# Rotation of Liquid Metal Droplets Solely Driven by the Action of Magnetic Fields
## 3 Results and Discussions  
We established an actuating platform to examine the hypothesis and investigate the self-rotational behaviors of the droplet (Figure 1a). Figure 1c shows the self-rotation of an EGaIn droplet submerged in 0.5 mol/L NaOH solution induced by the magnetic field (also see Video S1); the measured magnetic flux density was \(\sim\)1 kGs at the center point between the magnets, and we set the DC motor speed to 420 RPM. Then, the EGaIn droplet self-rotated following the same direction of rotation as the magnets (counterclockwise) with a speed of \(\sim\)100 RPM, which aligns with our analysis given in Figure 1b. Figure 1: Self-rotation behavior of a liquid metal droplet (LMD). (**a**) Schematic of the self-rotation inducing setup. (**b**) Forces schematic of the equivalent coils in an EGaIn droplet; the magnetic field directions are indicated by the blue arrows, the magnetic field rotating direction (with a velocity of \(V_{m}\)) is indicated by the green arrow, the self-rotation direction of the EGaIn droplet (with a velocity of \(V_{d}\)) is indicated by the red arrow, and the forces experienced on the equivalent coils are indicated by the black arrows. (**c**) Continuous captures of the self-rotation of an EGaIn droplet (volume of 0.08 mL). On the basis of successfully demonstrating of magnetic field driven self-rotation of EGaIn droplet, we carried out a set of experiments to ascertain the performance of self-rotation. We found that motor speed, the LMDs size, as well as the NaOH solution concentration are the three main factors that affect the self-rotational speed. In Figure 2a, we can see that the self-rotational speed increases along with the increase of the DC motor rotational speed since larger rates of magnetic flux change d\(\varphi\) can be induced by higher motor speeds. A larger rate of magnetic flux change further induces a larger eddy current which eventually converts into a greater \(\mathbf{M_{e}}\) (see Equation 2). We also studied the influence of the magnetic flux density \(\mathbf{B}\) on the self-rotational performance, as shown in Figure 2a. Obviously, a higher \(\mathbf{B}\) can induce a larger torque and lead to a larger self-rotational speed. Figure 2b shows that the self-rotational speed increases along with the increase of the size of the EGaIn droplets until the droplet volume reaches \(\sim\)0.06 mL, and then the speed gradually decreases and eventually remains stable. This is probably due to that, in a larger droplet, the increasing \(\mathbf{S}\) and decreasing \(R_{e}\) enlarge the driving force. When the volume of the EGaIn droplets is larger than 0.06 mL, the friction between the droplet and the sidewall may give a negative effect on the rotational speed of the droplet which has been elucidated by repeating the experiment with a bigger tube, as discussed in Supporting Information S1. As the rotational speed decreases, the relative rotational speed of the droplet and the magnetic field increases (that is, d\(\varphi\) increases), which then can cause the increase of \(I\), the driven force, and the rotational speed. Next, increasing the rotational speed reduces the relative speed, and finally, the driving force and resistance are balanced, which is manifested in the fact that the rotation speed was basically stable during our experiments. Moreover, the depth of EGaIn droplet immersion in the NaOH solution (represented by the percentage of the height of the droplet immersed) also influences the speed of rotation (Figure 2b). For smaller droplets (<0.06 mL), the difference in rotational speed is not obvious for different immersion depths. However, for droplets larger than 0.06 mL, a larger immersion depth leads to a higher speed of rotation. This is probably due to the fact that despite the increase in viscous friction for larger immersion depths, the solid oxide layer formed on the EGaIn droplet surface can be efficiently removed by NaOH solution, thus a slip layer between the droplet and the container wall is formed.