Experimental study and mathematical modelling of self-oscillation at the electrode-magnetic fluid interface in an electric field

Keywords: Magnetic fluid, Interface, Near-electrode layer, Electric field, Self-oscillation, Mathematical model


The article describes a mathematical model of self-oscillation in the form of a boundary value problem for a nonlinear system of partial differential equations, with a numerical solution. The numerical results were compared to the experimental data to confirm the adequacy of the model. The model uses the classical system of differential equations of material balance, Nernst-Planck and Poisson equations without simplifications or fitting parameters. The aim of the article was to study the parameters of concentration self-oscillation in a layer of the dispersed phase particles of magnetic fluid at the interface with an electrode in an electric field. For this purpose, we developed a mathematical model, the consistency of which was
confirmed by the corresponding physical mechanism.
As a result of numerical experiments, we found the critical value of the potential jump after which self-oscillation began. We also determined the oscillation growth period and other characteristics of the process. We developed software called AutoWave01 with an intuitive user interface and advanced functionality for the study of self-oscillation in a thin layer of magnetic colloid.


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Author Biographies

Vladimir S. Chekanov, North-Caucasus Federal University, 1 Pushkina ul., Stavropol 355017, Russian Federation

PhD in Technical Sciences,
Associate Professor at the Department of Information
Systems and Technologies, North-Caucasus Federal
University, Stavropol, Russian Federation; e-mail:

Evgeniya V. Kirillova, RheinMain University of Applied Sciences 18 Kurt-Schumacher-Ring, Wiesbaden 65197, Germany

PhD in Physics and
Mathematics, Professor at the RheinMain University
of Applied Sciences in Wiesbaden, Germany; e-mail:

Anna V. Kovalenko, Kuban State University, 149 Stavropolskaya ul., Krasnodar 350040, Russian Federation

DSc in Physics and Mathematics,
Associate Professor, Head of the Department of Data
Analysis and Artificial Intelligence, Kuban State
University, Krasnodar, Russian Federation; e-mail:

Elena N. Diskaeva, MIREA – Russian Technological University, 8 Kulakova pr., Stavropol 355000, Russian Federation

PhD in Physics and Mathematics,
Associate Professor at the Department of Industrial
Technologies, Branch of “MIREA – Russian
Technological University” in Stavropol, Stavropol,
Russian Federation; e-mail: diskaevapes@mail.ru


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How to Cite
Chekanov, V. S., Kirillova, E. V., Kovalenko, A. V., & Diskaeva, E. N. (2021). Experimental study and mathematical modelling of self-oscillation at the electrode-magnetic fluid interface in an electric field. Condensed Matter and Interphases, 23(4), 626-636. https://doi.org/10.17308/kcmf.2021.23/3683
Original articles