Perturbation Theory for Nonuniform Fluids: Surface Tension

1971 ◽  
Vol 55 (7) ◽  
pp. 3116-3120 ◽  
Author(s):  
So/ren Toxvaerd
Keyword(s):  
Surface Tension ◽  
Perturbation Theory ◽  
Nonuniform Fluids

The collapse of a non-hemispherical bubble attached to a solid wall

1977 ◽  
Vol 80 (2) ◽  
pp. 369-391 ◽  
Author(s):  
A. Shima ◽  
K. Nakajima
Keyword(s):  
Surface Tension ◽  
Perturbation Theory ◽  
Variational Method ◽  
Solid Wall ◽  
Oblate Spheroid ◽  
Prolate Spheroid ◽  
The Other ◽  
Adiabatic Process ◽  
Gas Bubble ◽  
Governing Equations

The problem of the collapse of a vapour/gas bubble attached to a solid wall and initially perturbed from a hemispherical shape is solved numerically by the variational method, in which the bubble's viscosity and compressibility in liquid are neglected. The effects of surface tension on the collapsing bubble are taken into account. The rebounding processes of a non-hemispherical gas bubble are simulated: the gas inside the bubble undergoes an adiabatic process. The results of numerical calculations are given for two initial shapes: one is close to a prolate spheroid, the other is close to an oblate spheroid. The governing equations for the motion of a bubble can be written in matrix form, which is simpler than that derived from perturbation theory. This analysis using the variational method may be applied to more complicated problems.

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