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

✍ Scribed by Giles S. Keen; John R. Blake

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 133 KB
• Volume: 180
• Category: Article
• ISSN: 0021-9797
• DOI: 10.1006/jcis.1996.0346

✦ Synopsis

NOTE A Note on the Formation and Rise of a Bubble from a Submerged Nozzle, Including Effects of Bulk-and Surface-Dilatational Viscosity 2. THE SPHERICAL BUBBLE MODEL A model of the formation, detachment, and rise of a bubble from a submerged orifice is derived, based upon a study using a 2.1. Previous Studies modified form of the Rayleigh-Plesset equation. Similar models Previous authors (1, 2, 4) assume the bubble is spherical and is governed have previously been proposed by Og ˜uz and Prosperetti (1), by the Rayleigh-Plesset equation, 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 Here R is the bubble's radius in time, r is the liquid phase density, s is bubble from the orifice. It is found that ''large'' surface dilatational the surface tension, p ϱ is the far-field pressure, and p B the bubble pressure.

viscosities significantly increase the time to detachment of the Og ˜uz and Prosperetti (1) calculate the pressure inside the bubble by assumbubble. In addition, through a drastic reduction in the rate of ing that it is given by the equation of state for a perfect gas, 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. ᭧ 1996 Academic Press, Inc.

where R is the gas constant, T the temperature, m(t) the mass of gas forming