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

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 wasconfirmed 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.