The influence of an outer bath on the dewetting of an ultrathin liquid film Articles uri icon

publication date

  • September 2023

start page

  • 092113-1

end page

  • 092113-7


  • 9


  • 35

International Standard Serial Number (ISSN)

  • 1070-6631

Electronic International Standard Serial Number (EISSN)

  • 1089-7666


  • We report a theoretical and numerical investigation of the linear and nonlinear dynamics of
    a thin liquid film of viscosity µ sandwiched between a solid substrate and an unbounded
    liquid bath of viscosity λ µ. In the limit of negligible inertia, the flow depends on two nondimensional parameters, namely λ and a dimensionless measure of the relative strengths of
    the stabilizing surface tension force and the destabilizing van der Waals force between the
    substrate and the film. We first analyze the linear stability of the film, providing an analytical dispersion relation. When the viscosity of the outer bath is much larger than that of the
    film, λ ≫ 1, the most amplified wavenumber decreases as km ∼ λ
    , indicating that very
    slender dewetting structures are expected when λ becomes large. We then perform fully
    nonlinear simulations of the complete Stokes equations to investigate the spatial structure
    of the flow close to rupture revealing that the flow becomes self-similar with the minimum
    film thickness scaling as hmin = K(λ)τ
    1/3 when τ → 0, where τ is the time remaining before the singularity. It is demonstrated that the presence of an outer liquid bath affects the
    self-similar structure obtained by16 through the prefactor of the film thinning law, K(λ),
    and the opening angle of the self-similar film shape, which is shown to decrease with λ.


  • Physics


  • linear stability analysis; thin films; liquid solid interfaces; van der waals forces; drop coalescence