Two-dimensional numerical investigation on the dynamics of ligament formation by Faraday instability

Ligament formation from the surface of a horizontal liquid layer subject to a vertical vibration (Faraday instability) is a crucial part of the atomization process because it is the transition phase for droplet generation. Based on the numerical solutions of the two-dimensional incompressible Euler equations for a prototype Faraday instability flow, we explored physically how a liquid ligament that is dynamically free from the vibrating liquid layer and behaves like a jet can be produced. According to linear theory, the suction of liquid from the trough portion to the crest portion creates an amplified crest. The amplified crest is always pulled back to the liquid layer in linear theory, no matter how largely the surface deforms; thus, a dynamically freed ligament never forms. However, under nonlinear conditions produced by large surface deformation, the impinging liquid flow from the trough portion enhances the pressure at the high crest (ligament) root. This pressure enhancement has two major effects. First, it reduces the amount of liquid sucked from the trough portion, which abates the increase in the crest height compared with that associated with linear theory. Second, it forms a local maximum pressure at the crest root; in this case, the ligament above this location becomes dynamically free from the motion of the bottom substrate in the laboratory reference frame. Liquid elements continuously enter the dynamically freed liquid region, producing a slender ligament from the liquid layer.