Suppression of the capillary instability in the Rayleigh–Taylor slot problem

Abstract

Stability of capillary-gravity interfacial waves between two bounded fluidsThe classical Rayleigh-Taylor instability for an interface of finite extent is modified by two independently controlled perturbation effects. A component of gravitational acceleration tangent to the interface is imposed and the interface is subjected to a flow-induced pressure field. The stability of the flat horizontal interface when surface tension holds heavier liquid above ambient gas is considered in a 2D model problem. The two perturbations are realized by tilting the interface to the horizontal and by inducing a flow with shear. It is found that the effect of tilt angle or shear on its own is destabilizing, while together, in the right combination, they can stabilize. It is thereby shown how to extend the stability limit over the classical Rayleigh-Taylor result. The framework for the analysis is the classical unperturbed pitchfork bifurcation ͑codimension 2͒. The coefficients in the unfolding are calculated by applying the Lyapunov-Schmidt technique to a pinned deformable interface that holds a shear-induced lubrication flow.

Stability of slender liquid bridges subjected to axial flows

“…The codimension-2 nature of the subcritical pitchfork gives an additional independent control parameter and thus provides access to a greater range of nonlinear behaviour. We remark that this nonlinear stabilization concept has also been predicted for the Rayleigh-Taylor instability in two contexts: a two-dimensional slot (Chen & Steen 1996a) and a Hele-Shaw thermal cell (Chen & Steen 1996b). In both cases, tilt angle and flow-induced pressures are the competing perturbations.…”

Drop fall-off from pendent rivulets

“…However, numerical search for blow-up behaviour is extremely tedious and an analytical estimate of its existence would be most convenient. Oron & Rosenau (1989) and Chen & Steen (1996) examined the existence of saturated small-amplitude solutions to the lubrication equations and use that as a sufficient condition for blow-up not to occur -their non-existence is a necessary condition for blow-up. Their saturated solutions are assumed to be either spatially periodic or confined to a finite box to simplify the bifurcation analysis.…”

Stabilizing the Interface in the Rayleigh–Taylor and the Saffman–Taylor Problems by Heating

“…Stabilization by evaporation has been demonstrated by Schubert and Straus 2 and by Adham-Khodaparast 3 et al; stabilization by combining two imperfections has been shown by Chen and Steen. 4 Rasenat 5 et al have shown that a stable density difference across a surface can stabilize two layers which, on average, are RayleighÀTaylor unstable.…”