Nonlinear dynamics and breakup of compound jets

Abstract

Finite-amplitude deformation and breakup of a compound jet, whose core and shell are both incompressible Newtonian fluids, that is surrounded by a passive gas are analyzed computationally by a temporal analysis. The means is a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. The dynamics are initiated by subjecting the inner and the outer interfaces of a quiescent compound jet to axially periodic perturbations that are either in phase (ω=0) or π radians out phase (ω=π), where ω is the phase shift between the disturbances imposed on the two interfaces. The initial growth rates of disturbances obtained from computations are compared and demonstrated to be in excellent agreement with predictions of linear theory [Chauhan et al., J. Fluid Mech. 420, 1 (2000)]. Computations reveal that recirculating flows occur commonly during the deformation and pinch-off of compound jets, and hence render inapplicable the use of slender-jet type approximations for analyzing the dynamics in such cases. Moreover, as the deformations of one or both of the interfaces of the compound jet grow, the resulting shapes at the incipience of pinch-off are asymmetric and lead to the formation of satellite drops. Calculations are carried out over a wide range of Reynolds numbers of the core fluid, ratios of the viscosity and density of the shell fluid to those of the core fluid, ratio of the surface tension of the outer interface to the interfacial tension of the inner interface, the ratio of the unperturbed radius of the outer cylindrical interface to that of the inner cylindrical interface, wavenumber, and perturbation amplitudes to determine their effects on breakup time and whether both interfaces pinch at the same instant in time to result in the formation of compound drops. Conditions are also identified for which the dynamical response of compound jets subjected to initial perturbations with ω=0 differ drastically from those subjected to ones with ω=π.