Self-Sustained Coalescence–Breakup Cycles of Ferrodrops under a Magnetic Field

Abstract

The self-sustained coalescence–breakup cycles of ferrodrops were investigated for the first time by a high-speed camera under various magnetic fields. Under an axial magnetic field, the upper ferrodrop would deform into a conic shape before coalescing with the bottom ferropeak. Within 0.2 ms after coalescence, the minimum width of the expanding neck obeys a power-law relationship with time, while the exponents increase with the magnetic field and deviate with a decreasing trend in the later coalescence. The cone angle of the upper ferrodrop before coalescence gradually decreases while it increases before breakup with the magnetic field. A critical magnetic field around 35 mT was reported, above which the ferrofluid column undergoes the periodic phenomenon of coalescence and breakup. The frequency for the whole coalescence–breakup cycle increases exponentially with the applied magnetic field. A simplified force balance allows capturing the periodic mechanism involved in this driven harmonic oscillator.

Experimental Investigation on the Dynamics of On-Demand Ferrofluid Drop Formation under a Pulse-Width-Modulated Nonuniform Magnetic Field

“…Utilizing the magnetic force to precisely control the ferrofluid droplet formation and breakup in microfluidics has been widely studied in the past decade. − Tan et al studied the formation process of a ferrofluid droplet in a T-junction under the effect of a permanent magnet. They demonstrated that if the magnet was placed downstream of the T-junction, the diameter of the droplet would be reduced.…”

Coalescence of a Ferrofluid Drop at Its Bulk Surface with or without a Magnetic Field

“…A proper pulsation ω 0 = σ ρ V can be deduced for this oscillator and related to a frequency ω 0 = 2π f . Both the oscillating frequency f and the magnetic flux density B were conversely correlated to the representative volume of the ferrodrop by means of an exponential function: f = 0.58 – 0.61 exp(–0.004 B ) . The oscillating frequency increases exponentially with the magnetic flux density, and the maximum coalescing width would exhibit an exponential decrease with the magnetic flux density: a faster oscillation does not give a sufficient time for the expansion of the coalescing width W .…”

“…By adjusting the fine-tuning platform, the magnetic flux density exerted on the ferrofluid becomes stronger when the magnet moves vertically upward toward the nozzle. The variation of the magnetic field B in the vertical direction z from the top surface of the magnet was reported in our previous study . The ferrofluid would be divided into more ferrofluid peaks; thus, the volume of each peak decreases and the height becomes lower.…”

“…The variation of the magnetic field B in the vertical direction z from the top surface of the magnet was reported in our previous study. 33 The ferrofluid would be divided into more ferrofluid peaks; thus, the volume of each peak decreases and the height becomes lower. As shown in Figure 3, there are 20, 22, and 28 ferrofluid peaks at the edge of the container, corresponding to the magnetic flux density of 73.10, 85.54, and 95.25 mT, respectively.…”

“…According to our previous work, the ferrofluid drop would exhibit self-sustained coalescence−breakup cycles with an adjustable frequency by the magnetic field. 33 Whether the initial coalescing width of ferrofluid drop at its bulk surface displays a similar trend as in the Newtonian and non-Newtonian liquids still remains unknown and requires further investigation. In the present study, the coalescence dynamics was privileged, aiming at investigating in a particular possible scaling law of coalescence for a pendant ferrofluid drop at its bulk surface with and without an external magnetic field.…”