Gilles Pfingstag

We study the stability of a thin, Newtonian viscous sheet floating on a bath of denser fluid. We first derive a general set of equations governing the evolution of a nearly flat sheet, accounting for geometrical nonlinearities associated with moderate rotations. We extend two classical models by considering arbitrary external body and surface forces; these two models follow from different scaling assumptions, and are derived in a unified way. The equations capture two modes of deformation… Voir plus

We study the stability of a thin, Newtonian viscous sheet floating on a bath of denser fluid. We first derive a general set of equations governing the evolution of a nearly flat sheet, accounting for geometrical nonlinearities associated with moderate rotations. We extend two classical models by considering arbitrary external body and surface forces; these two models follow from different scaling assumptions, and are derived in a unified way. The equations capture two modes of deformation, namely viscous bending and stretching, and describe the evolution of thickness, mid-surface and in-plane velocity as functions of two-dimensional coordinates. These general equations are applied to a floating viscous sheet, considering gravity, buoyancy and surface tension. We investigate the stability of the flat configuration when subjected to arbitrary in-plane strain. Two unstable modes can be found in the presence of compression. The first one combines undulations of the centre-surface and modulations of the thickness, with a wavevector perpendicular to the direction of maximum applied compression. The second one is a buckling mode; it is purely undulatory and has a wavevector along the direction of maximum compression. A nonlinear analysis yields the long-time evolution of the undulatory mode. Voir moins

We derive the equations governing the dynamics of thin viscous sheets having non-homogeneous viscosity, via asymptotic expansion methods. We consider distributions of viscosity that are inhomogeneous in the longitudinal and transverse directions and arbitrary (bulk and surface) external forces. Two specific problems are solved as an illustration. In a first example, we study the effects of purely in-plane variations of viscosity, which lead to thickness modulations when the sheet is stretched… Voir plus

We derive the equations governing the dynamics of thin viscous sheets having non-homogeneous viscosity, via asymptotic expansion methods. We consider distributions of viscosity that are inhomogeneous in the longitudinal and transverse directions and arbitrary (bulk and surface) external forces. Two specific problems are solved as an illustration. In a first example, we study the effects of purely in-plane variations of viscosity, which lead to thickness modulations when the sheet is stretched or compressed. In a second example, we study a stretched viscous sheet whose viscosity varies both across thickness and in-plane; in that case, we find that in-plane strain leads to out-of-plane displacement as the in-plane forces become coupled to transverse ones. Voir moins