Investigation of the eccentricity of a drop of magnetic fluid floating in a non-magnetic liquid under the influence of a magnetic field

Purpose. To investigate in detail the hydrodynamic parameters of a magnetic fluid droplet with a variable volume concentration of the magnetic phase, in a suspended state within a volume of non-magnetic liquid, under the influence of an external magnetic field with varying strength.

Methods. The experimental part of the work was carried out using an original laboratory setup with standard measuring equipment. To measure the magnetic field strength, a standard TPU-01 teslameter equipped with a precision Halleffect sensor was used, ensuring high accuracy of field registration in the working area. In addition to direct measurements, a computer simulation of the spatial configuration of the magnetic field was performed using the FEMM software package integrated into the MATLAB environment; this allowed for a detailed analysis of the spatial distribution of the magnetic field and its visualization. The processing of video data recording the dynamics of deforming magnetic fluid droplets in the surrounding non-magnetic liquid was carried out using specialized image analysis software, Digimizer, which made it possible to track changes in the geometric parameters of the droplet over time with high accuracy. The obtained experimental data were interpreted using fundamental principles of condensed matter physics and the laws of classical and magnetic hydrodynamics of viscous fluids.

Results. The results of experimental studies were obtained, which are consistent with the numerical simulation results describing the shape change of a ferrofluid droplet suspended in a non-magnetic medium, as well as its eccentricity, as functions of the magnetic phase concentration in the ferrofluid and the strength of the magnetic field generated by the solenoid. The obtained numerical simulation results and experimental data are in good agreement with each other.

Conclusion. The control of the behavior of dispersed droplets of magnetic fluid in a non-magnetic medium using a magnetic field creates the foundation for new technologies in microfluidics and "soft" robotics.

1. Oehlsen O., Cervantes-Ramírez S. I., Cervantes-Avilés P., Medina-Velo I. A. Approaches on ferrofluid synthesis and applications: Current status and future perspectives. ACS omega. 2022;7(4):31343150. https://doi.org/10.1021/acsomega.1c05631.

2. Ryapolov P., Vasilyeva A., Kalyuzhnaya D., Churaev A., Sokolov, Shel’deshova E.E. Magnetic fluids: the interaction between the microstructure, macroscopic properties, and dynamics under different combinations of external influences. Nanomaterials. 2024;(14)2:222. https://doi.org/10.3390/nano14020222.

3. Mehta M. Bhandari A. Advancement in biomedical applications of ferrofluids. Journal of the Brazilian Society of Mechanical Sciences and Engineering. 2025;(47):10:490. https://doi.org/10.1007/S40430025-05806-4.

4. Zhu G., Wu S.-H., Zheng S.Z., Li L., Nguyen N.T. Investigation of ferrofluid sessile droplet tensile deformation in a uniform magnetic field. Magnetochemistry. 2023;9(10):215. https://doi.org/10.3390/magnetochemistry9100215.

5. Elkalla E., Khizar S., Ait-Touchente Z., Lebaz N. Synthesis and characterization of silica-coated oil-in-water (O/W) magnetic emulsion. Emergent Materials. 2023;6(6):2027-2039. https://doi.org/10.1007/s42247-023-00563-3.

6. Vinod S., Philip J. Field induced deformation of sessile ferrofluid droplets: effect of particle size distribution on magnetowetting. Journal of Magnetism and Magnetic Materials. 2018;466:295-300. https://doi.org/10.1016/j.jmmm.2018.06.074.

7. Nguyen N.T., Beyzavi A., Ng K.M., Huang X. Kinematics and deformation of ferrofluid droplets under magnetic actuation. Microfluidics and Nanofluidics. 2007;3(5):571-579.

8. Zhu G.P., Wang Q.Y., Ma Z.K., Wu S.H., Guo Y.P. Droplet manipulation under a magnetic field: A review. Biosensors. 2022;12(3):156. https://doi.org/10.3390/bios12030156.

9. Capobianchi P., Lappa M., Oliveira M. S. N. Deformation of a ferrofluid droplet in a simple shear flow under the effect of a constant magnetic field. Computers & Fluids. 2018;(173):313-323. https://doi.org/10.1016/j.compfluid.2018.06.024.

10. Kichatov B., Sudakov V., Kalyuzhnaya D., Korshunov A., Ryapolov P. Active droplet generation in flow-focusing microfluidics under influence of transverse magnetic field. Lab on a Chip. 2025;25(23): 6306-6313. https://doi.org/10.1039/D5LC00805K.

11. Ho P.C., Yap Y.F., Nguyen N.T., Chai J.C.Thermally mediated droplet formation at a microfluidic T-junction. Micro and Nanosystems. 2011;3(1):65-75. https://doi.org/10.2174/1876402911103010065.

12. Lazarus N., Cortazar J. Stretchable magnetic materials and devices for soft robotics. MRS Communications. 2025;15(6):1362-1377. https://doi.org/10.1557/s43579-025-00811-z.

13. Gao Q.H., Zhang W.M., Zou H.X., Li W.B., Yan H., Peng Z.K. [et al.] Label-free manipulation via the magneto-Archimedes effect: fundamentals, methodology and applications. Materials Horizons. 2019;6(7):1359-1379. https://doi.org/10.1039/C8MH01616J.

14. Ince Ö.D., Tekin H.C. MagSity platform: a hybrid magnetic levitation-based lensless holographic microscope platform for liquid density and viscosity measurements. Lab on a Chip. 2025;25(15). https://doi.org/10.1039/D5LC00144G.

15. Sokolov E.A., Kalyuzhnaya D.A., Pribylov A.A., Politov R.E., Ryapolov P.A. Dynamics of floating droplets of a magnetic liquid in glycerol in a flat channel under the influence of a magnetic field. Izvestiya Rossiiskoi akademii nauk. Seriya fizicheskaya = Bulletin of the Russian Academy of Sciences: Physics. 2024;88(10):1636-1641. https://doi.org/10.1134/S1062873824707967.