Stagnant-cap bubbles with both diffusion and adsorption rate-determining

When a gas bubble rises in an impure liquid, its surface often has an upper spherical cap with negligible shear stress, a lower spherical cap with negligible tangential velocity, and a very small transition region between the two caps. This paper gives the diffusion boundary-layer theory for the dis...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 521; pp. 115 - 123
Main Author HARPER, J. F.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 25.12.2004
Subjects
Drops and bubbles
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Nonhomogeneous flows
Physics
Bubbles
Bubble ascent
Creeping flow
Boundary layer equation
Theoretical study
Boundary conditions
Surfactants
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Summary:When a gas bubble rises in an impure liquid, its surface often has an upper spherical cap with negligible shear stress, a lower spherical cap with negligible tangential velocity, and a very small transition region between the two caps. This paper gives the diffusion boundary-layer theory for the distribution of surfactant around a stagnant-cap bubble, allowing for slowness of both adsorption and diffusion. The resulting singular Volterra integro-differential equations are solved numerically for creeping flow (small Reynolds number). The main result is the relation between the surface pressure of surfactant in the bulk solution, the cap angle and Péclet number of the bubble, and the adsorption depth and adsorption speed of the surfactant. The values of the latter two parameters affect the validity of the approximations much more than the numerical results.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112004001843