Disertācijas (FMOF) / Doctoral Theses

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Browsing Disertācijas (FMOF) / Doctoral Theses by Subject "Boundary element methods"

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    Magnetic fluid droplets in rotating fields: theory, experiments and simulations
    (Sorbonne University, 2022-10-14) Stikuts, Andris Pāvils; Cēbers, Andrejs; PERZYNSKI, Régine
    Due to a combination of responsiveness to external magnetic fields and their deformability, magnetic fluid droplets make an interesting material that has found many applications in microfluidics. This work explores the dynamics of such droplets in a rotating magnetic field. The droplets are examined using multiple approaches – theoretically, experimentally and using simulations. When the rotating magnetic field is weak and the droplet’s deformation is small, the droplet’s motion is calculated analytically. It is found that the droplet’s shape evolution is governed by a system of three nonlinear differential equations. In the small deformation limit, the motion of the droplet is qualitatively governed by a parameter proportional to the capillary number – the ratio of viscous drag to surface tension forces. The experimental observation of magnetic droplets obtained by the separation of a ferrofluid in two liquid phases, qualitatively follows the analytic solution, however, there is a significant quantitative discrepancy. A simulation based on the boundary element methods is developed to calculate the dynamics of the droplets up to medium deformations. It is found that good mesh maintenance is required to produce accurate simulation results. A phase diagram is produced, which shows the droplet dynamics depending on the rotating field strength and frequency. Finally, the collective dynamics of the droplets is examined experimentally. For a certain magnetic field strength and frequency, the droplets form rotating ensembles with a triangular order – two dimensional rotating crystals. The dynamics of small ensembles is reproduced by treating the droplets as point torques.