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.

Viscous Stability Criterion for Hydrodynamic Differential Rotation

“…𝑄 used to obtain the critical point for stability are given in Reference [2]. Moreover, viscous stability keeps being an important subject till recently; for instance, in getting asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology [6] or in the study of viscous stability and instability when polymers are involved [5]. Moreover, an applicable method is introduced recently to verify global stability of a laminar fluid flow against all perturbations [3]; another recent work is on the electro-hydrodynamics stability [1].…”

Instabilities and pattern formation in viscoelastic fluids

“…Here, Ā denotes the Jacobian where Ā(t) = Ā(t + T ) with T = 2π/ω due to Eq. (15). A matrix M which transform the system one period ahead is introduced.…”

“…: V,-vol model one can find in [14]. Reference [15] studies the stability of a viscous fluid layer covered with an elastic polymer film under external vibration by usage of Floquet's theorem.…”

Resonant Phenomena of Faraday Waves: Reproducibility

“…Since their discovery, they have been the subject of successive investigations allowing for advanced applications across a myriad of fields. For example, as noted by Liu [3]: measuring the surface tension of soft materials [4]; developing new photonic devices [5,6]; metamaterials [7,8]; applications in cell culture patterns [9,10]; detecting physiological processes of organisms [11]; monitoring earthworms [12]; modifying soil structure to increase crop yields [13][14][15]; medical ultrasound and photoacoustic imaging modalities [16]; Brillouin Light Scattering spectroscopy [17]; laser vibrometry [18]; and the development of new methods for eradicating viruses and bacteria [19][20][21]. Furthermore, as noted by Sheldrake [22], the behaviour of the observed resonant phenomena offers a model for analogous behaviour observed in both physical systems, e.g., [23][24][25][26], and biological systems, e.g., [27][28][29][30].…”