A rotating spherical liquid drop in an electric field

1972 ◽  
Vol 56 (2) ◽  
pp. 305-312 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Electric Field ◽  
Equilibrium Shape ◽  
Dielectric Fluid ◽  
Inviscid Fluid ◽  
Axis Of Rotation ◽  
Field Parallel ◽  
Electric Field Parallel ◽  
Fluid Drop ◽  
The Stability ◽  
Small Deformations

It is shown that the equilibrium shape of an incompressible dielectric fluid drop rotating with constant angular velocity in the presence of a uniform external electric field of appropriate magnitude along the axis of rotation is spherical. For an inviscid fluid drop, the stability of this spherical configuration to small deformations is investigated by means of Chandrasekhar's virial method. We find that a rotating drop in the presence of an electric field parallel to the axis of rotation is, in some respects, more stable than when either only the electric field or only rotation is present. This is due to the fact that the application of an electric field parallel to the axis of a rotating drop, or of rotation parallel to an electric field in which a drop is immersed, shifts the instability mechanism to another normal mode.

Effect of Horizontal Alternating Current Electric Field on the Stability of Natural Convection in a Dielectric Fluid Saturated Vertical Porous Layer

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
B. M. Shankar ◽  
Jai Kumar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Prandtl Number ◽  
Traveling Wave ◽  
Effective Viscosity ◽  
Darcy Number ◽  
Wave Mode ◽  
Dielectric Fluid ◽  
Fluid Viscosity ◽  
The Stability

The stability of natural convection in a dielectric fluid-saturated vertical porous layer in the presence of a uniform horizontal AC electric field is investigated. The flow in the porous medium is governed by Brinkman–Wooding-extended-Darcy equation with fluid viscosity different from effective viscosity. The resulting generalized eigenvalue problem is solved numerically using the Chebyshev collocation method. The critical Grashof number Gc, the critical wave number ac, and the critical wave speed cc are computed for a wide range of Prandtl number Pr, Darcy number Da, the ratio of effective viscosity to the fluid viscosity Λ, and AC electric Rayleigh number Rea. Interestingly, the value of Prandtl number at which the transition from stationary to traveling-wave mode takes place is found to be independent of Rea. The interconnectedness of the Darcy number and the Prandtl number on the nature of modes of instability is clearly delineated and found that increasing in Da and Rea is to destabilize the system. The ratio of viscosities Λ shows stabilizing effect on the system at the stationary mode, but to the contrary, it exhibits a dual behavior once the instability is via traveling-wave mode. Besides, the value of Pr at which transition occurs from stationary to traveling-wave mode instability increases with decreasing Λ. The behavior of secondary flows is discussed in detail for values of physical parameters at which transition from stationary to traveling-wave mode takes place.

scholarly journals Effect of Horizontal AC Electric Field on the Stability of Natural Convection in a Vertical Dielectric Fluid Layer

2016 ◽  
Vol 9 (6) ◽  
pp. 3073-3086 ◽  
Author(s):  
B. M. Shankar ◽  
J. Kumar ◽  
I. S. Shivakumara ◽  
S. B. Naveen Kumar ◽  
◽  
...  
Keyword(s):  
Natural Convection ◽  
Electric Field ◽  
Fluid Layer ◽  
Dielectric Fluid ◽  
Ac Electric Field ◽  
The Stability

Surface instability of a dielectric fluid in an electric field

1968 ◽  
Vol 64 (4) ◽  
pp. 1203-1207 ◽  
Author(s):  
D. H. Michael
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Gravity Waves ◽  
Normal Mode Analysis ◽  
Horizontal Layer ◽  
Mode Analysis ◽  
Dielectric Fluid ◽  
Inviscid Fluid ◽  
Static Displacement ◽  
The Stability

This paper is a sequel to a recent paper (1) in which the author discussed gravity waves on a horizontal layer of conducting fluid with a normal electrostatic field at the free surface. In this work results are given for waves in an incompressible dielectric fluid, in a similar configuration. Treating the dielectric as an inviscid fluid the stability of the system is first described in terms of the changes in potential energy in a small static displacement. The result so obtained is then confirmed by a normal mode analysis in which a dispersion relation is obtained for the inviscid model. The paper gives finally a discussion of the results for a viscous dielectric fluid, the main point of which is that, as in (1), in the transition from stable to unstable disturbances viscosity plays no part, and that the stability characteristics are the same as those for an inviscid dielectric fluid.

A dielectric fluid drop in an electric field

1969 ◽  
Vol 312 (1511) ◽  
pp. 473-494 ◽  
Keyword(s):  
Electric Field ◽  
Applied Field ◽  
Dielectric Permeability ◽  
Uniform Electric Field ◽  
Dielectric Fluid ◽  
Equilibrium Configurations ◽  
Prolate Spheroids ◽  
Fluid Drop ◽  
Equilibrium Shapes ◽  
The Moment

In this paper an appropriate extension of the virial method developed by Chandrasekhar is used to systematically re-examine the equilibrium and stability of an incompressible dielectric fluid drop situated in a uniform electric field. The equilibrium shapes are initially assumed to be ellipsoidal; and it is shown that only prolate spheroids elongated in the direction of the applied field are compatible with the moment equations of lowest order. The relation between the equilibrium elongation a/b and the dimensionless parameter x = FR 1/2 /T 1/2 , where F is the applied field, R = ( ab 2 ) 1/2 , and T is the surface tension, is obtained for every dielectric permeability e . This relation is monotonic if e ≤ 20.801; but if 20.801 < e < ∞, there exist as many as three different equilibrium elongations (configurations) for some values of x less than 2.0966. Conditions for the onset of instability are obtained from an examination of the characteristic frequencies of oscillation associated with secondharmonic deformations of the equilibrium configurations. Dielectrics having e > 20.801 exhibit instability while those having e ≤ 20.801 do not. In the former case, where there are three different equilibrium configurations for the same value of x , only the middle one is unstable.

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