Maximum spreading of a liquid metal droplet under a horizontal magnetic field

We conduct a numerical investigation on the spreading characteristics of a liquid metal droplet impacting onto a solid substrate, specifically under the influence of a horizontal magnetic field. In such circumstances, we propose a theoretical model to predict the maximum spreading area of the droplet. In the absence of a magnetic field, available models attempting to predict the maximum spreading of an impacting droplet based on the principle of energy conservation have been proven to be unsuitable for our current context. We find that this inadequacy arises from the notably high surface tension exhibited by the liquid metal. In response, we have developed a new model that evaluates the residual kinetic energy and gives a more precise estimation of the spreading time. Our model demonstrates a remarkable congruence with our experimental and numerical results. Subsequently, we extend our inquiry to encompass the influence of the horizontal magnetic field on the droplet's spreading characteristics. We identify an anisotropic spreading behavior attributed to the nonaxisymmetric distribution of the Lorentz force. Notably, we propose a theoretical model for predicting the maximum spreading in this magnetic field scenario by incorporating the work of Lorentz force into the energy balance equation. The predictions exhibit excellent agreement with our numerical results, even if the impacting conditions are varied in a large extent of parameter space. Furthermore, we generalize this model to situations involving a vertical magnetic field, recognizing that the residual kinetic energy is no longer independent of magnetic field strength.