Collision dynamics of binary liquid metal droplets under horizontal magnetic field

The present paper aims to investigate the magnetohydrodynamic effects on binary liquid metal droplet collision in the presence of horizontal magnetic field ($0<B<1.5$  T) normal to collision velocity. Here we observe that for small magnetic interaction parameter $N$ ($<0.4$), one type of collision regimes, reflexive separation, could be obviously facilitated by magnetic field in comparison with no magnetic cases. For collision regimes except reflexive separation, we present a correlation of $N$ = $f(B/B_0,\text{We}/48)$ as well as a $N-\text{We}/48$ map that could help to interpret why little influence of magnetic field on them and predict possible remarkable influences when $B$ is larger than a critical value of 4 T. Furthermore, we draw the possible geometrical morphology of droplets after collision based on our understanding of the physical process of liquid metal droplets collision under the horizontal magnetic field.

Figure 1

Schematic view of the collision between two droplets under horizontal magnetic field.

Figure 2

(a) Sketch of the experimental setup. (b) Photo of liquid reservoir. (c) Top view of image-forming principle by ${45}^{\circ }$ plane mirror.

Figure 3

Schematic of the speculation of effects of magnetic field on binary collision from droplet impacting onto solid plate: (a) a single droplet impact onto a plate under vertical magnetic field; (b) a single droplet impact onto a plate under horizontal magnetic field; (c), (d) binary droplet collision under horizontal magnetic field: (c) the direction of magnetic field is parallel with relative velocity of two droplets, (d) the direction of magnetic field is perpendicular to relative velocity of two droplets.

Figure 4

The snapshots of different colliding processes for $B$ = 1.5 T. Every sequence is a specific pair of droplets cut out from continuous shots. (a) Coalescence, We = 12.84, $X$ = 0.1787, $D$ = 424 $\mu \mathrm{m}, U$ = 1.593 m/s; (b) reflexive separation, We = 50.13, $X$ = 0.0088, $D$ = 428 $\mu \mathrm{m}, U$ = 3.132 m/s; (c) coalescence after finger, We = 110.90, $X$ = 0.0996, $D$ = 436 $\mu \mathrm{m}, U$ = 4.615 m/s; (d) separation of finger, We = 121.73, $X$ = 0.0579, $D$ = 446 $\mu \mathrm{m}, U$ = 4.785 m/s; (e) break-up after finger, We = 187.08, $X$ = 0.0431, $D$ = 425 $\mu \mathrm{m}, U$ = 6.0724 m/s; and (f) stretching separation, We = 55.69, $X$ = 0.8565, $D$ = 403 $\mu \mathrm{m}, U$ = 4.8951 m/s. The interval between two snapshots is $1/18000$ s. The red rectangular represents the 0.8 $\mathrm{m}\mathrm{s}$ moment after impact, which is the characteristic time of obvious difference for reflexive separation with magnetic field. The detailed information on the characteristic time of 0.8 $\mathrm{m}\mathrm{s}$ is discussed in Sec. 3.

Figure 5

Maps of regimes for binary collision of same-sized GaInSn droplets with and without magnetic field. The droplet diameter ranges from 336 to 418 $\mu \mathrm{m}$. The relative velocity is varied from 1 to 7 m/s. (a) B = 0 T and (b) B = 1.5 T.

Figure 6

Onset: We numbers of reflexive separation for different fluids (by adding liquid metal GaInSn, mercury, and alumina droplets) in variance with Oh numbers.

Figure 7

(a) Collision outcome of reflexive separation for same-sized GaInSn droplets under imposed magnetic field of 1.3 T. We = 60.25, $X$ = 0.0186, $D$ = 414 $\mu \mathrm{m}, U$ = 3.494 m/s. (b) Schematic of reflexive separation changes over time. (c) Collision outcome of reflexive separation for same-sized GaInSn droplets without magnetic field. We = 61.77, $X$ = 0.0094, $D$ = 427 $\mu \mathrm{m}, U$ = 3.481 m/s. (d) Collision outcome of coalescence for same-sized GaInSn droplets without magnetic field. We = 63.41, $X$ = 0.0790, $D$ = 415 $\mu \mathrm{m}, U$ = 3.579 m/s. For (a), (c), and (d), the interval between two snapshots is $3\times 1/18000$ s.

Figure 8

The spreading diameters $D_y$ and lateral length $D_x$ normalized by droplet diameter $D$, and $U_x, U_y$ normalized by relative velocity $U$ vary with time $t$.

Figure 9

The spreading diameters $D_y$ and lateral length $D_x$ normalized by droplet diameter $D$ varies with time $t$ for $\text{We}\approx 50$.

Figure 10

(a) The dimensionless maximum spreading diameter ${\xi }_y$ varies with magnetic parameter number $N$ for $\text{We}\approx 50$. (b) ${\xi }_y$ varies with We for B = 0.5 T, 1.0 T, and 1.5 T, and the theoretical and fitting maximum dimensionless spreading diameter ${\xi }_y$ in variance with We number are, respectively, $\text{We}=24{{\xi }_y}^2+64\frac{1}{{\xi }_y}-96$ and ${\xi }_y=0.6{\text{We}}^{1/3}$, see details in Ref. [22].

Figure 11

(a) The maximum reflexive stretching length $D_{x\left(\text{max}\right)}$ normalized by droplet diameter $D, {\xi }_x$, varies with magnetic interaction parameter $N$ for $\text{We}\approx 50$. (b) The maximum reflexive stretching length $D_{x\left(\text{max}\right)}$ normalized by the vertical length at this moment $D_{y\_m}, \zeta$, varies with $N$ for $\text{We}\approx 50$.

Figure 12

(a) Magnetic parameter number $N$ in variance with $\text{We}/48$ for near head-on collisions. (b) Magnetic parameter number $N$ in variance with ${(B/B_{\text{critical}})}^2/{(\text{We}/48)}^{0.5}$ for near head-on collisions, in which $B_{\text{critical}}$ = 4 T.

Figure 13

Possible collisional process for large intensity of horizontal magnetic field ($B>$ 4 T) (the grey dotted squares in lateral view are the cross-sectional drawing of grey dotted lines in front view).