Newton-Cartan Submanifolds and Fluid Membranes

Dec 3, 2019
25 pages
Published in:
  • Phys.Rev.E 101 (2020) 6, 062803
  • Published: Jun 19, 2020
e-Print:
Report number:
  • EMPG-19-25,
  • NORDITA 2019-109

Citations per year

20202021202220232024736
Abstract: (APS)
We develop the geometric description of submanifolds in Newton-Cartan spacetime. This provides the necessary starting point for a covariant spacetime formulation of Galilean-invariant hydrodynamics on curved surfaces. We argue that this is the natural geometrical framework to study fluid membranes in thermal equilibrium and their dynamics out of equilibrium. A simple model of fluid membranes that only depends on the surface tension is presented and, extracting the resulting stresses, we show that perturbations away from equilibrium yield the standard result for the dispersion of elastic waves. We also find a generalization of the Canham-Helfrich bending energy for lipid vesicles that takes into account the requirements of thermal equilibrium.
Note:
  • 56 pages including appendices, v2: updated to published version
  • Films and Interfaces
  • fluid: model
  • Cartan
  • membrane
  • space-time
  • thermal
  • surface tension
  • hydrodynamics
  • perturbation
  • covariance