Mathematical Biology Seminar

Pilhwa Lee, CIMS, NYU
Monday Jan. 29, 2007
4:20pm in LCB 215
"Immersed Boundary Method with Advection-Electrodiffusion "

Abstract: The immersed boundary method is a mathematical and computational framework for problems involving the interaction of a fluid with immersed structures. In the talk, we consider also the role of solutes (possibly charged) and their interactions with membranes. We propose a numerical scheme for the advection-diffusion of solutes in fluid-solute-structure interaction. The transport of solute across possibly moving boundaries is controlled by a chemical barrier along the boundary. Moreover, when the solutes are electrical ions, they generate an electrical potential according to the Poisson equation, and they drift relative to the fluid according to the gradient of the electrical potential. Both explicit and implicit numerical schemes are considered for the advection-electrodiffusion equations. The results show electroneutrality except in space charge layers near membranes, and agree with the Nernst equation for the potential difference across membranes.