A Note on the Formation and Rise of a Bubble from a Submerged Nozzle, Including Effects of Bulk- and Surface-Dilatational Viscosity

A model of the formation, detachment, and rise of a bubble from a submerged orifice is derived, based upon a study using a modified form of the Rayleigh–Plesset equation. Similar models have previously been proposed by Oguz and Prosperetti (1), Avramidis and Jiang (2), and also Chakraborty and Tuteja (3). We seek to re-examine these models and implement a number of additional physical features. In particular, we demonstrate the relative importance of the surface dilatational viscosity of surfactant added to the liquid in the growth and detachment of the bubble from the orifice. It is found that “large” surface dilatational viscosities significantly increase the time to detachment of the bubble. In addition, through a drastic reduction in the rate of radial expansion of the bubble in the early stages of development (given an initial condition on the radial velocity for “fast” bubble growth), the rise velocity of the bubble centroid at this time is greater with a large surface dilatational viscosity than when this property is neglected.