Exact solutions for the shape of a two-dimensional conducting liquid drop in a non-uniform electric field

2012 ◽  
Vol 241 (9) ◽  
pp. 921-928 ◽  
Author(s):  
N.M. Zubarev ◽  
O.V. Zubareva
Keyword(s):  
Electric Field ◽  
Exact Solutions ◽  
Liquid Drop ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Conducting Liquid

Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

On fluid motions induced by an electromagnetic field in a liquid drop immersed in a conducting fluid

1972 ◽  
Vol 51 (3) ◽  
pp. 585-591 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Flow Field ◽  
Electric Field ◽  
Lorentz Force ◽  
Liquid Drop ◽  
Conducting Fluid ◽  
Uniform Electric Field ◽  
Tangential Electric Field ◽  
Set Up

The deformation of a liquid drop immersed in a conducting fluid by the imposition of a uniform electric field is investigated. The flow field set up is due to the surface charge and the tangential electric field stress over the surface of the drop, and the rotationality of the Lorentz force which is set up by the electric current and the associated magnetic field. It is shown that when the fluids are poor conductors and good dielectrics the effects of the Lorentz force are minimal and the flow field is due to the stresses of the electric field tangential to the surface of the drop, in agreement with other authors. When, however, the fluids are highly conducting and poor dielectrics the effects of the Lorentz force may be predominant, especially for larger drops.

Effect of Quincke Rotation and Taylor Circulation on Mass Transfer from a Fluid Drop in a Constant Electric Field

2011 ◽  
Vol 312-315 ◽  
pp. 259-264
Author(s):  
Tov Elperin ◽  
A. Fominykh
Keyword(s):  
Mass Transfer ◽  
Electric Field ◽  
Similarity Transformation ◽  
Constant Electric Field ◽  
Analytical Form ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Convective Mass Transfer ◽  
Fluid Drop ◽  
Quincke Rotation

We consider non-stationary convective mass transfer in a binary system comprising a stationary dielectric two-dimensional fluid drop embedded into an immiscible dielectric liquid under the influence of a constant uniform electric field. The partial differential equation of diffusion is solved by means of a similarity transformation, and the solution is obtained in a closed analytical form. Dependence of Sherwood number vs. the strength of the applied electric field is analyzed. It is shown that an electric field can be used for enhancement of the rate of mass transfer in terrestrial and reduced gravity environments.

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