Effect Of The Spontaneous Odd Viscosity On Faraday Wave Instability

When the time-reversal symmetry of the viscous fluid is broken spontaneously or due to external magnetic fields or rotations,fluids can display a dissipationless viscosity that is called odd viscosity.In recent years,the odd viscosity problem has become a new research hotspot in fluid mechanics.Researchers have paid attention to the hydrodynamic phenomena caused by odd viscosity in theories and experiments.The influence of odd viscosity is reflected in the fluid interface.Therefore,the effect of odd viscosity in interface instability has been widely concerned.The Faraday waves arise in fluid systems with a free surface subjected to vertical oscillations of sufficient strength as a result of parametric resonance.Compared with classical mechanical Faraday waves,electrostatic Faraday waves powered by external alternating electric fields are easier to control,but relevant research is rare.Based on the research status of odd viscosity and Faraday wave,we study the two-dimensional Faraday thin liquid film driven by mechanical vibration and external vertical periodic electric fields through theoretical analysis and numerical simulation.The influence of odd viscosity and related parameters on fluid interface stability is qualitatively investigated by linear analysis;the mechanism of odd viscosity in interface problems is quantitatively analyzed by numerical simulation.These studies are divided into the following four parts.1.Effect of the odd viscosity on classic Faraday wave instability.The effect of odd viscosity on classic Faraday instability of the thin liquid film in an infinite horizontal plate is investigated by utilizing both linear Floquet theory and nonlinear lubrication theory based upon the weighted residual model.Based on the weighted residual model,the nonlinear evolution equations about flow rate and free surface height are derived,and linear stability analysis is performed again to achieve a damped Mathieu equation.Results show that the neutral stability curves derived from linear Floquet analysis agree well with those obtained by the Mathieu equation,especially in lower viscosity ratio;however,at a high viscosity ratio,the stability results of the latter method are more consistent with the long wave evolution.In addition,the presence of the odd viscosity brings several new characteristics,which completely disagree with the classical Faraday waves system.A unidirectional wave propagating in a horizontal direction appears at the interface without any horizontal force,that is,odd viscosity produces forces perpendicular to the direction of the imposed electric field.2.Electrostatically induced Faraday instability of perfect conductive thin film with spontaneous odd viscosity.Electrostatic Faraday waves induced by imposed vertical alternating electric field are examined in horizontal perfect conductive liquid films with spontaneous odd viscosity.Based on the nonlinear lubrication theory and the weighted residual model,the nonlinear evolution equations about the flow rate and free surface height are derived.The linear stability analyses of two cases of constant and varying wall potentials are performed by normal-mode analysis and Floquet theory.The effect of odd viscosity is investigated and the results show that odd viscosity plays a stabilizing role in the electrostatic Faraday system,but that has little effect on the wavelength of thin film.Furthermore,the Fourier spectrum method is utilized to numerically simulate the spatiotemporal evolution of thin liquid films.The Maxwell stress on the interface causes the harmonic oscillation frequency of the interface to be twice that of the applied electric field.Consistent with the previous conclusion,the numerical results display that the odd viscosity effect gives rise to the ‘sliding’ of wave configuration parallel to the wall,and then the interface wave translates into a travelling wave.3.External two frequencies electric field induced Faraday instability of thin leaky dielectric film with spontaneous odd viscosity.The interfacial stability of thin leaky dielectric liquid film with spontaneous odd viscosity is studied under the excitation of vertical two frequencies electric field.The fluidic nonlinear evolution equations are obtained by lubrication approximation and linear analysis and numerical simulation are carried out.It is found that the interface charges gather at the crest of the wave.However,in the external AC field,the charges gathered at the crest delay the change of the interface mode,which makes the periods of interface inconsistent with the external excitation.In addition,the interface stability regions excited by two frequencies electric field are greatly affected by parameters(such as amplitude ratio and phase),but it can bring rich interface modes.4.Electrostatically induced Faraday instability of surfactant-covered thin film with spontaneous odd viscosity.The interfacial stability of surfactant-covered thin liquid film with spontaneous odd viscosity is studied under the excitation of an extended electric field.The fluidic nonlinear evolution equations are obtained by lubrication approximation and linear analysis and numerical simulation are achieved.Surfactant,surface tension,electrical stress and odd viscosity effect compete with each other to affect the interface mode.It is found that the Ma number plays a great role in stabilizing the region,but the Pe number has little influence on the stable region,and both of the two dimensionless parameters do not change the wavelength of the fluid interface.The surfactant is consistent with the interface and does not change the periodicity of the interface.However,the transversely propagated waves at the interface caused by odd viscosity are limited by surfactants.