Viscoelastic effects and anomalous transient levelling exponents in thin films

Abstract

-We study theoretically the profile evolution of a thin viscoelastic film supported onto a no-slip flat substrate. Due to the nonconstant initial curvature at the free surface, there is a flow driven by Laplace pressure and mediated by viscoelasticity. In the framework of lubrication theory, we derive a thin film equation that contains local viscoelastic stress through the Maxwell model. Then, considering a sufficiently regular small perturbation of the free surface, we linearise the equation and derive its general solution. We analyse and discuss in details the behaviour of this function. We then use it to study the viscoelastic evolution of a Gaussian initial perturbation through its transient levelling exponent. For initial widths of the profile that are smaller than a characteristic length scale involving both the film thickness and the elastocapillary length, this exponent is shown to reach anomalously high values at the elastic-to-viscous transition. This prediction should in particular be observed at sufficiently short times in experiments on thin polymer films.Over the past decades, the study of soft materials in confined geometries and thin films [1][2][3] has widely attracted the interest of physicists, biophysicists, chemists and engineers. In particular, thin polymer films are nowadays of major importance in several industrial applications such as biocompatible coatings, organic microelectronics and polymeric data storage devices. In order to gain insights into the behaviour of these films and their constitutive macromolecules, a wide class of experiments, including dewetting [4,5], nanoindentation with gold particles [6], and levelling of stepped films [7][8][9], have been performed. Enhanced mobility effects in ultra-thin polymer films have been predicted [10,11], and observed [12][13][14]. Film preparation by spincoating has also been widely studied [15][16][17][18], and is known to govern surface instabilities and pattern formation [19][20][21].The evolution of the free surface of a thin Newtonian liquid film with nonconstant curvature is driven by the Laplace pressure and mediated by viscosity. This is well understood from the theoretical point of view through the so-called capillary-driven thin film equation [1][2][3]22]. Extensive analytical work on the thin film equation [23][24][25][26][27] and numerous accurate numerical schemes [28][29][30][31] have been performed in the past decades, and have allowed for a deeper understanding of its mathematical features. Long-term traveling-wave solutions have been discussed [32]. Convergence of the solutions to intermediate asymptotic regimes [33] has also been revealed. In particular, it was shown that the vertically-rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely given by the Green's function of the capillary-driven linear thin film equation multiplied by the initial algebraic volume of the perturbation [34].The aforementioned capillary-driven thin fi...

Influence of slip on the Plateau–Rayleigh instability on a fibre

“…Conversely, a shear-thinning liquid is expected to accelerate the rise of the instability. In the case of a viscoelastic material, Maxwell-like rheological models [35] can be implemented and may reveal interesting physics, beyond the scope of the present study.…”

Approach to universal self-similar attractor for the levelling of thin liquid films

“…Levelling experiments on thin polymer films in the vicinity of the glass transition temperature have recently given insights into the surface flow in glassy polymers 41 . The effect of viscoelasticity related to the polymeric nature of these films has been addressed as well [42][43][44] .…”

A thin-film equation for a viscoelastic fluid, and its application to the Landau-Levich problem

“…A thin-film equation for a linear viscoelastic fluid of Jeffreys type was derived in [31] where it was used to study the shape of rim in a dewetting film. The model was also used to study viscoelastic effects in thin-film phenomena such as instability, film rupture, film levelling, and drop spreading [3,4,5,39]. The linear Jeffreys model does not have geometric non-linear terms of models like upper-convected Maxwell which ensure frame invariance of the constitutive equation [25].…”