On the spreading of impacting drops under the influence of a vertical magnetic field

A theoretical model is developed to predict the maximum spreading of liquid metal drops when impacting onto dry surfaces under the influence of a vertical magnetic field. This model, which is constructed based on the energy conversion principle, agrees very well with the numerical results, covering a wide range of impact speeds, contact angles and magnetic strengths. When there is no magnetic field, we found that the maximum spreading factor can be predicted well by an interpolating scheme between the viscous and capillary effects, as proposed by Laan et al. (Phys. Rev. Appl., vol. 2 (4), 2014, 044018). However, when gradually increasing the magnetic field strength, the induced Lorentz forces are dominant over the viscous and capillary forces, taking the spreading behaviour into the 'Joule regime', where the Joule dissipation is significant. For most situations of practical interest, namely when the strength of the magnetic field is less than 3 T, all three energy conversion routes are important. Therefore, we determine the correct scaling behaviours for the magnetic influence by first equating the loss of kinetic energy to the Joule dissipation in the Joule regime, then by interpolating it with the viscous dissipation and the capillary effects, which allows for a universal rescaling. By plotting the numerical results against the theoretical model, all the results can be rescaled onto a single curve regardless of the materials of the liquid metals or the contact angles of the surfaces, proving that our theoretical model is correct in predicting the maximum spreading factor by constructing a balanced formula between kinetic energy, capillary energy, viscous dissipation energy and Joule dissipation energy.