A numerical study of the evolution of quasi-two-dimensional magnetic fluid shapes

A. Cebers¹ - I. Drikis²

¹ Institute of Physics, Latvian Academy of Sciences, Salaspils-1, LV-2169, Latvia
² Department of Physics, University of Latvia, Riga, LV-1586, Latvia

Abstract
Fingering instabilities of magnetic fluid droplets in Hele-Shaw cells are considered. The hydrodynamics of this process is studied numerically using the boundary integral equation method. The numerical simulation results of magnetic fluid droplet long-time behaviour are presented. Attention has been focused on a n-fold vertex splitting instability. Competition between magnetic and surface energies at transient stages is illustrated by calculations of characteristic energies during the evolution of a droplet. Similarity of the figures of equilibrium obtained with observed in 2D soap films is emphasized. An extremely slow rearrangement of the Steiner trees to the configurations with simpler topologies is confirmed. From the numerical simulation results it is concluded that the reason why rupture of the magnetic fluid stripes due to the overextension instability was never observed in experiment could be connected with its nonlinear damping due to the development of rows of alternating fingers. Tabl. 5, figs 7, refs 16.