Finite element simulation of multi‐component vesicle morphologies undergoing phase separation

PAMM, vol. 20

Abstract

Abstract Morphological changes in lipid bilayer vesicles are due to phase transitions and surface deformations occurring in unison. We present a dynamic chemo‐mechanical finite element model to study such changes. This is achieved by coupling two fourth order partial differential equations (PDEs): The Cahn‐Hilliard [2] mass balance equation based on irreversible thermodynamics, and the Kirchhoff‐Love [1] rotation free thin shell equation. The Helmholtz free energy consists of Helfrich energy to model elastic bending, and also includes in‐plane elastic energy with a finite shear modulus for the purpose of regularization. The geometry is discretized by C1‐continuous NURBS shape functions. An implicit second order accurate generalized‐α scheme is used for time integration. Newton‐Raphson iterations are utilized to solve the resulting linearized weak form monolithically. The proposed formulation is illustrated by a numerical example.

Authors 3

1. Eshwar J. Savitha Aachen Aachen Institute for Advanced Study in Computational Engineering Science (AICES)

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES) RWTH Aachen University Templergraben 55 52056 Aachen Germany

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

2. Kranthi Kiran Mandadapu

   Lawrence Berkeley National Laboratory · University of California, Berkeley

   Affiliation as printed

   Chemical Sciences Division Lawrence Berkeley National Laboratory Berkeley CA 94720 USA

   Department of Chemical and Biomolecular Engineering University of California at Berkeley 110A Gilman Hall Berkeley CA 94720-1460 USA

   Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 USA

   Department of Chemical and Biomolecular Engineering, University of California at Berkeley, 110A Gilman Hall, Berkeley, CA, 94720-1460 USA

3. Roger A. Sauer corresponding Aachen Aachen Institute for Advanced Study in Computational Engineering Science (AICES)

   RWTH Aachen University · Aachen Institute for Advanced Study in Computational Engineering Science · Indian Institute of Technology Kanpur

   Affiliation as printed

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES) RWTH Aachen University Templergraben 55 52056 Aachen Germany

   Department of Mechanical Engineering Indian Institute of Technology Kanpur Kanpur UP 208016 India

   Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

   Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, UP 208016 India

   Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, UP 208016, India

   Fax: +49 241 80 628498

   Roger A. Sauer

   Telephone: +49 241 80 99129