Instability of gas-surrounded Rayleigh viscous jets: Weakly nonlinear analysis and numerical simulation

Abstract

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.

Minimal formulation of the linear spatial analysis of capillary jets: Validity of the two-mode approach

“…In this way, our results will be valid for a wider range of Weber numbers. These findings correct previous attempts found in the literature [8,9].…”

“…We can find in the literature several attempts to describe the breakup length as a function of impulsive conditions, some of them very recent [8,9], where the procedure is to look for an equivalent pure deformation condition. In García and González [7], the authors clarified this question.…”