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The instability of gas-surrounded Rayleigh viscous jets is investigated analytically and numerically in this paper. Theoretical analysis is based on a second-order perturbation expansion for capillary jets with surface disturbances, while the axisymmetric two-dimensional, two-phase simulation is conducted by applying the Gerris code for jets subjected to velocity disturbances. The relation between the initial surface and velocity disturbance amplitude was obtained according to the derivation of Moallemi et al. ["Breakup of capillary jets with different disturbances," Phys. Fluids 28, 012101 (2016)], and the breakup lengths resulting from these two disturbances agree well. Analytical and numerical breakup profiles also coincide satisfactorily, except in the vicinity of the breakup point, which shrinks forcefully. The effects of various parameters (i.e., oscillation frequency, Reynolds number, Weber number, and gas-to-liquid density ratio) have also been examined by comparing spatial growth rate, second-order disturbance amplitude, breakup length, and the breakup profiles at low frequency, where obvious satellite droplets form, versus different parameters. In addition, the competition between Rayleigh instability and Kelvin-Helmholtz instability has been examined using an energy approach. [ABSTRACT FROM AUTHOR]

This paper investigates the spatial instability of a double-layer viscous liquid sheet moving in a stationary gas medium. A linear stability analysis is conducted and two situations are considered, an inviscid-gas situation and a viscous-gas situation. In the inviscid-gas situation, the basic state of the entire gas phase is stationary and the analytical dispersion relation is derived. Similar to single-layer sheets, the instability of double-layer sheets presents two unstable modes, the sinuous and the varicose modes. However, the result of the base-case double-layer sheet indicates that the cutoff wavenumber of the dispersion curve is larger than that of a single-layer sheet. A decomposition of the growth rate is performed and the result shows that for small wavenumbers, the surface tension of all three interfaces and the aerodynamic forces of both the lower and upper gases contribute significantly to the unstable growth rate. In contrast, for large wavenumbers the major contribution to the unstable growth rate is only the surface tension of the upper interface and the aerodynamic force of the upper gas. In the viscous-gas situation, although the majority of the gas phase is stationary, gas boundary layers exist at the vicinity of the moving liquid sheet, and the stability problem is solved by a spectral collocation method. Compared with the inviscid-gas solution, the growth rate at large wavenumber is significantly suppressed. The decomposition of growth rate indicates that all the aerodynamic and surface tension terms behave consistently throughout the entire unstable wavenumber range. The effects of various parameters are discussed. In addition, the effect of gas viscosity and the gas velocity profile is investigated separately, and the results indicate that both factors affect the maximum growth rate and the dominant wavenumber, although the effect of the gas velocity profile is stronger than that of the gas viscosity. [ABSTRACT FROM AUTHOR]

This paper investigates the axisymmetric instability of a viscoelastic compound jet, for which the constitutive relation is described by the Oldroyd B model. It is found that a viscoelastic compound jet is more unstable than a Newtonian compound jet, regardless of whether the viscoelastic compound jet is inner-Newtonian-outerviscoelastic, inner-viscoelastic-outer-Newtonian, or fully viscoelastic. It is also found that an increase in the stress relaxation time of the inner or outer fluid renders the jet more unstable, while an increase in the time constant ratio makes the jet less unstable. An analysis of the energy budget of the destabilization process is performed, in which a formulation using the relative rate of change of energy is adopted. The formulation is observed to provide a quantitative analysis of the contribution of each physical factor (e.g., release of surface energy and viscous dissipation) to the temporal growth rate. The energy analysis reveals the mechanisms of various trends in the temporal growth rate, including not only how the growth rate changes with the parameters, but also how the growth rate changes with the wavenumber. The phenomenon of the dispersion relation presenting two local maxima, which occurred in previous research, is explained by the present energy analysis. [ABSTRACT FROM AUTHOR]

A weakly nonlinear stability analysis has been conducted for viscous planar liquid sheets moving in a resting inviscid gas medium by a perturbation expansion technique. In the first-order linear area, the disturbances are considered purely varicose. The solutions to the second-order interface displacement have been derived for both temporal instability and spatial instability analyses. It is found that the first harmonic of the fundamental varicose mode is also varicose, and the first-order and second-order varicose waves interact with each other, forming satellite ligaments and causing the eventual breakup of the liquid sheet at full-wavelength intervals of the fundamental wave. The interface deformation has been presented and the breakup time (or length) has been calculated in temporal (or spatial) instability analysis. The results indicate that liquid viscosity always weakens instability for all conditions in the varicose mode, which is different from viscosity that plays a dual role in instability for the sinuous mode concluded by previous researchers. In addition, an energy method is adopted both in the linear segment and nonlinear segment of the temporal instability analysis to further explain the mechanism of instability onset. [ABSTRACT FROM AUTHOR]