Capillary-driven flow induced by a stepped perturbation atop a viscous film
arXiv:1210.5905 · doi:10.1063/1.4763569
Abstract
Thin viscous liquid films driven by capillarity are well described in the lubrication theory through the thin film equation. In this article, we present an analytical solution of this equation for a particular initial profile: a stepped perturbation. This initial condition allows a linearization of the problem making it amenable to Fourier analysis. The solution is obtained and characterized. As for a temperature step in the heat equation, self-similarity of the first kind of the full evolution is demonstrated and a long-term expression for the excess free energy is derived. In addition, hydrodynamical fields are described. The solution is then compared to experimental profiles from a model system: a polystyrene nanostep above the glass transition temperature which flows due to capillarity. The excellent agreement enables a precise measurement of the capillary velocity for this polymeric liquid, without involving any numerical simulation. More generally, as these results hold for any viscous system driven by capillarity, the present solution may provide a useful tool in hydrodynamics of thin viscous films.
Accepted for publication in Physics of Fluids
References in corpus (3)
Cited by in corpus (18)
- A direct quantitative measure of surface mobility in a glassy polymer
- Self-Similarity and Energy Dissipation in Stepped Polymer Films
- Printing wet-on-wet: attraction and repulsion of drops on a viscous film
- Deformation and relaxation of viscous thin films under bouncing drops
- Elastocapillary Levelling of Thin Viscous Films on Soft Substrates
- Adsorption-Induced Slip Inhibition for Polymer Melts on Ideal Substrates
- Relaxation and Intermediate Asymptotics of a Rectangular Trench in a Viscous Film
- Ripples in Thin Films
- Using Mw dependence of surface dynamics of glassy polymers to probe the length scale of free surface mobility
- Capillary Levelling of Immiscible Bilayer Films
- The influence of van der Waals interactions on a bubble moving in a tube
- Viscoelastic effects and anomalous transient levelling exponents in thin films
- Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green's function, and intermediate asymptotics for a finite thin film with elastic resistance
- Molecular dynamics simulation of the capillary leveling of viscoelastic polymer films
- Surface and Bulk Relaxation of Vapour-Deposited Polystyrene Glasses
- Universal Self-Similar Attractor in the Bending-Driven Leveling of Thin Viscous Films
- Comparison of Lubrication Approximation and Navier-Stokes Solutions for Dam-Break Flows in Thin Films
- Soft nanobubbles can deform rigid glasses