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Center for Nonlinear Studies |
We consider the evolution and rupture dynamics of an incompressible, thin viscous planar fluid sheet subject to symmetric initial disturbances in the thermal and velocity fields. We consider the long-wave limit where deviations from the mean sheet velocity are small, but thermocapillary stresses, fluid inertia, van der Waals effects, capillarity, and heat transfer to the environment can be significant. The result is a coupled system of three equations that describe the sheet thickness, the sheet velocity, and the sheet temperature. When van der Waals effects are dominant, the sheet ruptures due to the disjoining pressures for sufficiently long-wave disturbances on a faster time-scale than convection or conduction. However in cases when disjoining pressures are small, we find a self-similar rupture process where inertia, viscous stresses, thermocapillarity, convection and conduction all balance. We quantify how solutions can transition from this similarity solution to the van-der-Waals driven self-similar solution when the thickness of the sheet becomes sufficiently thin. We discuss extensions of these results to jets.
Host: Ivan Christov