Shaping of sessile liquid metal drops using high-frequency magnetic fields

An analytical model for the electromagnetic shaping of sessile liquid metal drops in high-frequency magnetic fields is presented. We deal with both an infinitely long drop and a circular drop. In each case, the arrangement of drop and inductor is symmetric. Applying the skin depth approximation reduces the Lorentz forces induced in the liquid metal drop to a magnetic pressure on the drop surface. We neglect the coupling between drop contour and magnetic field distribution. In this case, the magnetic field can be calculated analytically applying the mirror-current method. Finally, we achieve an analytical solution of the static drop contours with the help of Green's functions. The theory is applied to three problems: (i) squeezing a drop while conserving its volume, (ii) drops with a fixed contact line, (iii) pumping up of drops. The results demonstrate the suitability of high-frequency magnetic fields for the shaping of liquid metals.