Thin viscoelastic dewetting films of Jeffreys type subjected to gravity and substrate interactions

TL;DR

This paper investigates the effects of gravity and substrate interactions on the stability and dewetting patterns of thin viscoelastic films modeled by Jeffreys' model, using linear stability analysis and nonlinear simulations.

Contribution

It introduces a long-wave model for viscoelastic films with gravity and substrate effects, analyzing stability and nonlinear dewetting behavior for the first time.

Findings

Gravity and disjoining pressure influence instability length scales.

Final dewetting configurations are affected by gravity and substrate interactions.

Satellite droplet formation is promoted or suppressed by slippage effects.

Abstract

This work presents a study of the interfacial dynamics of thin viscoelastic films subjected to the gravitational force and substrate interactions induced by the disjoining pressure, in two spatial dimensions. The governing equation is derived as a long-wave approximation of the Navier-Stokes equations for incompressible viscoelastic liquids under the effect of gravity, with the Jeffreys model for viscoelastic stresses. For the particular cases of horizontal or inverted planes, the linear stability analysis is performed to investigate the influence of the physical parameters involved on the growth rate and length scales of instabilities. Numerical simulations of the nonlinear regime of the dewetting process are presented for the particular case of an inverted plane. Both gravity and the disjoining pressure are found to affect not only the length scale of instabilities, but also the final configuration of dewetting, by favoring the formation of satellite droplets, that are suppressed by the slippage with the solid substrate.