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Summer Program Seminars 2006

Thursday, July 20, 2006 @ 10:00AM
Cullimore Hall, Room 611
New Jersey Institute of Technology

The Effect of Surfactant on the Deformation and
Breakup of a Bubble in a Viscous Surrounding

Michael Siegel

Department of Mathematical Sciences

New Jersey Institute of Technology

Newark, New Jersey

ABSTRACT

The effect of  surfactant on the pinch-off of an inviscid bubble surrounded by a viscous fluid  is studied theoretically and numerically. Equations governing the evolution of the interface and surfactant concentration in zero-Reynolds-number flow are derived using a long wavelength approximation. Results of the long wavelength model are  compared against numerical simulations of the full Navier-Stokes equations, performed using an accurate arbitrary Lagrangian-Eulerian method. The presence of insoluble surfactant is found to significantly retard pinch-off. This is due to the development of a long, slender, quasi-steady cylindrical thread at the location of minimum radius, where the destabilizing influence of surface tension is balanced by the internal pressure. For soluble surfactant, depending on parameter values, a thin thread forms first but pinches off later due to the exchange of surfactant  between the  bulk fluid and the interface.