Steady deformation and tip-streaming of a slender bubble with surfactant in an extensional flow

Document Type

Article

Publication Date

12-10-2005

Abstract

Slender-body theory is used to investigate the steady-state deformation and time-dependent evolution of an inviscid axisymmetric bubble in zero-Reynolds-number extensional flow, when insoluble surfactant is present on the bubble surface. The asymptotic solutions reveal steady ellipsoidal bubbles covered with surfactant, and, at increasing deformation, solutions distinguished by a cylindrical surfactant-free central part, with stagnant surfactant caps at the bubble endpoints. The bubble shapes are rounded near the endpoints, in contrast to the pointed shapes found for clean inviscid bubbles. Simple expressions are derived relating the capillary number Q to the steady bubble slenderness ratio ε. These show that there is a critical value Qc above which steady solutions no longer exist. Equations governing the time-evolution of a slender inviscid bubble with surfactant, valid for large capillary number, are also derived. Numerical solutions of the slender bubble equations for Q > Qc exhibit spindle shapes with tip-streaming filaments. © 2005 Cambridge University Press.

Identifier

28644434646 (Scopus)

Publication Title

Journal of Fluid Mechanics

External Full Text Location

https://doi.org/10.1017/S0022112005006622

e-ISSN

14697645

ISSN

00221120

First Page

243

Last Page

275

Volume

544

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