Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit. The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure. The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant. © 2008 Cambridge University Press.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed, J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier-Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With soluble surfactant, depending on parameter values, a slender thread forms but can pinch-off later due to exchange of surfactant between the interface and exterior bulk flow. © 2009 American Institute of Physics.