Backholm, M.

Baumchen, O.

Benzaquen, M.

Dalnoki-Veress, K.

Fowler, P.

McGraw, J. D.

Raphael, E.

Salez, Thomas

arXiv

International audienceThe 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

Mcgraw, J. D.

HAL: Hyper Article en Ligne

Relaxation and intermediate asymptotics of a rectangular trench in a viscous film

Oliver Bäumchen

Michael Benzaquen

Thomas Salez

Joshua D. McGraw

Matilda Backholm

Paul Fowler

Elie Raphaël

Kari Dalnoki-Veress

Crossref

Physical Review E

HAL Portal ESPCI (Ecole Supérieure de Physique et de Chimie Industrielles)

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

Relaxation and intermediate asymptotics of a rectangular trench in a viscous film

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HAL: Hyper Article en Ligne

Crossref

HAL Portal ESPCI (Ecole Supérieure de Physique et de Chimie Industrielles)

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