Abstract
Steady-state flow patterns and deformation modes of coaxial liquid columns in transverse electric fields are studied analytically. The governing creeping flow equations are solved for Newtonian and (mutually) immiscible fluids in the framework of leaky dielectric theory. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the columns, in terms of the direction of the external flow (top-to-sides/bottom-to-sides vs. sides-to-top/sides-to-bottom) and the number of vortices (single vortex vs. double vortices) in the shell, and that the senses of the net electric shear stresses at the inner and the outer interfaces and their relative importance are the key parameters in setting these patterns. Equilibrium shapes of the interfaces are also found and it is shown that there are four distinct modes of deformation, depending on the governing nondimensional parameters of the problem. The instability of the jet is also examined qualitatively using the observations pertaining the instability of single-phase drops and jets and the scaling arguments based on the present solution.
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A. Jaworek, Powder Technol. 10, 18 (2007).
R. Tao, K. Huang, H. Tang, D. Bell, Energy Fuels 22, 3785 (2008).
J.U. Park, M. Hardy, S.-J. Kang, K. Barton, K. Adair, D.K. Mukhopadhyay, C.-Y. Lee, M.S. Strano, A.G. Alleyne, J.G. Georgiadis, P.M. Ferreira, J.A. Rogers, Nat. Mater. 6, 782 (2007).
J.H. Wendorff, S. Agarwal, A. Greiner, Electrospinning: Materials, Processing, and Applications (Wiley-VCH, Weinheim, 2012).
Q. Wang, S. Mählmann, D.T. Papageorgiou, Phys. Fluids 21, 032109 (2009).
S. Gadkari, R. Thaokar, Int. J. Chem. Biol. Eng. 6, 102 (2012).
A.B. Basset, Am. J. Math. 16, 93 (1894).
J.R. Melcher, Field-Coupled Surface Waves (MIT Press, Cambridge, USA, 1963).
G.I. Taylor, Proc. R. Soc. London, Ser. A 313, 453 (1969).
D.A. Saville, Phys. Fluids 14, 1095 (1971).
D.A. Saville, J. Fluid Mech. 48, 815 (1971).
D.A. Saville, Phys. Fluids 13, 2987 (1970).
A.J. Mestel, J. Fluid Mech. 312, 311 (1996).
A.J. Mestel, J. Fluid Mech. 274, 93 (1994).
R.J. Turnbull, IEEE Trans. Ind. Appl. 32, 837 (1996).
P.H. Son, K. Ohba, Int. J. Multiphase Flows 24, 605 (1998).
J. Schneider, N. Lindblad, C. Hendricks, J. Crowley, J. Appl. Phys. 38, 2599 (1967).
A.L. Huebner, H.N. Chu, J. Fluid Mech. 49, 316 (1971).
R.J. Turnbull, IEEE Trans. Ind. Appl. 32, 1432 (1992).
F.J. Higuera, Phys. Fluids 22, 112107 (2010).
A. Ramos, H. González, A. Castellanos, Phys. Fluids 6, 3206 (1994).
R.H. Magarvey, L.E. Outhouse, J. Fluid Mech. 13, 151 (1962).
I.G. Loscertales, A. Barrero, I. Guerrero, R. Cortijo, M. Márquez, A.M. Gañán-Calvo, Science 295, 1695 (2002).
J.M. López-Herrera, A. Barrero, A. López, I.G. Loscertales, M. Márquez, J. Aerosol Sci. 34, 535 (2003).
Z. Sun, E. Suzzman, A.L. Yarin, J.H. Wendorff, A. Greiner, Adv. Mater. 15, 1929 (2003).
F. Li, X.-Y. Yin, X.-Z. Yin, J. Fluid Mech. 632, 199 (2009).
S. Paruchuri, M. Brenner, Phys. Rev. Lett. 98, 134502 (2007).
G. Taylor, Proc. R. Soc. London, Ser. A 280, 383 (1964).
P.H. Rhodes, R.S. Snyder, G.O. Roberts, J. Colloid Interface Sci. 129, 78 (1989).
M. Trau, S. Sankaran, D.A. Saville, I.A. Aksay, Langmuir 11, 4665 (1995).
N.M. Zubarev, O.V. Zubareva, Physica A 385, 35 (2007).
M.N. Reddy, A. Esmaeeli, Int. J. Multiphase Flow 35, 1051 (2009).
G.I. Taylor, Proc. R. Soc. London, Ser. A 291, 159 (1966).
J.R. Melcher, G.I. Taylor, Ann. Rev. Fluid Mech. 1, 111 (1969).
E. Lac, G.M. Homsy, J. Fluid Mech. 590, 239 (2007).
H.N. Oguz, S.S. Sadhal, Mech. Appl. Math. 42, 65 (1989).
J.W. Ha, S.M. Yang, Phys. Fluids 11, 1029 (1999).
T. Tsukada, J. Mayama, M. Sato, M. Hozawa, J. Chem. Eng. Jpn. 30, 215 (1997).
J.C. Baygents, D.A. Saville, in Drops and Bubbles: Third International Colloquium, edited by T.G. Wang (American Institute of Physics, New York, 1989).
J.C. Baygents, D.A. Saville, J. Colloid Interface Sci. 146, 9 (1991).
E. Zholkovskij, J.H. Masliyah, J. Czarnecki, J. Fluid Mech. 472, 1 (2002).
G. Supeene, C.R. Koch, S. Bhattacharjee, J. Colloid Interface Sci. 318, 463 (2008).
D.A. Saville, Ann. Rev. Fluid Mech. 29, 27 (1997).
D.D. Joseph, Arch. Ration. Mech. Anal. 51, 295 (1973).
L.G. Leal, Advanced Transport Phenomena (Cambridge University Press, New York, 2007).
J.W. Ha, S.M. Yang, J. Rheol. 44, 235 (2000).
S. Torza, R.G. Cox, S.G. Mason, Phil. Tran. R. Soc. London, Ser. A. 269, 295 (1971).
H.K. Yeoh, Q. Xu, O.A. Basaran, Phys. Fluids 19, 114111 (2007).
C.G. Garton, Z. Krasucki, Proc. R. Soc. London, Ser. A 280, 211 (1964).
C.E. Rosenkilde, Proc. R. Soc. London, Ser. A. 312, 473 (1969).
M.J. Miksis, Phys. Fluids 24, 1967 (1981).
J.D. Sherwood, J. Fluid Mech. 188, 133 (1988).
A. Behjatian, A. Esmaeeli, in preparation.
C.T. O’Konski, H.C. Thacher, J. Phys. Chem. 57, 955 (1953).
J.Q. Feng, T.C. Scott, J. Fluid Mech. 311, 289 (1996).
O.O. Ajayi, Proc. R. Soc. London, Ser. A 364, 499 (1970).
H.A. Stone, L.G. Leal, J. Fluid Mech. 211, 123 (1990).
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Behjatian, A., Esmaeeli, A. Flow patterns and deformation modes of coaxial liquid columns in transverse electric fields. Eur. Phys. J. E 36, 114 (2013). https://doi.org/10.1140/epje/i2013-13114-0
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DOI: https://doi.org/10.1140/epje/i2013-13114-0