Continuum theory of a moving membrane

Dan Hu, Pingwen Zhang, Weinan E

Research output: Contribution to journalArticlepeer-review


We derive a set of equations for the dynamics of evolving fluid membranes, such as cell membranes, in the presence of bulk fluids. We model the membrane as a surface endowed with a director field, which describes the local average orientation of the molecules on the membrane. A model for the elastic energy of a surface endowed with a director field is derived using liquid crystal theory. This elastic energy reduces to the well-known Helfrich energy in the limit when the directors are constrained to be normal to the surface. We then derive the full dynamic equations for the membrane that incorporate both the elastic and viscous effects, with and without the presence of bulk fluids. We also consider the effect of local spontaneous curvature, arising from the presence of membrane proteins. Overall, the systems of equations allow us to carry out stable, accurate, and robust numerical modeling for the dynamics of the membranes.

Original languageEnglish (US)
Article number041605
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
StatePublished - Apr 26 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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