Tip Streaming Instabilities for Slender Axisymmetric Bubbles with Surfactant: an Asymptotic Approach

Wednesday, January 10, 2001 - 4:00pm - 4:25pm
Keller 3-180
Michael Siegel (New Jersey Institute of Technology)
Tipstreaming refers to the process by which a bubble in an extensional flow develops cusp-like ends, which subsequently emit slender filaments or bubbles into the exterior fluid. G. I. Taylor first identified this process in a seminal paper describing experiments performed in a four- roller mill. More recent experiments have shown that the presence of surfactant is critical for the onset of tipstreaming.

In this talk slender body theory is applied to investigate the deformation of an inviscid bubble in the presence of an insoluble surfactant. Of particular interest are the conditions for the breakup of a single drop in uniaxial zero Reynolds number extensional flow. We first discuss the steady state solutions; these include a class for which stagnant caps of surfactant partially coat the bubble surface. Although it is well known that steady slender drops exist for all capillary number Q in the absence of surfactant, our results show that steady drops with surfactant can only exist if Q is below a critical value, which is determined in the analysis. The breakup of inviscid bubbles in the presence of surfactant is therefore identified with the lack of a steady solution, rather than the instability of an existing solution at a critical Q. This behavior is analogous to that for drops of low viscosity, for which steady shapes do not exist above a critical capillary number. However, it is suggested that surfactant effects provide the dominant mechanism for breakup in very low viscosity drops. Time dependent studies employing the slender drop approximation show that, above the critical capillary number, the drop breaks by a rapid growth at its end. A possible connection between the observed behavior and the phenomenon of tip-streaming is discussed.