Rim dynamics and instability of a curved liquid sheet formed by jet impinging on a circular plane

The free liquid sheet formed by jet impingement often has a certain bending, and this paper focuses on the influence of this bending on the rim dynamics and instability. The derivations of the rim retraction and the flow trajectory of the curved liquid sheet show that the length of the flow trajectory reaching the equator is the same as the Taylor–Culick radius representing the rim retraction equilibrium. It is inferred that the stable radius corresponding to the curved trajectory must be less than the Taylor–Culick radius, that is, a curved liquid sheet cannot reach the stable position by the rim retraction equilibrium alone. Experimental results confirm that the greater the degree of liquid sheet bending, the farther the stable radius from the Taylor–Culick radius. In addition to the rim retraction, the rim can remain in a stable position with the help of the fingerlike cusp, formed due to instability, deflecting liquid momentum. The dispersion equation of rim instability is derived to obtain the maximum growth rate of disturbance and corresponding wavelength. The surface tension is the main driving force of rim instability, and the liquid flow from the liquid sheet into the rim inhibits the rim instability. With increasing We, the decreasing local liquid sheet thickness increases the growth rate of disturbance and decreases the instability wavelength, which causes the rim to destabilize at a smaller rim radius, resulting in the corresponding decrease in droplet radius. The experimental results agree well with the theoretical prediction.