Pascal Damman
Laboratoire InFluX, Université de Mons, Belgique
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Universal wrinkling dynamics of a sheet on viscous liquid
We investigate the wrinkling dynamics of a sheet that is indented or compressed while floating on top of a viscous liquid. The speed at which the sheet is deformed affects the wrinkling dynamics, resulting in a much smaller wrinkle wavelength compared to that observed during quasistatic compression. Moreover, once active compression ends, the induced wrinkles coarsen until their wavelength relaxes to the equilibrium value. We propose a theoretical model that couples the Stokes equations for fluid flow to the beam equation for the solid deformation, thereby determining the initial wavelength that is observed and its coarsening over time. We show that similar mechanisms are at work for both two-dimensional and axisymmetric geometries. Finally, we suggest a geophysical application of our model, able to describe the formation of ropey lava, or pahoehoe, in some volcanic eruptions.
