A theoretical model for bubble formation at an orifice submerged in an inviscid liquid

A new theoretical model for calculating bubble formation at an orifice submerged in an inviscid liquid is presented. Simplified equations of motion for the gas—liquid interface were developed, and together with thermodynamic equations for the gas in the bubble and the chamber below the orifice plate, the instantaneous shape of the bubble during its formation was calculated. In contrast with previous models, the present model is able to determine the instant of detachment as the moment at which the neck of the bubble closes. The present model gives also a more detailed treatment of the flow through the orifice, and is suitable for low as well as high chamber volumes. Calculated results are presented for a wide range of orifice radii (0.0175–0.48 cm), gas flow rates (0.4–100 cm3/sec) and chamber volume (1–5000 cm3), including examples of calculated bubble shapes. The present model is restricted to single bubble formation, but it is able to calculate the critical flow rates and critical chamber volumes which limit this region.