NONLINEAR DYNAMICS OF VISCOUS DROPLETS

Nonlinear viscous droplet oscillations are analysed by solving the Nav ier-Stokes equation for an incompressible fluid. The method is based o n mode expansions with modified solutions of the corresponding linear problem. A system of ordinary differential equations, including all no nlinear and viscous terms, is obtained by an extended application of t he variational principle of Gauss to the underlying hydrodynamic equat ions. Results presented are in a very good agreement with experimental data up to oscillation amplitudes of 80% of the unperturbed droplet r adius. Large-amplitude oscillations are also in a good agreement with the predictions of Lundgren & Mansour (boundary integral method) and B asaran (Galerkin-finite element method). The results show that viscosi ty has a large effect on mode coupling phenomena and that, in contradi ction to the linear approach, the resonant mode interactions remain fo r asymptotically diminishing amplitudes of the fundamental mode.