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{"title":"Viscous Potential Flow Analysis of Electrohydrodynamic Capillary Instability through Porous Media","authors":"Mukesh Kumar Awasth, Mohammad Tamsir","volume":76,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":702,"pagesEnd":707,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/16793","abstract":"<p>The effect of porous medium on the capillary instability&nbsp;of a cylindrical interface in the presence of axial electric field has&nbsp;been investigated using viscous potential flow theory. In viscous&nbsp;potential flow, the viscous term in Navier-Stokes equation vanishes as<br \/>\r\nvorticity is zero but viscosity is not zero. Viscosity enters through normal&nbsp;stress balance in the viscous potential flow theory and tangential&nbsp;stresses are not considered. A dispersion relation that accounts for the&nbsp;growth of axisymmetric waves is derived and stability is discussed&nbsp;theoretically as well as numerically. Stability criterion is given by&nbsp;critical value of applied electric field as well as critical wave number.&nbsp;Various graphs have been drawn to show the effect of various physical&nbsp;parameters such as electric field, viscosity ratio, permittivity ratio on&nbsp;the stability of the system. It has been observed that the axial electric&nbsp;field and porous medium both have stabilizing effect on the stability&nbsp;of the system.<\/p>\r\n","references":"<p>[1] A. E. K. Elcoot, Electroviscous potential flow in nonlinear analysis of\r\ncapillary instability, European J. of Mech. B\/ Fluids 26, (2007) 431\u2013443.\r\n[2] A. R. F. Elhefnawy and G. M. Moatimid,The effect of an axial electric\r\nfield on the stability of cylindrical flows in the presence of mass and heat\r\ntransfer and absence of gravity, Phys. Scr. 50 (1994) 258\u2013264.\r\n[3] C. Weber, Zum Zerfall eines Flussigkeitsstrahles. Ztshr. angew., Math.\r\nAnd Mech. 11 (1931) 136\u2013154.\r\n[4] D. D. Joseph and T. Liao, Potential flows of viscous and viscoelastic\r\nfluids, J. Fluid Mechanics, 256 (1994) 1\u201323.\r\n[5] L. Rayleigh, On the capillary phenomenon of jets, Proc. Roy. Soc. London\r\nA, 29 (1879) 71\u201397.\r\n[6] L. Rayleigh, On the instability of a cylinder of viscous liquid under\r\ncapillary force, Philos. Mag. 34 (1892) 145\u2013154.\r\n[7] M. K. Awasthi and G. S. Agrawal, Viscous contributions to the pressure\r\nfor the Electroviscous potential flow analysis of capillary instability, Int.\r\nJ. Theo. App. Multi. Mech., 2 (2011) 131\u2013145.\r\n[8] M. K. Awasthi and R. Asthana, Viscous potential flow analysis of capillary\r\ninstability with heat and mass transfer through porous media, Int. Comm.\r\nHeat. Mass. Transfer (Accepted).\r\n[9] P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge\r\nUniversity Press, Cambridge, 1981.\r\n[10] Plateau, Statique experimentale et theorique des liquide somis aux seules\r\nforces moleculaire, vol. ii (1873) 231.\r\n[11] R. Asthana and G. S. Agrawal, Viscous potential flow analysis of\r\nelectrohydrodynamic Kelvin-Helmholtz instability with heat and mass\r\ntransfer, Int. J. Engineering Science, 48 (2010) 1925\u20131936.\r\n[12] S. Chandrashekhar, Hydrodynamic and Hydromagnetic Stability, Dover\r\npublications, New York, 1981.\r\n[13] S. Tomotica, On the instability of a cylindrical thread of a viscous\r\nliquid surrounded by another viscous fluid Proc. Roy. Soc. London A,\r\n150 (1934) 322\u2013337.\r\n[14] T. Funada and D. D. Joseph, Viscous potential flow analysis of Capillary\r\ninstability, Int. J. Multiphase Flow, 28 (2002) 1459\u20131478.\r\n[15] W. K. Lee and R. W. Flumerfelt, Instability of stationary and uniformly\r\nmoving cylindrical fluid bodies. I. Newtonian systems, International\r\nJournal of Multiphase Flows 7(1981) 363-383.<\/p>\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 76, 2013"}