Numerical study on the nonlinear dynamics of the ligament formation and its breakup of a spherical droplet induced by Faraday instability

Faraday instability is an important mechanism for the secondary atomization of a spherical liquid droplet. In this paper, a numerical simulation model was established to study the nonlinear dynamics of the ligament formation and its breakup of a spherical droplet caused by Faraday instability. A set of simulations were firstly carried out to find out the optimum grid size to accurately capture the gas-liquid interface. Then the simulation model was validated by comparing the simulated results with the experimental ones under the same conditions. Based on the simulation model built in this paper, a series of simulations were conducted to study the ligament formation mechanism of a spherical droplet placed on a vertically vibrating plate, which provides a sinusoidal inertial acceleration to the droplet. By analyzing the microscopic information such as the pressure field, velocity field and surface wave displacement, it was found that the ligament formation and breakup were actually the results of the interaction of inertial force and surface tension. Ligament formation and breakup can also be seen as a process of absorbing energy, storing energy, converting energy, delivering energy and erupting. When the inertial force does positive work on a certain surface wave, the kinetic energy of this surface wave increases. Under the action of surface tension, the kinetic energy is transformed into pressure potential energy. After a while, the pressure potential energy is converted back to kinetic energy, combined with the positive work imposed on the surface wave by inertial force. The kinetic energy of the surface wave further increases and part of the kinetic energy is passed to the adjacent surface waves. The adjacent surface waves have the similar process of energy conversion and transmission. After several cycles, more and more energy is absorbed by the surface wave from the inertial force, and the displacement amplitude of the surface wave becomes larger and larger. Finally, a liquid ligament is formed from the droplet surface. When the velocity difference between the top and bottom of the ligament is large enough, the ligament breaks and atomization occurs.