Stability of interface between liquids with high viscosity contrast in unevenly rotating cavity

Abstract

The effect of modulation of the cavity rotation rate on the interface of liquids of different densities and high viscosity contrast is studied experimentally. The cavity is a short horizontal cylinder rotating around its axis. The end walls of the cavity form a narrow gap. Under uniform rotation the interface has an axisymmetric shape. With the modulation growth, the axisymmetric boundary loses stability. Instability manifests itself in the appearance of a regular quasistationary relief at the interphase. The relief excitation is associated with the Kelvin-Helmholtz instability. Tangential velocity discontinuity under modulation arises due to various interaction of liquids with the cavity end walls because of viscosity contrast. The viscosity contrast, on the one hand, is responsible for tangential velocity discontinuity; on the other, it has a significant effect on the threshold of Kelvin-Helmholtz instability. It results in decrease of stability threshold and an increase of relief wavelength.

Liquid free boundary in vertical gap subject to modulated rotation

“…In the case when liquids are in cramped channels (slot gaps), as a result of different interaction with the boundaries of the cavity, liquids of different viscosities perform inertial oscillations in the cavity reference system with different amplitudes, which is accompanied by the manifestation of averaged forces acting on the interphase boundary. In a slot gap that rotates unevenly around the axis normal to the gap, at a certain ratio of the modulation frequency and the rotation rates, the stable interface of liquids formed by centrifugal force changes its axisymmetric shape [2,3]. The movement of liquids in a slot channel (Hele-Shaw cell) simulates movement in a porous medium.…”

“…The movement of liquids in a slot channel (Hele-Shaw cell) simulates movement in a porous medium. Thus, the results of [2,3] are important, in particular, for understanding the processes occurring at the interphase boundaries in the case of applying the method of oscillatory action on the interface of liquids of different viscosities in slot channels [4] and for oil recovery improvement [5].…”

Experimental study of liquids interface oscillatory dynamics in rotating slot gap

“…The vibrational dynamics of multiphase systems is of great scientific interest, especially in the case of liquids with a high viscosity contrast. The latter is clearly manifested in porous media and narrow slotted gaps, when a high-viscosity liquid vibrates with the cavity, while a low-viscosity liquid moves as an inviscid one during the vibrations [1]. In oscillating inertial force fields, as a result of different interactions with the cavity boundaries, the liquids of different viscosities oscillate in the reference frame of the cavity with different amplitudes.…”

“…In oscillating inertial force fields, as a result of different interactions with the cavity boundaries, the liquids of different viscosities oscillate in the reference frame of the cavity with different amplitudes. The loss of stability of the interface and the appearance of a quasi-stationary relief at the interface of liquids in a non-uniformly rotating Hele-Shaw cell were discovered and described in [1]. It was shown that the generation of the relief is explained by the Kelvin-Helmholtz instability of the interface between two liquids undergoing oscillating tangential motion [2].…”

“…The studies mentioned correspond to the translational vibrations of the systems. In [1] it is shown that in the slotted gap, which performs modulated rotation according to the law…”