The instability of a thin sheet of viscous and dielectric liquid moving in the same direction as an air stream in the presence of a uniform horizontal electric field has been carried out using viscous potential flow theory. It is observed that aerodynamic-enhanced instability occurs if the Weber number is much less than a critical value related to the ratio of the air and liquid stream velocities, viscosity ratio of two fluids, the electric field, and the dielectric constant values. Liquid viscosity has stabilizing effect in the stability analysis, while air viscosity has destabilizing effect. 1. Introduction The past decade has witnessed a rapid advancement in the study of instability of a liquid sheet because of its importance in several scientific and technological processes. Application of plane liquid sheets is an interesting phenomenon, which can be seen in power generation and propulsion systems [1], chemical and pharmaceutical processes [2], surface curtain coatings, and in the adhesive industry [3]. A host of efforts have been devoted to study the behavior of a thin liquid sheet sprayed with an air stream. The instability and breakup process of a thin inviscid liquid sheet in a stationary gaseous medium have been investigated by Squire [4] and Hagerty and Shea [5]. Their results show that the surface tension resists the development of instability in a liquid sheet. Fraser [6] has defined four modes of disintegration of a liquid sheet, namely, rim, wavy sheet, perforated sheet, and air impact. In rim, the disintegration takes place due to the contraction of the liquid sheet edges under the effect of surface tension. In wavy sheet, the disintegration occurs due to any small protuberance on the sheet which is subjected to two opposing forces: surface tension force, which draws the liquid back to the original undisturbed shape, and aerodynamic force, which pulls the liquid outward. If the aerodynamic force exceeds to the surface tension force, then any small disturbance present in the sheet will grow rapidly, causing sheet instability. In perforated sheet disintegration, disturbances on the sheet puncture it when the sheet becomes thin enough, and the resulting holes expand regularly by surface tension until they coalesce, forming threads. In air impact disintegration, the disruption of the liquid is very near to that of a twin-fluid nozzle, where two streams of air and liquid are caused to impinge together. Squire [4] has studied the disintegration according to the wavy sheet mode. Dombrowski and Johns [7] extended the above analysis including the
References
[1]
A. H. Lefebvre, Atomization and Sprays, Hemisphere, New York, NY, USA, 1989.
[2]
K. Masters, Spray Drying Handbook, Wiley, New York, NY, USA, 4th edition, 1985.
[3]
S. P. Lin and W. C. Liu, “Instability of film coating of wires and tubes,” AIChE Journal, vol. 21, no. 4, pp. 775–782, 1975.
[4]
H. B. Squire, “Investigation of the instability of a moving liquid film,” British Journal of Applied Physics, vol. 4, no. 6, article no. 302, pp. 167–169, 1953.
[5]
W. W. Hagerty and J. F. Shea, “A study of the stability of plane fluid sheets,” Journal of Applied Mechanics, vol. 22, p. 509, 1955.
[6]
R. P. Fraser, “The fluid kinetics of applications of pesticidal chemicals,” Advances in Pest Control Research, vol. 11, pp. 1–106, 1958.
[7]
N. Dombrowski and W. R. Johns, “The aerodynamic instability and disintegration of viscous liquid sheets,” Chemical Engineering Science, vol. 18, no. 3, pp. 203–214, 1963.
[8]
J. G. H. Joosten, A. Vrij, and H. M. Fijnaut, in Physicochemical Hydrodynamics, Proceedings of the International Conference on Physical Chemistry and Hydrodynamics, D. B. Spalding, Ed., vol. II, p. 639, Advance Publications, Guernsey, UK, 1978.
[9]
M. I. I. Rashed, M. A. Ghazi, and H. Elbanna, “Aerodynamic instability of a liquid sheet sprayed with an air stream,” Journal of Physics D, vol. 12, no. 10, article 009, pp. 1679–1684, 1979.
[10]
E. A. Ibrahim and S. L. Jackson, “Spatial instability of a liquid sheet in a compressible gas,” Journal of Colloid and Interface Science, vol. 180, no. 2, pp. 629–631, 1996.
[11]
E. A. Ibrahim and E. T. Akpan, “Liquid sheet instability,” Acta Mechanica, vol. 131, no. 3-4, pp. 153–167, 1998.
[12]
E. A. Ibrahim, “Instability of a liquid sheet of parabolic velocity profile,” Physics of Fluids, vol. 10, no. 4, pp. 1034–1036, 1998.
[13]
A. A. Ibrahim and M. A. Jog, “Nonlinear instability of an annular liquid sheet exposed to gas flow,” International Journal of Multiphase Flow, vol. 34, no. 7, pp. 647–664, 2008.
[14]
J. R. Melcher, Continuum Electromechanics, MIT Press, Cambridge, Mass, USA, 1981.
[15]
M. F. El-Sayed, “Electro-aerodynamic instability of a thin dielectric liquid sheet sprayed with an air stream,” Physical Review E, vol. 60, no. 6B, pp. 7588–7591, 1999.
[16]
D. D. Joseph and T. Y. Liao, “Potential flows of viscous and viscoelastic fluids,” Journal of Fluid Mechanics, vol. 265, pp. 1–23, 1994.
[17]
D. D. Joseph, J. Belanger, and G. S. Beavers, “Breakup of a liquid drop suddenly exposed to a high-speed airstream,” International Journal of Multiphase Flow, vol. 25, no. 6-7, pp. 1263–1303, 1999.
[18]
T. Funada and D. D. Joseph, “Viscous potential flow analysis of Kelvin-Helmholtz instability in a channel,” Journal of Fluid Mechanics, vol. 445, pp. 261–283, 2001.
[19]
M. K. Awasthi and G. S. Agrawal, “Viscous Potential flow analysis of Kelvin-Helmholtz instability of cylindrical interface,” International Journal of Applied Mathematics and Computation, vol. 3, no. 2, pp. 131–138, 2011.
[20]
A. M. Ardekani and D. D. Joseph, “Instability of stationary liquid sheets,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 13, pp. 4992–4996, 2009.
