Article

# Electrohydrodynamic linear stability of two immiscible fluids in channel flow

Electrochimica Acta 04/2006; 51206585(85). DOI: 10.1016/j.electacta.2006.02.002

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**ABSTRACT:**In this paper, we have discussed the linear stability analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the effects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical parameter β is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of interfacial structures are more sensitive to the variation of the β corresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing β, has a dual role in-fluence (de-stabilizing effects) depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is exchanged to a regularly stabilizing influence at small values of such coefficient.Acta Mechanica Sinica 28(6). · 0.69 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider nonlinear aspects of the flow of an inviscid two-dimensional jet into a second immiscible fluid of different density and unbounded extent. Velocity jumps are supported at the interface, and the flow is susceptible to the Kelvin–Helmholtz instability. We investigate theoretically the effects of horizontal electric fields and surface tension on the nonlinear evolution of the jet. This is accomplished by developing a long-wave matched asymptotic analysis that incorporates the influence of the outer regions on the dynamics of the jet. The result is a coupled system of long-wave nonlinear, nonlocal evolution equations governing the interfacial amplitude and corresponding horizontal velocity, for symmetric interfacial deformations. The theory allows for amplitudes that scale with the undisturbed jet thickness and is therefore capable of predicting singular events such as jet pinching. In the absence of surface tension, a sufficiently strong electric field completely stabilizes (linearly) the Kelvin–Helmholtz instability at all wavelengths by the introduction of a dispersive regularization of a nonlocal origin. The dispersion relation has the same functional form as the destabilizing Kelvin–Helmholtz terms, but is of a different sign. If the electric field is weak or absent, then surface tension is included to regularize Kelvin–Helmholtz instability and to provide a well-posed nonlinear problem. We address the nonlinear problems numerically using spectral methods and establish two distinct dynamical behaviors. In cases where the linear theory predicts dispersive regularization (whether surface tension is present or not), then relatively large initial conditions induce a nonlinear flow that is oscillatory in time (in fact quasi-periodic) with a basic oscillation predicted well by linear theory and a second nonlinearly induced lower frequency that is responsible for quasi-periodic modulations of the spatio-temporal dynamics. If the parameters are chosen so that the linear theory predicts a band of long unstable waves (surface tension now ensures that short waves are dispersively regularized), then the flow generically evolves to a finite-time rupture singularity. This has been established numerically for rather general initial conditions.Zeitschrift für angewandte Mathematik und Physik ZAMP 01/2012; 63(1). · 0.94 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we study the linear stability of the interface between an Upper Convective Maxwell fluid and a hydrodynamically passive fluid subject to an electric field applied either parallel or normal to the flat interface between the two fluids. The fluids are leaky-dielectric and we apply surface-coupled model. We solve the model equations analytically and study the dispersion and neutral curves for various parameters representing the applied potential, the fluid’s elasticity, the physical and the electrical properties of the fluids, and the heights of the fluids in the presence of both normal and parallel electric fields. It is found that the critical wavenumber is independent of the Weissenberg number. However, increasing the Weissenberg number increases the maximum growth rate for both the normal and the parallel fields. The critical wavenumber increases with the dimensionless applied voltage for the normal field. Lastly for the normal field, for some values of the dimensionless parameters, the growth rate reached very large values representing some type of singularity as has been observed in the literature. However, for the same values of the parameters no singularity is observed for the parallel field.The European Physical Journal Special Topics 219(1). · 1.80 Impact Factor

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