Dynamics of three ferrofluid droplets in a rotating magnetic field

doi:10.1007/s10483-025-3224-7

Abstract

Abstract:

Two-dimensional (2D) direct numerical simulations on the dynamics of three identical ferrofluid droplets suspended in a non-magnetic ambient fluid under a rotating uniform magnetic field are conducted, and the motion and deformation of the three ferrofluid droplets are studied in this paper. Results show that there are four modes (i.e., the three droplets' direct coalescence (TC), the coalescence of two droplets and the subsequent planetary motion with the third droplet (CAP), the three droplets' planetary motion (TP), and the independent spin (IS)) for the three ferrofluid droplets, dependent on the magnetic Bond number $(B o m)$ and the initial distance $(d 0)$ between two of the droplets. It is found that the decrease in $d 0$ and the increase in $B o m$ can make the droplets' mode change from the IS to the planetary motion, and then turn to the CAP. Furthermore, reducing $B o m$ or $d 0$ is helpful for the droplets to become merged.

Key words: ferrofluid droplet, rotating magnetic field, capillary force

2010 MSC Number:

O352

Xinping ZHOU, Wencai XIAO, Qi ZHANG, Chunyue LIANG, Wanqiu ZHANG, Fei ZHANG. Dynamics of three ferrofluid droplets in a rotating magnetic field. Applied Mathematics and Mechanics (English Edition), 2025, 46(3): 591-600.

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Figures/Tables 7

Fig. 1

Table 1

The range or value of the main parameters"

Parameter	Value
$B o m$	1.5–4
$d 0$	2–15
$f$	0.012 5
$L a m$	75
$χ$	2
$λ$	1

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

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