Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

Abstract

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed viscoelastic Walters B= dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg-Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of twodimensional disturbances. While in the nonlinear analysis, for both two-and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.Résumé : La méthode d'analyse du potentiel d'écoulement nous permet d'étudier l'instabilité électrodynamique non linéaire de type Kelvin-Helmholtz, de deux fluides diélectriques viscoélastiques de type Walter B= superposés, en présence d'un champ électrique tangentiel. Nous utilisons la méthode à échelles multiples pour obtenir la relation de dispersion du problème linéaire, alors que l'équation non linéaire de Ginzburg-Landau avec coefficients complexes pour le problème non linéaire. Nous obtenons et discutons les conditions de stabilité pour les cas linéaire et non linéaire, analytiquement et numériquement. Dans l'analyse de stabilité linéaire, nous trouvons que les vitesses de fluide et les viscosités cinématiques ont des effets déstabilisants, alors que le champ électrique, les viscoélasticités cinématiques et la tension superficielle sont stabilisants. Le système est plus stable contre les perturbations tridimensionnelles que contre les perturbations bidimensionnelles. Dans le cas non linéaire, pour des perturbations en deux et trois dimensions, nous trouvons que les vitesses de fluide, la tension superficielle et les viscosités cinématiques sont déstabilisants, alors que le champ électrique, les viscoélasticités cinématiques sont stabilisants. De plus, le système est plus instable dans son comportement sous perturbations en trois dimensions qu'en deux dimensions pour la plupart des paramètres physiques, sauf les viscosités cinématiques. [Traduit par la Rédaction]

Nonlinear EHD Instability of Two-Superposed Walters’ B Fluids Moving through Porous Media

“…El has a stabilizing influence on the considered system in the occurrence of a vertical electric field. This result is in conformity with that which was gained earlier by El-Sayed et al [38].…”

“…To this end, our interest focuses on the inequality of Equation (38). For this objective, the potential Bond number 2  Log will be designed against the wavenumber k of the surface waves.…”

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“…For recent surveys regarding the developments of linear and nonlinear electromagnetic flows in porous media, see refs. [26][27][28][29][30][31][32][33][34][35][36].…”

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