Relaxation and Intermediate Asymptotics of a Rectangular Trench in a Viscous Film

Abstract

The surface of a thin liquid film with nonconstant curvature flattens as a result of capillary forces. While this leveling is driven by local curvature gradients, the global boundary conditions greatly influence the dynamics. Here, we study the evolution of rectangular trenches in a polystyrene nanofilm. Initially, when the two sides of a trench are well separated, the asymmetric boundary condition given by the step height controls the dynamics. In this case, the evolution results from the leveling of two noninteracting steps. As the steps broaden further and start to interact, the global symmetric boundary condition alters the leveling dynamics. We report on full agreement between theory and experiments for: the capillary-driven flow and resulting time dependent height profiles; a crossover in the power-law dependence of the viscous energy dissipation as a function of time as the trench evolution transitions from two noninteracting to interacting steps; and the convergence of the profiles to a universal self-similar attractor that is given by the Green's function of the linear operator describing the dimensionless linearized thin film equation.

Accepted for publication in Physical Review E

References in corpus (4)

• Self-Similarity and Energy Dissipation in Stepped Polymer Films
• Capillary-driven flow induced by a stepped perturbation atop a viscous film
• Slippage and Nanorheology of Thin Liquid Polymer Films
• Interplay of internal stresses, electric stresses and surface diffusion in polymer films

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• Universal Self-Similar Attractor in the Bending-Driven Leveling of Thin Viscous Films