Electrohydrodynamics

Melcher, James R.

doi:10.1007/978-3-642-65590-6_16

Cited by 12 publications

(6 citation statements)

References 67 publications

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“…Since the fluid layer is an ionic conductor, the conductivity varies with the local ion concentration. Accordingly, it has been shown by Melcher (1973) that the fluid conductivity could be described by…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

2009

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The stability of electrohydrodynamic flow between two horizontal plates with a vertical electrical conductivity gradient has been investigated in the presence of an imposed weak shear flow. The weak shear flow is driven by the horizontal pressure gradient, and the electrical conductivity gradient is generated by the concentration variation of the charge-carrying solute. An external electric field is applied across the fluid layer, and then the interaction between the unstable stratification of electrohydrodynamic flow and the shear arising from the plane Poiseuille flow is studied. A linear stability analysis has been implemented by considering both the longitudinal and transverse modes. Unlike the thermally stratified plane Poiseuille flow in which the longitudinal mode always dominates the onset of instability and is virtually unaffected by the superimposed shear flow, the instability of this mixed electrohydrodynamic–Poiseuille flow system is found to depend heavily on the shear flow, and the transverse mode may prevail over the longitudinal mode when the momentum of shear flow is sufficiently small. Particularly, an oscillatory longitudinal mode is found to exist, and it may become the critical mode when the conductivity gradient is small enough. The present results verify that an imposed weak shear flow may enhance the electrohydrodynamic instability in a fluid layer with electrical conductivity gradient.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

2009

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“…Taylor introduced the leaky dielectric model to account for the presence of (possibly weak) conduction processes in common dielectric fluids owing to the inevitable presence of ions. Typically the propagation time of electromagnetic waves is very fast compared to the times characteristic of the electrohydrodynamic motions (Melcher 1973) and thus, for times longer than the charge relaxation time 0 /σ, which is typically less than a second, any free charge is confined to the interfacial region. It follows that the electric field in the two fluid phases is irrotational (∇ ∧ E = 0, E = −∇φ) and so according to Gauss' law…”

Section: The Electric Fieldmentioning

confidence: 99%

Electrohydrodynamic deformation and interaction of drop pairs

1998

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The motion of two drops in a uniform electric field is considered using the leaky dielectric model. The drops are assumed to have no native charge and a dielectrophoretic effect favours translation of the drops toward one another. However, circulatory flows that stem from electrohydrodynamic stresses may either act with or against this dielectrophoretic effect. Consequently, both prolate and oblate drop deformations may be generated and significant deformation occurs near drop contact owing to enhancement of the local electric field. For sufficiently widely spaced drops, electrohydrodynamic flows dominate direct electrical interactions so drops may be pushed apart, though closely spaced drops almost always move together as a result of the electrical interaction or deformation.

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“…Note that we focused on the static wrinkling behaviour of electro-elastic plates, and that viscosity [43] of the conductive fluid was not considered.…”

Section: (B) Limitationsmentioning

confidence: 99%

The effect of an exterior electric field on the instability of dielectric plates

Chen

Dorfmann

et al. 2020

Proc. R. Soc. A.

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We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean dielectric plate, we show that a potential difference between the electrodes can induce a thinning of the plate and thus an increase of its planar area, similar to the scenarios encountered when there is no silicone oil. However, we also find that, depending on the material and geometric parameters, an increasing applied voltage can also lead to a thickening of the plate, and thus a shrinking of its area. In that scenario, Hessian instability and wrinkling bifurcation may then occur spontaneously once some critical voltages are reached.

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Electrohydrodynamics

Cited by 12 publications

References 67 publications

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

Electrohydrodynamic instability in a horizontal fluid layer with electrical conductivity gradient subject to a weak shear flow

Electrohydrodynamic deformation and interaction of drop pairs

The effect of an exterior electric field on the instability of dielectric plates

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