Vibration and Jumping of Ferrofluid Marbles under an Initial Magnetic Perturbation

Liquid marbles are being promoted as a replacement for conventional droplets in digital microfluidics. Liquid marbles can be remotely controlled by an external magnetic field if ferrofluid is utilized as their liquid cores. In this study, the vibration and jumping of a ferrofluid marble is experimentally and theoretically investigated. An external magnetic field is utilized to induce deformation in a liquid marble and an increase in its surface energy. As the magnetic field is switched off, the stored surface energy converts to gravitational potential and kinetic energies until it is dissipated. An equivalent linear mass-spring-damper system is used to study the vibration of the liquid marble, and the effect of its volume and initial magnetic stimulus on the vibrational characteristics, such as natural frequency, damping ratio, and deformation of the liquid marble, is experimentally examined. By analyzing these oscillations, the effective surface tension of the liquid marble is evaluated. Also, a novel theoretical model is proposed to obtain the damping ratio of the liquid marble, suggesting a new tool for the measurement of liquid viscosity. Interestingly, it is observed that the liquid marble jumps from the surface in the case of high initial deformation. Based on conservation law of energy, a theoretical model for predicting the liquid marbles jumping height and the boundary between jumping and non-jumping zones in terms of nondimensional numbers, namely, magnetic and gravitational Bond numbers and Ohnesorge number, is proposed with an acceptable error compared to experimental data.