Buckling of thin, viscous films

Collaborating with Richard Craster (Imperial College London), I have recently begun to explore the qualitative and quantitative analogy between the buckling of thin elastic membranes (e.g. Saran^TM wrap) and viscous films. Fortuitously, the analogy turns out to be relatively robust, allowing fluid mechanicians to borrow equations from the field of elasticity in describing e.g. the regular pattern of wrinkles that appears when a thin film is subject subjected to in-plane shear. For experimental simplicity, our work to date has focused on an idealized axisymmetric scenario, though buckles of the type illustrated below appear in numerous less-idealized circumstances, both industrial and in the natural environment.

Plan view of shear-driven buckling in a rectilinear and axisymmetric channel.

The associated out-of-plane displacement of the viscous film.

Numerial results from solving the linearized "fluidic" Foppl-von Karman equation. The inner circular boundary is assumed to rotate in the anti-clockwise direction at a fixed speed whereas the outer boundary is fixed.

Publication:

Buckling of a thin, viscous film in an axisymmetric geometry (Phys. Fluids 25, with S. Bhattacharya and R.V. Craster) (.pdf)
[Copyright 2013 American Inst. of Physics. The above article may be downloaded for personal use only. Any other use requires prior permission of the author and the AIP. The above article may be found at http://dx.doi.org/10.1063/1.4798825]