Viscous instability of a sheared liquid-gas interface: Dependence on fluid properties and basic velocity profile

Abstract

In the framework of linear stability theory, we analyze how a liquid-gas mixing layer is affected by several parameters: viscosity ratio, density ratio, and several length scales. These scales reflect the presence of a velocity defect induced by the wake behind the splitter plate and the presence of boundary layers which develop ahead of the plate trailing edge. Incorporating such effects, we compute the various temporal and spatial instability modes and identify their driving instability mechanism based on their Reynolds number dependence, spatial structure, and energy budget. It is examined how the velocity defect modifies the temporal and the spatial stability properties. In addition, the transition from convective to absolute instability occurs at lower velocity contrast between gas and liquid free streams when a defect is present. This transition is also promoted by surface tension. Compared to inviscid stability computations, our spatial stability analysis displays a better agreement with measured growth rates obtained in two recent air-water experiments.

Vortices catapult droplets in atomization

“…In the case of two phase mixing layers, thanks to a large body of experimental evidence [9][10][11][12][13][14][15] , it is now well-established that the instability wavelength is governed by the gas boundary layer thickness δ g . Combining both experimental and numerical investigations, Otto et al 16 & Fuster et al 17 show that depending on the momentum ratio M = ρ g U 2 g /ρ l U 2 l (where ρ g , ρ l represent the gas and liquid density and U g , U l represent the gas and liquid freestream velocity), such an instability leads to a noise amplifier or a nonlinear global mode 18 that beats at a particular frequency. A two-stage mechanism for interface destabilization has been demonstrated by Marmottant and Villermaux 19 for co-axial gas-liquid jets.…”

Azimuthal shear instability of a liquid jet injected into a gaseous cross-flow

“…Recently, more advanced stability analyses have been exploited to understand other plausible modes of instability for two-phase parallel flows (e.g. Boeck & Zaleski 2005;Otto, Rossi & Boeck 2013). In this study, we present a theoretical investigation on the instabilities of a jet in cross-flow set-up.…”

Inviscid instability of two-fluid free surface flow down an incline

“…The above investigations [45,46,48] indicate that it is possible to gain insight into the perturbation growth mechanism in the present study by understanding the modal instabilities in terms of the interaction between the interfaces, namely the free surface with or without surface tension and the liquid-liquid interface with viscosity jump. The paper is organized as follows: Section 2 presents the governing equations, the base state profiles and the derivation of the dispersion relation.…”

“…There are also some earlier work relevant to the present study [45,46,48]. The viscous temporal stability problem of a planar gas-liquid mixing layer with a single interface and without confinement is analyzed by Yecko et al [45] and Boeck & Zaleski [46] for basic velocity profiles characterized by boundary layers adjacent to the interface.…”

“…The viscous linear stability analysis of the gas-liquid mixing layers considered by Otto et al [48] depends on the basic velocity profiles, the density ratio and on the Reynolds number. Their inviscid computations for growth rates is only favourable for low air velocities when the experimental frequencies are used and a small or moderate velocity deficit is incorporated.…”