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
Recommended Citation
Booty, M. R. and Siegel, M., "Steady deformation and tip-streaming of a slender bubble with surfactant in an extensional flow" (2005). Faculty Publications. 19296.
https://digitalcommons.njit.edu/fac_pubs/19296
