Capillary instability of a streaming fluid-core liquid jet underself-gravitating forces

Abstract

The stability criterion of a fluid cylinder (density ρ(1)) embedded in a different fluid (density ρ(2)) is derived and discussed. The model is capillary unstable in the domain 0 < x < 1 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 ρ(2) / ρ(1) 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 ρ(2) < ρ(1), while as ρ(2) = ρ(1) it is marginally stable but when ρ(2) > ρ(1) the model is purely unstable for all short and long wavelengths. In m ≠ 0 modes, the self-gravitating model is neutrally stable as ρ(1) = ρ(2), ordinarily stable as ρ(2) < ρ(1), but is purely unstable as ρ(2) > ρ(1). 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 ρ(2) < ρ(1) the capillary force and the axial flow have destabilizing influences but the ratio of the densities ρ(2) / ρ(1) has a stabilizing effect on the gravitating instability. If ρ(1) = ρ(2), the streaming is destabilizing but the capillary force is strongly stabilizing and could suppress the gravitational instability. When ρ(2) > ρ(1) the capillary force improves the gravitational instability and creates domains of much stability and moreover the instability of the self-gravitating force disappears in several cases of axisymmetric disturbances. PACS No.: 47.17+e