ESPCI web site
Elastohydrodynamic Singularity and Self-similarity in Contacting Sheets
The dynamics of contact between a thin elastic film and a solid arises in many scientific and engineering applications, from the simple saran-wrap to cellular adhesion to grounding lines in ice sheets. Elastohydrodynamic lubrication theory allows us to derive a partial differential equation coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion and the viscous thin film flow. We use a combination of numerical simulations of the governing equation and a scaling analysis to describe the self-similar solution of the touchdown and spreading of an elastic sheet on a solid substrate. The analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics and adhesion.