Circular hydraulic jump on finite surfaces with capillary limit

A round liquid jet impinging on a circular disc with free edge generates a thin liquid film in the center surrounded by a thick film. For low flow rates, the thick film is bounded by a stable rim around the disc edge and flows off only from one spot at the edge. The outer Froude number remains constant for varied flow rates and disc sizes but changes with the surface tension of the fluid. The jump radius increases linearly with the flow rate, and the linear slope varies with the surface tension. Due to the stable-rim edge condition, the constant outer Froude numbers observed in our study are different from the constant value reported by Duchesne et al. [Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection, Europhys. Lett. 107, 54002 (2014)]. Despite the constant outer Froude numbers being independent of the flow rate, the inner Froude number changes with the flow rate, which is due to the surface tension force at the jump location. Force analysis is conducted by taking into account the stable rim, and the derived equations provide the relationship of jump radius with the contact angle of the stable rim, disc size, and jet flow. The maximum outer Froude number and the minimum inner Froude number are theoretically analyzed. Depending on the pre-jump velocity profile and the surface tension force at the jump, the maximum outer Froude number could be larger than unity. The shape of free surface at the jump is analyzed to evaluate the theoretical assumption of steep jump. (C) 2015 AIP Publishing LLC.