# Rotation of Liquid Metal Droplets Solely Driven by the Action of Magnetic Fields
## 1 Introduction  
\"Liquid metal\" such as gallium and its several alloys exhibit a liquid state at room temperature [1; 2; 3]. Droplets of such liquid metal have shown to be platforms for applications such as stretchable and reconfigurable electronics [3; 4; 5; 6], microfluidics actuators [2; 7; 8], as well as forming three-dimensional structures [9; 10; 11]. Liquid metal droplets (LMDs) have demonstrated many unique properties, for instance, large surface tension, favorable thermal and electrical conductivity, strong stability, and extremely excellent biosafety compared with mercury [12; 13]. Over the past few years, benefitting from the flexibility and operability of liquid metal surfaces, investigations of formation, actuation, and application of their droplets have gained momentum [2; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. As has been recently reported, LMDs can act as self-fueled motors, paving the way without human intervention [14; 23]; also, a LMD can be used to drive a wheeled robot by changing its center of gravity under electrical fields [22]. Moreover, a potential gradient was applied to explore inducing the Marangoni flow along the surface ofLMDs and making microactuators in microfluidics [2; 24; 25; 26; 27]. Further studies have demonstrated that LMDs coating modest nanoparticles can be propelled by bubbles generated through photochemical reactions [28; 29; 30].  
Chaotic advection is the key mechanism for enabling applications such as heat transfer, fluid mixing, and chemical reaction improvement [24; 31; 32; 33; 34; 35], in particular, in some areas including microfluidic systems, chemical and biological transport, etc., smooth and steady methods for inducing chaotic advection are needed, and inexpensive and simple systems are urgently required [36; 37; 38; 39]. Self-rotation of LMDs with negligible solubility in most solvents may be a promising candidate for providing a solution [7]. Nevertheless, to the best knowledge of the authors, there is still a lack of investigations focused on the self-rotational motion of LMDs.  
Self-rotation of LMDs has the potential to be widely used in fluid cooling and mixing. Therefore, we have been motivated to explore novel methods for inducing self-rotation of LMDs that are smooth, simple, steady, and, especially, that do not introduce undesired violent chemical reactions. According to our previous report, we introduced a simple and violent chemical reaction-free method in which we utilized Lorenz force induced by magnetic fields to control the locomotion of LMDs [38]. Inspired by this, we report here the self-rotation of EGaIn droplets (consisting of 75% gallium and 25% indium) which are solely driven by magnetic fields without mixing or coating ferromagnetic particles. The relative motion of the magnetic fields and LMDs generates an eddy current in the droplet and further induces the Lorenz force to actuate the self-rotation of the droplet. The theory behind the method was developed and the experiments conducted to validate this approach. Moreover, we demonstrate applications of accelerating cooling and mixing liquids based on the self-rotational LMDs.