MEchanics GAthering –MEGA- Seminar: Intro + Unstable waves on a liquid filament

Following a brief introduction and welcome from the MEGA seminar committee there will be an inaugural short seminar.

Abstract: We investiagte the nonlinear dynamics of a thin liquid stream flowing between two parallel glass plates that are narrowly spaced (forming what is known as a
Hele-Shaw cell). The behavior of this rivulet is governed by a complex coupling between the internal flow and the geometry of the capillary interfaces. The competition between gravity, inertia, capillarity, and viscosity in this system leads to a rich variety of dynamical regimes. 
When subjected to time-periodic acoustic overpressure, the rivulet undergoes a parametric pattern-forming instability, reminiscent of the Faraday instability in vibrated liquids. This instability arises from the forced coupling between transverse and longitudinal deformation modes. By employing a weakly nonlinear analysis, we derive a first-principles model that describes the evolution of the rivulet under forcing. Our theoretical results show excellent agreement with experimental observations, accurately capturing the spatiotemporal structure of the observed patterns.