Effect of the odd viscosity on Faraday wave instability

Abstract

Faraday waves arise in fluid systems with free surfaces subject to vertical oscillations of sufficient strength due to parametric resonance. The odd viscosity is a peculiar part of the viscosity stress tensor that does not result in dissipation and is allowed when parity symmetry is broken spontaneously or due to external magnetic fields or rotations. The effect of the odd viscosity on the classic Faraday instability of thin liquid films in infinite horizontal plates is investigated by utilizing both linear Floquet theory and nonlinear lubrication theory based on the weighted residual model. This work derives the nonlinear evolution equations about the flow rate and free surface height, and linear stability analysis is performed to achieve the damped Mathieu equation. The results show that the neutral stability curves derived from the Mathieu equation agree well with those obtained from the linear Floquet analysis, especially for lower viscosity ratios μ. The nonlinear numerical results simulated by the method of lines indicate interesting results where the odd viscosity gives rise to a “sliding” of the wave configuration parallel to the wall, and the interface wave then translates into a traveling wave.