WIAS Preprint No. 1070, (2005)

Linear stability of a ridge


  • King, John R.
  • Münch, Andreas
  • Wagner, Barbara
    ORCID: 0000-0001-8306-3645

2010 Mathematics Subject Classification

  • 76A20 76D27 76M45 34B15 65M06


  • Lubrication theory, numerics, asymptotic approximation, sharp interface




We investigate the stability of the three-phase contact-line of a thin liquid ridge on a hydrophobic substrate for flow driven by surface tension and van der Waals forces. We study the role of slippage in the emerging instability at the three-phase contact-line by comparing the lubrication models for no-slip and slip-dominated conditions at the liquid/substrate interface. For both cases we derive a sharp-interface model via matched asymptotic expansions and derive the eigenvalues from a linear stability analysis of the respective reduced models. We compare our asymptotic results with the eigenvalues obtained numerically for the full lubrication models.

Appeared in

  • Nonlinearity, 19 (2006) pp. 2813-2831.

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