Faraday Instability in Viscous Fluids Covered with Elastic Polymer Films

Abstract

Faraday instability has great application value in the fields of controlling polymer processing, micromolding colloidal lattices on structured suspensions, organizing particle layers, and conducting cell culture. To regulate Faraday instability, in this article, we attempt to introduce an elastic polymer film covering the surface of a viscous fluid layer and theoretically study the behaviors of the Faraday instability phenomenon and the effect of the elastic polymer film. Based on hydrodynamic theory, the Floquet theory is utilized to formulate its stability criterion, and the critical acceleration amplitude and critical wave number are calculated numerically. The results show that the critical acceleration amplitude for Faraday instability increases with three increasing bending stiffness of the elastic polymer film, and the critical wave number decreases with increasing bending stiffness. In addition, surface tension and viscosity also have important effects on the critical acceleration amplitude and critical wave number. The strategy of controlling Faraday instability by covering an elastic polymer film proposed in this paper has great application potential in new photonic devices, metamaterials, alternative energy, biology, and other fields.