Theoretical analysis on the predominant surface wave mode for the vibration induced atomization

The quality of fuel-gas mixing in the cylinder of the internal combustion engine is to a large extent determined by the sizes of sub-droplets formed from the secondary atomization. Because the motion of airflow in the cylinder is turbulent, with strong pulsation and transience, it is of great importance to understand the intrinsic connection between the time-independent force and sub-droplet size. Both experimental and theoretical studies were done in this paper to illustrate the problem. In the experimental part, the deformation and fragmentation process of a semi-sphere droplet under sinusoidal inertial forces were recorded by high-speed camera. It is found that the average diameter of sub-droplets satisfies Lang's equation after analyzing the processed experimental data. Then, with the incompressible and inviscid assumptions, a linear analysis on Faraday instability was conducted theoretically on a sphere, which can explain why the experimental results could satisfy Lang's equation and specify the limitation of Lang's equation.