Dynamical pattern formation in a low-concentration magnetorheological fluid under two orthogonal sinusoidal fields

•A weighted average of the time-dependent Mason number is proposed.•The self-propelling clusters appear when a vertical rotating magnetic field is applied.•The largest average chain lengths are reached when frequencies are multiples one another.•Rotating and unidirectional alternating fields produce the largest average chain length values.

The dynamical pattern formation of clusters of magnetic particles in a low-concentration magnetorheological fluid, under the influence of a superposition of two perpendicular sinusoidal fields, is studied experimentally. By varying the frequency and phase shift of the perpendicular fields, this configuration enables us to experimentally analyze a wide range of field configurations, including the case of a pure rotating field and the case of an oscillating unidirectional field. The fields are applied parallel to the horizontal plane where the fluid lies or in the vertical plane. For fields applied in the horizontal plane, we observed that, when the ratio of the frequencies increases, the average cluster size exhibits a kind of periodic resonances. When the phase shift between the fields is varied, the average chain length reaches maximal values for the cases of the rotating field and the unidirectional case. We analyze and discuss these results in terms of a weighted average of the time-dependent Mason number. In the case of a rotating field on the vertical plane, we also observe that the competition between the magnetic and the viscous forces determines the average cluster size. We show that this configuration generates a series of physically meaningful self-organization of clusters and transport phenomena.

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