Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

El‐Dib, Yusry O.; Matoog, R. T.

doi:10.1006/jcis.2000.6855

Cited by 15 publications

(16 citation statements)

References 37 publications

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“…Therefore, condition [37] is replaced by condition [42]. Using the boundary conditions [34]- [36] and [42], the solution of Laplace equation [7] yields another profile for the distribution of the electric potential φ 1 as given in the Appendix. Accordingly, Eq.…”

Section: Derivation Of the Characteristic Equationsmentioning

confidence: 99%

“…In deriving the characteristic equations when there are no surface charges on the unperturbed interfaces y = ±a, condition [20] will be taken into account. The electric conditions that have to be satisfied at y = ±a are conditions [34]- [37]; with these boundary conditions the solutions of Laplace equation [7] yield the distribution of the potential field φ in the three layers as given in the Appendix. At this stage the normal stress condition [41] yields…”

Section: Derivation Of the Characteristic Equationsmentioning

confidence: 99%

“…In the case of pure viscous flow, El-Dib (33) successfully applied this technique to the viscous fluid column stability, following Feng and Beard (32). In addition, the same technique has been successfully applied to Maxwellian-type viscoelastic fluid by El-Dib and Matoog (34).…”

Section: Introductionmentioning

confidence: 95%

See 2 more Smart Citations

Instability for Shearing of an Electrified Kelvin Fluid Sheet with or without Supporting Surface Charges

El‐Dib

2002

Journal of Colloid and Interface Science

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Section: Derivation Of the Characteristic Equationsmentioning

confidence: 99%

Section: Derivation Of the Characteristic Equationsmentioning

confidence: 99%

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Instability for Shearing of an Electrified Kelvin Fluid Sheet with or without Supporting Surface Charges

El‐Dib

2002

Journal of Colloid and Interface Science

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“…The absence of surface viscous forces leads to decay in the surface charge density and growth occurs in the stability. The variety of small viscoelastic effects of linear interfacial stability has been discussed by El-Dib and Matoog [23]. They discussed the influence of a vertical periodic electric field in the absence of surface charges.…”

Section: Introductionmentioning

confidence: 98%

Electrorheological Kelvin–Helmholtz instability of a fluid sheet

El‐Dib

Matoog

2005

Journal of Colloid and Interface Science

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“…In the KHI model, the streaming has a destabilizing influence through the linear approach as presented in the pioneer book of Chandrasekhar. 4 El-Dib and Matoog 5 have studied the KHI for the Maxwellian fluid sheet. In their analysis, they considered that the contributions of the weak viscoelastic effects are only demonstrated in the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium

2014

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Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted for different sets of physical parameters. A new stability as well as instability region, in the parameter space, appears due to the nonlinear effects.

show abstract

Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

Cited by 15 publications

References 37 publications

Instability for Shearing of an Electrified Kelvin Fluid Sheet with or without Supporting Surface Charges

Instability for Shearing of an Electrified Kelvin Fluid Sheet with or without Supporting Surface Charges

Electrorheological Kelvin–Helmholtz instability of a fluid sheet

Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium

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