Pearling bifurcations in the strong functionalized Cahn-Hilliard free energy

Noa Kraitzman, Keith Promislow

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

The functionalized Cahn--Hilliard free energy supports phase-separated morphologies of distinct codimension, including codimension-one bilayer and codimension-two filament morphologies. We characterize the linear stability of bilayer and filament morphologies associated to hypersurfaces within the strong functionalization scaling. In particular, we show that the onset of the pearling instability, which triggers fast in-plane oscillations associated to bifurcation to higher codimensional morphology, is controlled by the functionalization parameters and the spatially constant value of the far-field chemical potential. Crucially, we show that onset of pearling is independent of the shape of the defining hypersurface.
Original languageEnglish
Pages (from-to)3395–3426
Number of pages32
JournalSIAM Journal on Mathematical Analysis
Volume50
Issue number3
DOIs
Publication statusPublished - 2018
Externally publishedYes

Keywords

  • functionalized Cahn–Hilliard
  • pearling stability
  • strong functionalization
  • generic hypersurfaces

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