Applied Math Seminar

Date: March 3, 2025

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Michael Siegel, New Jersey Institute of Technology, Newark

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. Soluble surfactant advects and diffuses in bulk fluids while adsorbing and desorbing from interfaces. Since the fluid velocity depends on the bulk surfactant concentration C, the advection-diffusion equation governing C is nonlinear, which 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 surprisingly permits a Green’s function formulation. Despite this, existing fast algorithms for similar BI formulations, such as those developed for the heat equation, do not readily apply. To address this challenge, we present a new fast algorithm for our formulation which gives a mesh-free solution to the fully coupled moving interface problem, including soluble surfactant effects. The method extends to other problems involving advection-diffusion in the large Peclet number limit. This is joint work with Michael Booty (NJIT), Samantha Evans (NJIT), and Johannes Tausch (SMU). Zoom: https://tamu.zoom.us/j/94220070032