Title: A fast mesh-free  boundary integral method for two-phase flow with soluble surfactant

 

Abstract: We present an accurate and efficient boundary integral (BI) method to simulate the deformation of drops and bubbles in Stokes flow with soluble surfactant.  Surfactant which is soluble advects and diffuses in bulk fluids and adsorbs/desorbs from interfaces.  Since the fluid velocity depends on the bulk surfactant concentration C, the advection-diffusion equation governing C is nonlinear. This precludes the Green's function formulation necessary for a BI method.  However, in the physically representative large Peclet number limit an analytical reduction of the surfactant dynamics does (surprisingly) admit a Green's function formulation.  Unfortunately, fast algorithms developed for similar boundary integral formulations in the case of the heat equation do not easily apply. We present a new fast algorithm for our formulation which gives a mesh-free method of solving the full moving interface problem, including soluble surfactant. The method applies to other problems involving advection-diffusion in the large Peclet number limit. Several challenging examples will be presented.  This is joint work with Michael Booty (NJIT), Samantha Evans (NJIT), and Johannes Tausch (SMU).

 

 

Bio: Michael Siegel joined the NJIT faculty as an Assistant Professor of Mathematics in 1995 and has been a Professor of Mathematics since 2005. He is currently the Director of NJIT’s Center for Applied Mathematics and Statistics (CAMS).  Siegel earned his BS in Physics and Mathematics from Duke University in 1984 and a PhD in Mathematics (1989) from New York University’s Courant Institute of Mathematical Sciences. In addition to his posts at NJIT, he has been a visiting researcher at the Courant Institute of Mathematical Sciences at NYU and Oxford University. He had an appointment as Wallenberg Guest Professor at KTH, Stockholm in 2015-2016. Before NJIT, he held a National Science Foundation (NSF) Postdoctoral Fellowship and was a Postdoctoral Research Fellow at Ohio State University. He also served as von Karman Instructor in Applied Mathematics at the California Institute of Technology from 1989 to 1991.