Berkeley Fluids Seminar
University of California, Berkeley
Bring your lunch and enjoy learning about fluids!
Wednesday, November 14, 2018
12:00-13:00, Fanuc Room, 6120 Etcheverry Hall
Amaresh Sahu (Chemical Engineering, UC Berkeley)
Abstract: Biological membranes make up the boundary of the cell as well as several of its internal organelles, including the nucleus, endoplasmic reticulum, and Golgi complex. Although much has been learned about biological membranes experimentally, they are different to model wholistically as they are arbitrarily curved, two-dimensional objects which bend elastically out-of-plane yet behave as a fluid in-plane. We develop the theory of irreversible thermodynamics for arbitrarily curved lipid membranes, and study the coupling between elastic membrane bending and the irreversible processes of in-plane lipid flow, intra-membrane phase transitions, and protein binding reactions. A balance law formulation, combined with an irreversible thermodynamic framework, is used to determine the equations of motion governing lipid membrane dynamics. However, these equations are highly nonlinear and cannot be solved analytically. We develop an arbitrary Lagrangian–Eulerian (ALE) finite element method for arbitrarily curved and deforming lipid membranes. An ALE theory is developed by endowing the surface with a mesh whose in-plane velocity is independent of the in-plane material velocity, and which can be specified arbitrarily. This framework is then used to study two-dimensional curved and deforming fluid films. A new physical insight is obtained, as two-dimensional fluid cylinders are numerically and analytically found to be unstable with respect to long-wavelength perturbations, when their length exceeds their circumference.