Interaction between gases and liquids in hollow, compound jets at low Reynolds numbers

Perturbation methods based on the slenderness ratio are used to develop the leading-order fluid dynamics equations of hollow, compound jets at low Reynolds numbers when the gases enclosed by these jets behave in a polytropic manner. It is shown that the leading-order equations are one-dimensional, and analytical solutions to the steady state equations are possible in several flow regimes. A linear stability analysis is employed to determine the eigenvalue problem, while a weakly nonlinear stability analysis' indicates that there is a supercritical Hopf bifurcation. Numerical studies indicate that the nonlinear dynamics of hollow, compound jets at low Reynolds numbers is affected by the compressibility of the gases enclosed by the jet and that the jet's shape and axial traction forces respond in an almost modulated manner.