Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31482
Viscous Potential Flow Analysis of Electrohydrodynamic Capillary Instability through Porous Media

Authors: Mukesh Kumar Awasth, Mohammad Tamsir

Abstract:

The effect of porous medium on the capillary instability of a cylindrical interface in the presence of axial electric field has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, viscosity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and porous medium both have stabilizing effect on the stability of the system.

Keywords: Capillary instability, Viscous potential flow, Porous media, Axial electric field.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335686

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1815

References:


[1] A. E. K. Elcoot, Electroviscous potential flow in nonlinear analysis of capillary instability, European J. of Mech. B/ Fluids 26, (2007) 431–443.
[2] A. R. F. Elhefnawy and G. M. Moatimid,The effect of an axial electric field on the stability of cylindrical flows in the presence of mass and heat transfer and absence of gravity, Phys. Scr. 50 (1994) 258–264.
[3] C. Weber, Zum Zerfall eines Flussigkeitsstrahles. Ztshr. angew., Math. And Mech. 11 (1931) 136–154.
[4] D. D. Joseph and T. Liao, Potential flows of viscous and viscoelastic fluids, J. Fluid Mechanics, 256 (1994) 1–23.
[5] L. Rayleigh, On the capillary phenomenon of jets, Proc. Roy. Soc. London A, 29 (1879) 71–97.
[6] L. Rayleigh, On the instability of a cylinder of viscous liquid under capillary force, Philos. Mag. 34 (1892) 145–154.
[7] M. K. Awasthi and G. S. Agrawal, Viscous contributions to the pressure for the Electroviscous potential flow analysis of capillary instability, Int. J. Theo. App. Multi. Mech., 2 (2011) 131–145.
[8] M. K. Awasthi and R. Asthana, Viscous potential flow analysis of capillary instability with heat and mass transfer through porous media, Int. Comm. Heat. Mass. Transfer (Accepted).
[9] P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press, Cambridge, 1981.
[10] Plateau, Statique experimentale et theorique des liquide somis aux seules forces moleculaire, vol. ii (1873) 231.
[11] R. Asthana and G. S. Agrawal, Viscous potential flow analysis of electrohydrodynamic Kelvin-Helmholtz instability with heat and mass transfer, Int. J. Engineering Science, 48 (2010) 1925–1936.
[12] S. Chandrashekhar, Hydrodynamic and Hydromagnetic Stability, Dover publications, New York, 1981.
[13] S. Tomotica, On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid Proc. Roy. Soc. London A, 150 (1934) 322–337.
[14] T. Funada and D. D. Joseph, Viscous potential flow analysis of Capillary instability, Int. J. Multiphase Flow, 28 (2002) 1459–1478.
[15] W. K. Lee and R. W. Flumerfelt, Instability of stationary and uniformly moving cylindrical fluid bodies. I. Newtonian systems, International Journal of Multiphase Flows 7(1981) 363-383.