Experimental investigation on the atomization of a spherical droplet induced by Faraday instability

Faraday instability plays an important role to realize liquid atomization which has been widely applied in various fields. The spherical Faraday instability has different characteristics from the planar one. It is of great importance to understand the fundamental mechanisms of the surface deformation evolution and atomization of a spherical droplet induced by Faraday instability. In this paper, we first experimentally recorded the deformation and fragmentation process of a spherical droplet on a vertically vibrated plate with high speed camera. The results showed that the zonal, meridional and approximately circular standing waves in proper order exist on the surface of the spherical droplet with the increase of excitation amplitude. When Bo<3.0, the modes of low (zonal) and high (meridional) order m of the spherical harmonic occur more easily, and as Bo is increased, the order m becomes closer to the intermediate value of spherical mode number l. The mechanism of droplet atomization is that a spike forms first on the droplet surface due to the impingement of the liquid flowing from the neighboring trough portions, and then a neck appears because of the velocity difference between the head and bottom of the spike, and the velocity difference determines whether the head liquid can form a sub-droplet ejected from the surface of the parent droplet. The Mathieu equation was derived by a linear theoretical analysis with inviscid and incompressible assumptions for the spherical Faraday instability, in which the parameters have different definitions from its planar counterpart. In the instability diagram, the iso-curves of larger linear growth rate deviate further from the ordinate axis and finally disappear. It is also validated that Lang's equation is applicable to the spherical Faraday instability in low frequency.