Dynamics of a bubble in oscillating viscous liquid

Abstract

This article is devoted to the investigation of gaseous bubble dynamics in oscillating viscous liquids of different density values. The study is conducted numerically using the level-set method with a non-stationary approach. The bubble is initially located near the upper wall of the container. The effects of the inclusion and host liquid viscosities on interaction of the bubble with the wall are analysed. The calculations show that in the absence of gravity, for low-viscosity fluids the bubble is attracted to the nearest wall, which is consistent with previous analytical and experimental results. With increasing viscosity, the vibrational attraction to the wall becomes weaker and is then replaced by repulsion, which can be explained by the decelerative effect of viscosity in the boundary layer near the rigid surface, where the average flow becomes less intensive. The dependencies of the repulsion force on the parameter values are obtained by using the balance method (investigation of the gravity level needed to attain the quasi-equilibrium state at a certain distance between the bubble and the wall). The calculations show that the repulsion force grows with decreasing Reynolds number (increase of the viscosity). This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.

The Shape of a Compressible Drop on a Vibrating Solid Plate

“…Our calculations demonstrated that under vibrations, drop height decreases, and the base area increases (see Figure 9). This result was predictable, since the tendency to maximize the cross-sectional area perpendicular to the vibration axis is typical for many fluid systems [4,13,27]. However, the dependence of the amplitude of the top point of the drop on frequency, shown in Figure 10, is not monotonic near resonance of drop volume oscillations.…”

“…Influence of viscosity on the vibration-induced motion of a gas bubble near a solid wall was reported in [13]. It has been observed that with the increase in viscosity, the vibrational attraction to the wall diminishes, subsequently being replaced by repulsion.…”

On the relationship between solid particle attractors and thermal inhomogeneities in vibrationally driven fluid-particle systems

“…Such a sinusoidal displacement dynamically enforces an acceleration g(t) varying with the same sinusoidal law in time and an amplitude given by the product of b and the square of the angular frequency, i.e., bx 2 . 14,38 This dynamical effect can be directly incorporated into the momentum balance equation through the standard Boussinesq approximation valid for liquids. The flow driving force, therefore, reduces to a source term qg(t) at the right-hand side of this equation where the fluid density q is replaced by a simplified expression by which it is assumed to scale linearly with the temperature.…”

“…Remarkably, the industrial relevance of these facts, in conjunction with the appeal that the related spatiotemporal behaviors exert on scholars at a more fundamental level, has stimulated the development of dedicated experimental and theoretical lines of inquiry, and resulted in a sound understanding of the underlying cause-and-effect relationships. 7,[9][10][11][12][13][14] Owing to space limitations, we do not strive to review all the aspects of the existing research on these subjects. Rather, we concentrate on a relatively recent avenue where new principles to design novel particle management technologies in fluid flow have been sought by leveraging the spontaneous ability of solid particles to undergo separation, sorting, and accumulation due to their inertial properties (finite size and mass).…”

Introduction to ‘New trends in pattern formation and nonlinear dynamics of extended systems’

“…A multiphase medium is another kind of physical system sensitive to vibrations. The interaction of a bubble with container walls in an oscillating viscous liquid is studied in [ 11 ]. The interface is described by means of the level set method.…”