Instability Of An Electrified Viscoelastic Sheet

The instability characteristic of the electrically viscoelastic fluid sheet is very of science and practical importance.In this study a linear instability analysis is performed for a viscoelastic liquid sheet under normal electrified field.The viscoelasticity of liquid is described by the Oldroyd-B constitutive model,and the liquid is supposed to be conducting.The dispersion relations are derived for both sinuous and varicose perturbations.The effects of the electrified field,the Weber number,the Reynolds number and the other parameters on the instability of the viscoelastic sheet are explored in the work.The numerical results of the temporal instability analysis shows that the viscoelastic sheet is more unstable than the corresponding Newtonian sheet.For the viscoelastic sheet,the growth rates of sinuous perturbations are larger than those of the varicose ones.The time constant ratio can enhance the stability of the viscoelastic fluid.The increase in Elastic number,the increase in Reynolds number or the increase in Weber number enhances the instability of the sheet.The effect of the electrified field,Weber number,Reynolds number and other parameters on the absolute and convective instability is also investigated.For sinuous disturbances,the instability of the electrified viscoelastic sheet has two kinds of modes.One named Mode 1 occurs in a small wavenumber region,and the other named Mode 2 occurs in a relatively large wavenumber region.Mode 1 is induced by electrified field,and Mode 2 is induced by the properties of the fluid itself.The Weber number and the Reynolds number have little effect on the instability of Mode 1.However,the Weber number,the Reynolds number and the electrified field all can influence the instability of Mode 2.The electrified field can enhance the instability of both Mode 1 and Mode 2.The increase in Weber number can enhance the instability of Mode 2 due to the stabilizing effect of surface tension.Increasing the Reynolds number can weaken the convective instability of Mode 2 with small Euler number,and can enhance the absolute instability of Mode 2 with large Euler number.The Euler number is the key parameter to determine the dominant unstable mode.As the Euler number increases,the dominant mode changes following the order of Mode 2-Mode 1-Mode 2.The increase of the Weber number can make the transitions occurs at smaller Euler number.And the increase of the Reynolds number can make the first transition occur at larger Euler number and the second transition occur with smaller Euler number.In this work,the dispersion relations of the electrified viscoelastic fluid including the integral electrified force are first derived for both sinuous mode and varicose mode.The effects of the electrified field,Weber number,Reynolds number and other parameters on the instability of the electrified viscoelastic liquid sheet are studied.At the same time,the mechanisms of the two instability modes of sinuous disturbances are clearly illuminated,and the competition between two modes for the dominant unstable mode is also studied for the first time.