The dynamics of the interface between two immiscible liquids with a high viscosity contrast is studied experimentally when the liquids are pumped through a radial Hele-Shaw cell. Two cases are considered: a monotonous radial displacement of the viscous fluid, when the classical Saffman–Taylor instability develops, and an oscillatory interface motion due to harmonic flowrate modulation in the absence of the average displacement flow. At small amplitudes of flowrate modulation, the interface performs axisymmetric radial oscillations, maintaining the ring shape during the entire period, while with an increase in the amplitude, it loses stability in a threshold manner. In the phase of fluid displacement, finger instability develops at the interface in the form of an azimuthally periodic structure during a fraction of the period. Fingers reach the greatest length in the phase of maximum fluid displacement, while in the contraction phase (maximum displacement toward the cell center), the interface restores its concentric shape. The threshold for the occurrence of finger instability is determined by the relative amplitude of interface oscillations and under conditions of high contrast of viscosities (one liquid oscillates following the “viscous” law and the other obeys the “inviscid” law) coincides at different oscillation frequencies and different average radii of the interface. The discovered type of instability is new and is studied for the first time. A comparison of the wavelengths of the pulsating fingers with the well-known case of continuous displacement of a viscous fluid in a Hele-Shaw cell indicates that the Saffman–Taylor instability mechanism underlies the observed phenomenon.
The dynamics of the interface between two immiscible liquids with a high viscosity contrast is studied experimentally under steady displacement of interface and periodic variation of the flow rate of the pumped liquid in radial Hele-Shaw cell. Classic Saffman–Taylor instability, which develops when the viscous fluid is monotonously displaced by the inviscid one, is well known. In the present work, the excitation of Saffman–Taylor instability by means of oscillations of the liquid-liquid interface is demonstrated. The interphase boundary performs axisymmetric radial oscillations at small amplitude of oscillations and in the absence of an average pumping. With the growth of the amplitude of radial oscillations the interface instability is excited, which manifests itself in the development of an azimuthally periodic finger structure during a part of the period. “Finger-like” instability is determined by the relative amplitude of the oscillations of the interphase boundary and under the conditions of the performed experiments depends neither on the oscillation frequency nor on the radial size of the interface.
The dynamics of a phase inclusion in a coaxial liquid layer divided with a radial partition is studied experimentally. The working volume of the container is filled with a viscous liquid, inside which an air bubble, immiscible with the main phase, is injected. This inclusion has a lower density than the surrounding liquid does. The container performs rotational oscillations as a whole with the zero average rotation. Such a motion brings to the generation of a harmonically oscillating azimuthal shear flow, which, as a consequence, excites the oscillations of the phase inclusion. During the bubble’s oscillations, the displacement of its geometric center follows the sinusoidal law. On the background of such a motion a periodic deformation of the bubble is observed, i.e. the phase boundary starts oscillating. A new and surprising result of the experiments is found, when the light bubble sinks and takes a quasi-steady position near the inner wall of the layer.
The effect of large-amplitude translational vibrations on the dynamics of a two-phase system (light cylinder in liquid or two immiscible liquids, placed in a rotating cylindrical cavity) is studied experimentally. The experiments are run at high rotation rate, when under the action of centrifugal force the light phase is located near the rotation axis. Vibrations are perpendicular to the rotation axis and their frequency is close to the rotation rate. When the frequencies coincide, the vibrations change the centrifugal field configuration. The light phase column shifts stationary in the rotating frame of reference.
Dynamics of a centrifuged system of two immiscible liquids in a rotating cylinder is studied experimentally. In experiments, the liquids fill a horizontal cylindrical container with transparent walls that rotates about its axis. The study is carried out in the case of fast rotation when under the action of the centrifugal force the light liquid forms an axi-symmetric column on the container axis (core), while the heavy liquid is distributed along the cylindrical wall (annulus). The gravity makes the core shift radially by a small distance, which is practically invariant along the axis. This effect excites the tangential oscillations of the interface leading to the generation of azimuthal steady flows in the rotating frame of reference and to the differential rotation of the interface. The profile of azimuthal velocity has a "discontiunity", which appears on the limits of a viscous boundary layer formed at the interface. The maximum velocity is observed in the outer liquid near the interface. The analysis of the velocity profiles reveals that the liquid-liquid interface is the essential generator of the azimuthal flow in the annulus, while the Ekman pumping appears to affect the flow velocity inside the core. The results of the study may be helpful for the determination of the distribution of inclusions or species on the rotating interface.
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