The relaxation-time limit in the compressible Euler–Maxwell equations

2011 ◽  
Vol 74 (18) ◽  
pp. 7005-7011 ◽  
Author(s):  
Jianwei Yang ◽  
Shu Wang ◽  
Juan Zhao
Keyword(s):  
Relaxation Time ◽  
Maxwell Equations ◽  
Time Limit ◽  
Compressible Euler

Instability of a viscous coflowing jet in a radial electric field

2008 ◽  
Vol 596 ◽  
pp. 285-311 ◽  
Author(s):  
FANG LI ◽  
XIE-YUAN YIN ◽  
XIE-ZHEN YIN
Keyword(s):  
Relaxation Time ◽  
Electric Field ◽  
Thin Layer ◽  
Euler Number ◽  
Radial Electric Field ◽  
Dispersion Relations ◽  
Time Limit ◽  
Liquid Viscosity ◽  
Electrical Relaxation ◽  
Thin Layer Approximation

A temporal linear instability analysis of a charged coflowing jet with two immiscible viscous liquids in a radial electric field is carried out for axisymmetric disturbances. According to the magnitude of the liquid viscosity relative to the ambient air viscosity, two generic cases are considered. The analytical dimensionless dispersion relations are derived and solved numerically. Two unstable modes, namely the para-sinuous mode and the para-varicose mode, are identified in the Rayleigh regime. The para-sinuous mode is found to always be dominant in the jet instability. Liquid viscosity clearly stabilizes the growth rates of the unstable modes, but its effect on the cut-off wavenumber is negligible. The radial electric field has a dual effect on the modes, stabilizing them when the electrical Euler number is smaller than a critical value and destabilizing them when it exceeds that value. Moreover, the electrical Euler number and Weber number increase the dominant and cut-off wavenumbers significantly. Based on the Taylor–Melcher leaky dielectric theory, two limit cases, i.e. the small electrical relaxation time limit (SERT) and the large electrical relaxation time limit (LERT), are discussed. For coflowing jets having a highly conducting outer liquid, SERT may serve as a good approximation. In addition, the dispersion relations under the thin layer approximation are derived, and it is concluded that the accuracy of the thin layer approximation is closely related to the values of the dimensionless parameters.

scholarly journals Switching behavior of a Stoner particle beyond the relaxation time limit

2000 ◽  
Vol 61 (5) ◽  
pp. 3410-3416 ◽  
Author(s):  
M. Bauer ◽  
J. Fassbender ◽  
B. Hillebrands ◽  
R. L. Stamps
Keyword(s):  
Relaxation Time ◽  
Time Limit ◽  
Switching Behavior
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