Capillary Instability of a Streaming Fluid - Core Liquid Jet Under Their Self Gravitating Forces

• Autorzy: Radwan, A. E. , Elmahdy, E. E.
• Języki publikacji: EN

Abstrakty

EN

The stability criterion of a fluid cylinder (density p) embedded into a different fluid (density p¹) is derived and discussed. The model is capillary unstable in the domain 0<xə as m = 0 where x and m are the axial and transverse wave numbers, while it is stable in all other domains. The densities ratio p¹ /p decreases the unstable domains but never suppress them. The streaming increases the unstable domains. Gravitationally, in m = 0 mode the model is unstable in the domain 0 < x < 1.0668 as p¹ < p, while as p¹ = p it is marginally stable but when p¹ > p the model is purely unstable for all short and long wavelengths. In m≠0 modes the self-gravitating model is neutrally stable as p = p¹ and ordinary stable as p¹ < p but it is purely unstable as p¹ > p. The streaming destabilizing effect makes the self-gravitating instability worse and shrinks the stable domains. The stability analysis of the model under the combined effect of the capillary and self-gravitating forces is performed analytically and verified numerically. When p¹ < p the capillary force and the axial flow have destabilizing influences but the densities ratio p¹/p has a stabilizing effect on the gravitating instability. If p = p¹ the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When p¹ > p the capillary force improved the gravitational instability and created much domains of stability and moreover the instability of the self-gravitating force disappeared in several cases of axisymmetric disturbances.

Słowa kluczowe

PL

kapilary; grawitacja

EN

capillary; streaming fluid; gravity forces

• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2005
• Tom: Vol. 9, nr 2
• Strony: 131--145
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Radwan, A. E.

• Mathematics Department, Faculty of Science, Ain-Shams University Cairo, Egypt,

autor

Elmahdy, E. E.

• Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

Bibliografia

• [1] Abramowitz, M and Stegun, I: Handbook of Mathematical Functions, (1970), Dover Publisher, New York.
• [2] Chandrasekhar, S and Fermi, E: Astrophysics. J., (1953), 118, 116.
• [3] Chandrasekhar, S: Hydrodynamic and Hydromagnetic Stability, (1981), Dover Publisher, New York.
• [4] Hertz, CH and Hermanrud, J: J. Fluid Mech., (1983), 131, 271.
• [5] Mayer, J and Weihs, D: J. Fluid Mech., (1987), 179, 531.
• [6] Petryanov, V and Shutov, A: Sov. Phys. Dokl., (1984), 29, 378.
• [7] Radwan, AE, Far East J. Appl. Math., (1997), 1, 193.
• [8] Radwan, AE: J. Magn. Magn. Matrs., (1991), 94, 311.
• [9] Radwan, AE: Appl.Sci., (1996), 15, 73.
• [10] Radwan, AE and Elogail, MA: Nuovo Cimento, (2003), 118B, 713.
• [11] Radwan, AE and Eltaweel, MA: Mechanics and Mechanical Engineering, (2004), 7, 127.
• [12] Radwan, AE: Applied Mathematics and Computation, (2005), 160, 213.
• [13] Rayleigh, JW: The Theory of Sound, (1945), Dover Publisher, New York.
• [14] Shutov, A: Fluid Dynamics, (1985), 20, 497.