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.
Experimental study and direct numerical simulation of dynamics of an isothermal low-viscosity fluid are done in a coaxial gap of a cylindrical container making rotational vibrations relative to its axis. On the inner surface of the outer wall of the container, semicircular deflectors are placed regularly, playing the role of flow activators. As a result of vibrations, the activators oscillate tangentially. In the simulation a two-dimensional configuration is considered, excluding the end-wall effects. In the experiment a container with large aspect ratio is used. Steady streaming is generated in the viscous boundary layers on the activators. On each of the latter, beyond the viscous domain, a symmetric vortices pair is formed. The steady streaming in the annulus has an azimuthal periodicity. With an increase in the vibration intensity, a competition between the vortices occurs, as a result of which one of the vortices (let us call it even) approaches the activator and the other one (odd) rolls away and couples with the vortices from the neighbouring pairs. Streamlines of the odd vortices close on each other, forming a flow of a cogwheel shape that encircles the inner wall. Comparison of the experiment and the simulation reveals an agreement at moderate vibration intensity.
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