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Fluid Dynamics Seminar

Monday, April 27, 2009, 4:00 PM
Cullimore Lecture Hall, Room 611
New Jersey Institute of Technology

The evolution of a two-dimensional Cartesian drop in an imposed linear flow: The influence of surfactant and surfactant solubility

Kuan Xu

Department of Mathematical Sciences, NJIT

Abstract

We study the evolution of a two-dimensional Cartesian drop or bubble in an imposed flow in the presence of soluble surfactant, i.e., a surface-active agent. The surfactant is distributed both on the drop surface and in the exterior bulk fluid. The governing equations in the zero Reynolds number of Stokes flow limit are solved by the boundary integral method using a complex-valued density. Specifically, the Goursat representation of the flow is used, in which solution of the biharmonic equation for the stream function and all primitive variables are given by construction of a pair of complex analytic functions, which can be found by constructing a single complex density that satisfies a Fredholm integral equation of second type. A recent study on solvability of this boundary integral equation is reported, as well as the results of several numerical examples. High-order numerical schemes have been devised. These include an equal-arclength frame, a spectrally-accurate quadrature method, and a spectrum filter.