence of an external magnetic field on the movement trajectory and the properties of active non-magnetic inclusions. The results of the study are presented in Table 5, in which the permanent magnet is added schematically; under the influence of its field, the bubbles’ trajectory changed.
From the presented results, we can conclude that when air is fed to the system, the inclusions, flying through the MF layer, are covered with a magnetic shell. Then, they continue their movement in the oil as active bubbles, the movement trajectory of which changes under the magnetic field’s influence, and the phenomenon of bubble self-organization is observed on the surface (the rightmost column of Table 5).
The results of the video recording of the dynamics of the ‘MF2.2-water’ phase boundary in the inhomogeneous magnetic field created by a magnetic field’s combined source are shown in Figure 3.
The points in the figure indicate the mass center of the detached droplets, which are tracked in the LabView program. The conversion of coordinates into millimeters was carried out by pixels, and time—by frame numbers.
The developed program also makes it possible to estimate the size of water droplets floating up. The inclusion area is also determined by converting pixels into linear dimensions through a scaling factor.
Based on the data obtained in the LabView program, plots of the dependence of the coordinate x of the droplet movement on time t were drawn (points in Figure 4). The moment of droplet separation is chosen for the zero moments of time (the penultimate column in Figure 3).
Coordinates of different drops for each time point are scattered within the measurement uncertainty. This allows us to construct an approximate dependence in the form of the equation of motion corresponding to a decelerated movement:
x = −a·t2 + v0·t + x0,
where x is the drop center coordinate, a is the drop acceleration, t is the time, v0 is the initial velocity, x0 is the initial coordinate.
These dependencies are shown as solid curves in Figure 4. The values of acceleration a and the velocity v0 determined from Equation (1) for each curve in Figure 4 are presented in Table 6. The value of the cross-sectional area of the detached droplets is also presented for each value of the current in electromagnet I.
Figure 5 and Figure 6 show changes in the acceleration and velocity of non-magnetic liquid inclusions floating up depending on the strength of the current supplied to the solenoid.
It can be seen from the plots that with an increase in the current supplied to the solenoid, the acceleration of the separating inclusions decreases, and their velocity increases.
The plot given in Figure 7 shows how the current supplied to the electromagnet affects the size of the droplets (cross-sectional areas).
The studied dependence shows that with an increase in the current strength in the solenoid, the size of the formed water drops decreases.

4. Discussion

The obtained results show that active bubbles and droplets can be formed in the inhomogeneous field of an annular magnet by injecting a non-magnetic phase into the magnetic fluid. The separation of nonmagnetic droplets and bubbles occurs from a levitating nonmagnetic volume (Table 4 and Figure 3), unlike applying the flow focusing technique, which is one of the main techniques in droplet microfluidics [44] when it occurs from a capillary. In this case, the levitating gas cavity acts as a receiver, making it possible to stabilize the size of the detached bubbles and increase the adjustment range, in contrast to the data presented in [45], the in which detachment of bubbles in a magnetic fluid occurred in a uniform magnetic field.
The experiments in this work, in contrast to the known works on active droplets [40,43], were carried out without the addition of surfactants in a thick liquid layer (1 mm). Even under these conditions, it was possible to choose a mode for the formation of active bubbles and droplets (Table 4 and Table 5), the size and dynamics of which can be controlled using an external magnetic field.
The influence of the magnetic field configuration on the velocity, acceleration, and size of active droplets obtained by injecting a non-magnetic fluid into a magnetic one was studied (Figure 2). It was found that their velocity increases, acceleration decreases, and the droplet’s size decreases when the current increases. This can be explained by a change in the configuration of the field, created by a combined source consisting of a permanent annular magnet and an electromagnet (Figure 2). With an increase in the current strength, the isolines of the modulus of the resulting magnetic field shift. As a result, the volumes of both the levitating non-magnetic fluid inclusion and the droplet detached from the latter decrease, as can be seen in Figure 3. A large ponderomotive force caused by the difference in the magnetic pressure at the edges of the drop acts on a larger drop in an inhomogeneous magnetic field. At the same time, the drag force increases significantly leading to a larger negative acceleration and a lower velocity of such a drop.
On the surface of the oil layer (the rightmost column of Table 5), the phenomenon of bubbles self-organization occurs; without applying a field, the bubbles are arranged somewhat randomly, but when applying a field, the ordering resembles a crystal lattice. Similar self-organization phenomena were observed for magnetic fluid droplets in [46]. The active bubbles formed are stable and do not collapse over time. Their size and magnetic shell thickness depend on the magnetic fluid concentration. The bubble diameter decreases with an increase in the magnetic fluid concentration; on the contrary, the shell thickness increases. When moving a powerful neodymium magnet toward bubbles, the magnetic shell of the bubbles becomes thinner leading further to the destruction of the bubbles for those bubbles, which are covered by the shell of MF1.3, MF1.4. In such a case, bubbles based on concentrated magnetic fluids MF 1.1, and MF 1.2 are not destroyed. Their destruction occurs only under the action of a pulsed field created by an electromagnet. This creates the background for the development of liquid multilayer capsules which can be controlled by a magnetic field, concentrated in a certain place, and destroyed under an action of the field’s pulses.

Author Contributions

Conceptualization, E.S. (Evgeniy Sokolov) and P.R.; methodology, E.S. (Evgeniy Sokolov), D.K. and P.R.; software, P.R.; validation, E.S. (Elena Shel’deshova), P.R. and D.K.; formal analysis, D.K.; investigation, E.S. (Evgeniy Sokolov); resources, E.S. (Evgeniy Sokolov); data curation, E.S. (Evgeniy Sokolov) and D.K.; writing—original draft preparation, E.S. (Evgeniy Sokolov); writing—review and editing, P.R.; visualization, E.S. (Evgeniy Sokolov); supervision, P.R.; project administration, P.R.; funding acquisition, P.R. All authors have read and agreed to the published version of the manuscript.

Funding

The research was carried out at the expense of the grant of the Russian Science Foundation No. 22-22-00311, https://rscf.ru/project/22-22-00311/.

Data Availability Statement

Data sharing not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Fluids 08 00002 g001 550
Figure 1. Experimental setup diagram.
Figure 1. Experimental setup diagram.
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Figure 2. The axial component of the magnetic field intensity is created by a combined source comprised of a permanent annular magnet and an electromagnet in dependence on the z coordinate.
Figure 2. The axial component of the magnetic field intensity is created by a combined source comprised of a permanent annular magnet and an electromagnet in dependence on the z coordinate.
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Figure 3. Dynamics of the interphase boundary “water-MF” for the specimen MF-2.
Figure 3. Dynamics of the interphase boundary “water-MF” for the specimen MF-2.
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Figure 4. Plots of the dependence of the coordinates of the movement of the droplet on time: (a) at 0A; (b) at 0.9A; (c) at 1.8A.
Figure 4. Plots of the dependence of the coordinates of the movement of the droplet on time: (a) at 0A; (b) at 0.9A; (c) at 1.8A.
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Figure 5. Dependence of the acceleration of the droplet movement on the change in the current applied to the solenoid.
Figure 5. Dependence of the acceleration of the droplet movement on the change in the current applied to the solenoid.
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Figure 6. Dependence of the droplet velocity on the change in the current applied to the solenoid.
Figure 6. Dependence of the droplet velocity on the change in the current applied to the solenoid.
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Figure 7. The dependence of the droplet size on the change in the current supplied to the solenoid.
Figure 7. The dependence of the droplet size on the change in the current supplied to the solenoid.
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Table
Table 1. Physical parameters of the MF.
Table 1. Physical parameters of the MF.
MF1.1MF1.2MF1.3MF1.4MF2.1MF2.2MF3.1MF3.2MF4.1
Base FluidWaterKeroseneMineral OilSynthetic Oil
ρ, kg/m312121082105610261382936127010181050
φ, %4.91.91.30.7214.23.6310.314.264.81
Ms, kA/m21.7116.983.74912,539.91727.3
η, mPa∙s5.62.151.651.52402.4559469650
Table
Table 2. Physical parameters of non-magnetic fluids.
Table 2. Physical parameters of non-magnetic fluids.
PMS 5PMS 100OilKeroseneWater
η, mPa∙s585371,31
ρ, kg/m39189668827831000
Table
Table 3. Results of Experiment No. 1.
Table 3. Results of Experiment No. 1.
MFSupplied Non-Magnetic PhaseResult
MF 1.1PMS 5The formation and separation of droplets from the cavity do not occur
MF 1.1PMS 100
MF 1.1Oil
MF 1.1Kerosene
MF 2.1Water
Table
Table 4. Results of Experiment No. 2.
Table 4. Results of Experiment No. 2.
MFLiquid in the Cavity and on the Surface MFSupply PhaseDynamics of Multi-Phase Magnetic SystemResult
MF1.1PMS 5AirFluids 08 00002 i001Fluids 08 00002 i002Fluids 08 00002 i003Fluids 08 00002 i004Active bubble in the membrane MF
MF1.1PMS 100AirFluids 08 00002 i005Fluids 08 00002 i006Fluids 08 00002 i007Fluids 08 00002 i008Active bubble in the membrane MF
MF1.1OilAirFluids 08 00002 i009Fluids 08 00002 i010Fluids 08 00002 i011Fluids 08 00002 i012Active bubble in the membrane MF
MF1.2OilAirFluids 08 00002 i013Fluids 08 00002 i014Fluids 08 00002 i015Fluids 08 00002 i016Active bubble in the membrane MF
MF1.3OilAirFluids 08 00002 i017Fluids 08 00002 i018Fluids 08 00002 i019Fluids 08 00002 i020Active bubble in the membrane MF
MF4.1WaterWaterFluids 08 00002 i021Fluids 08 00002 i022Fluids 08 00002 i023Fluids 08 00002 i024Bubble in the membrane MF
MF1.3OilOilFluids 08 00002 i025Fluids 08 00002 i026Fluids 08 00002 i027Fluids 08 00002 i028Jet stream formation
MF2.1WaterOilFluids 08 00002 i029Fluids 08 00002 i030Fluids 08 00002 i031Fluids 08 00002 i032Jet stream formation
Table
Table 5. Dynamics of active bubbles in the multiphase system MF-oil.
Table 5. Dynamics of active bubbles in the multiphase system MF-oil.
MFBubbles TrajectorySelf-Organization
MF1.1Without magnetic fieldFluids 08 00002 i033Fluids 08 00002 i034
Under the influence of a magnetic fieldFluids 08 00002 i035Fluids 08 00002 i036
MF1.2Without magnetic fieldFluids 08 00002 i037Fluids 08 00002 i038
Under the influence of a magnetic fieldFluids 08 00002 i039Fluids 08 00002 i040
MF1.3Without magnetic fieldFluids 08 00002 i041Fluids 08 00002 i042
Under the influence of a magnetic fieldFluids 08 00002 i043Fluids 08 00002 i044
MF1.4Without magnetic fieldFluids 08 00002 i045Fluids 08 00002 i046
Under the influence of a magnetic fieldFluids 08 00002 i047Fluids 08 00002 i048
Table
Table 6. Acceleration, velocity, and cross-sectional area of water droplet movement in the channel at different values of the current applied to the solenoid.
Table 6. Acceleration, velocity, and cross-sectional area of water droplet movement in the channel at different values of the current applied to the solenoid.
I, A00.91.8
a, mm/s274.3471.0367.58
v0, mm/s87.7290.5196.28
s, mm214.0912.3111.30
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Sokolov, E.; Kaluzhnaya, D.; Shel’deshova, E.; Ryapolov, P. Formation and Behaviour of Active Droplets and Bubbles in a Magnetic Fluid in an Inhomogeneous Magnetic Field. Fluids 2023, 8, 2. https://doi.org/10.3390/fluids8010002

AMA Style

Sokolov E, Kaluzhnaya D, Shel’deshova E, Ryapolov P. Formation and Behaviour of Active Droplets and Bubbles in a Magnetic Fluid in an Inhomogeneous Magnetic Field. Fluids. 2023; 8(1):2. https://doi.org/10.3390/fluids8010002

Chicago/Turabian Style

Sokolov, Evgeniy, Dariya Kaluzhnaya, Elena Shel’deshova, and Petr Ryapolov. 2023. "Formation and Behaviour of Active Droplets and Bubbles in a Magnetic Fluid in an Inhomogeneous Magnetic Field" Fluids 8, no. 1: 2. https://doi.org/10.3390/fluids8010002

APA Style

Sokolov, E., Kaluzhnaya, D., Shel’deshova, E., & Ryapolov, P. (2023). Formation and Behaviour of Active Droplets and Bubbles in a Magnetic Fluid in an Inhomogeneous Magnetic Field. Fluids, 8(1), 2. https://doi.org/10.3390/fluids8010002

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