Capillary Instability of a Streaming Fluid - Core Liquid Jet Under Their Self Gravitating Forces (original) (raw)
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Il Nuovo Cimento B, 2001
The self-gravitating instability of a compressible-inviscid fluid cylinder immersed into a self-gravitating tenuous medium of negligible motion is developed. The stability criterion is derived based on the linear perturbation technique. Some previous reported works are recovered. The effect of different factors on the fluid cylinder instability is discussed. The compressibility has a tendency for a stabilizing the model in particular
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Il Nuovo Cimento B, 1991
The stability of a self-gravitating gas jet ambient with a selfgravitating liquid is discussed analytically and the results are confwmed numerically. A general eigenvalue relation describing the characteristics of the gas-core liquid jet, based on the linear perturbation techniques, is derived by employing the energy principle. It is found that the fluid densities ratio S plays an important role in the (de-)stabilizing of the present model. If 0 <~ S < 1 (S = s2/sl, where s2 is the liquid density and sl is the gas density), the model is unstable for certain values of the longitudinal wave number x (mainly 0 ~< x < 1.0668) and stable for the rest. However with increasing S values provided that 0 < S < 1 the unstable domain is fastly decreasing but never vanishing. As S> 1, unexpected results have been obtained according to which the model is unstable gravitationally not only for long wavelengths but also for very short wavelengths. These analytical results are interpreted physically and confLrmed numerically and the disturbance wave numbers at which stability as well as instability are tabulated. If S = 0 we recover the reported works in the literature. PACS 03.40.Gc -Fluid dynamics: general mathematical aspects.
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Journal of Magnetism and Magnetic Materials, 1991
there are stable as well as unstable regions and the latter are decreasing: with increasing p@)/p(') values in the domain 0 < p (2) /p (I) <1 and also with increasing thickness of the liquid shells but surroundmg the gas orifice and with the same value of p@)/p('). 0304-8853/91/$03.50 0 1991 -Elsevier Science Publishers B.V. (North-Holland)
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Applied Mathematical Modelling, 2009
The self-gravitating instability of a fluid cylinder pervaded by magnetic field and endowed with surface tension has been discussed. The dispersion relation is derived and some reported works are recovered as limiting cases from it. The capillary force is destabilizing only in the small axisymmetric domain and stabilizing otherwise. The magnetic field has a strong stabilizing effect in all modes of perturbation for all wavelengths. The self-gravitating force is destabilizing in the axisymmetric perturbation. However the magnetic field effect modified a lot the destabilizing character of the model and could overcome the capillary and self-gravitating instability of the model for all short and long wavelengths.
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The fundamental equations are formulated using cylindrical polar coordinates and then solved in the unperturbed state. The perturbation equations are determined, simplified, integrated and the constants of integrations are identified by applying appropriate boundary conditions across the perturbed fluid i~nterface. A cumbersome stability criterion for MHD inviscid compressible self-gravitating streaming fluid cylinder is derived. The magnetic field is stabilizing, the streaming is destabilizing while both of the self-gravitating and compressibility are stabilizing or not according to restrictions and that the gravitational instability of sufficiently long waves will persist. Several approximations are required to obtain Chandrasekhar's and Fermi's dispersion relation .
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Journal of Magnetism and Magnetic Materials, 1991
The electrodynamic instability of a self-gravitating dielectric fluid cylinder (density ~0 i ) surrounded by another self-gravitating dielectric fluid of different density pe pervaded by a radial varying electric field is investigated. A general eigenvalue relation valid to all possible modes of perturbation is derived, studied analytically and the results are confirmed numerically. The system is gravitationally marginal stable if pe = pi there will be stable and unstable domains as pe < pi and it is purely unstable for all (short and long) wavelengths if pe > pi in all axisymmetric and non-axisymmetric perturbations. The electric fields interior and exterior to the fluid cylinder are strongly stabilizing for all values of pi, pe, for all wavelengths. The restrictions required for suppressing the gravitational instability are identified; these results are interpreted physically. The results of Chandrasekhar and Fermi are recovered from ours as a limiting case. 0304-8853/91/$03.50 © 1991 -Elsevier Science Publishers B.V. (North-Holland)
Australian Journal of Physics, 1968
The instability of a self-gravitating fluid layer of finite thickness surrounded by another fluid of different density has been studied recently by Uberoi (1963) and Tassoul (1967)� under varying conditions. Now the condition can arise when the fluid inside the layer and the surrounding material are in relative horizontal motion. It is interesting to study the combined effects of the Kelvin-Helmholtz (KH) instability associated with short wavelengths and the gravitational instability associated with long wavelengths on this layer.
Effect of gravity on capillary instability of liquid jets
Physical Review E, 2013
The effect of gravity on the onset and growth rate of capillary instabilities in viscous liquid jets is studied. To this end, a spatial linear stability analysis of Cosserat's equations is performed using a multiscale expansion technique. A dispersion relation and expressions for the perturbation amplitude are derived to evaluate the growth rate of the most unstable axisymmetric disturbance mode. Modeling results are compared with classical results in the limit of zero Bond number, confirming the validity of this approach. Expressions for the critical Weber number, demarcating the transition between convective and absolute instability are derived as functions of capillary and Bond numbers. Parametric investigations for a range of relevant operating conditions (characterized by capillary, Weber, and Bond numbers) are performed to examine the jet breakup and the perturbation growth rate. In addition to the physical insight that is obtained from this investigation, the results that are presented in this work could also be of relevance as test cases for the algorithmic development and the verification of high-fidelity multiphase simulation codes.
Gravitational instability of cylinder with surface tension and self-gravitating
Abstract In this paper we study the stability of stable fluid of cylinder with some forces like intension, surface tension and self-gravitating. We write some problems and definitions about fluid and note the conditions of stability for. We write all the boundary conditions wish help to determine the constants of integration and we say the effect of self-gravitating and surface tension in the stability of fluid for axisymmetric and non-axisymmteric for different of velocity of fluid and this study determine by some figures for different values of M and and calculate this results by computer.