Instability and dynamics of thin viscoelastic liquid films

Abstract

The instability, rupture, and subsequent growth of holes in a thin Jeffreys-type viscoelastic film under the influence of long-range van der Waals force are investigated using both linear stability analysis and nonlinear numerical solutions. The linear stability analysis of full governing equations valid for arbitrary wave numbers shows that although fluid rheology does not influence the dominant length scale of the instability, it significantly affects the growth rate. It is shown that neglect of inertia and solvent dynamics results in a nonphysical singularity in the growth rate beyond a critical value of relaxation time. We further carry out numerical simulations of a set of long-wave, nonlinear differential equations (also derived in Rauscher et al., Eur. Phys. J. E 17, 373 (2005)) governing the evolution of the free surface. The nonlinear simulations, in their domain of validity, confirm the results of the linear analysis. Interestingly, results from nonlinear simulations further show that both for Newtonian and viscoelastic liquids, the shape and the dewetting dynamics of a hole are identical when examined in terms of a rescaled time which depends on rheological parameters. Thus, viscoelasticity of Jeffreys type merely accelerates the growth rate, without however affecting the important morphological characteristics.