Natural oscillations of a gas bubble in a liquid-filled cavity located in a viscoelastic medium

Abstract

The present study is motivated by cavitation phenomena that occur in the stems of trees. The internal pressure in tree conduits can drop down to significant negative values. This drop gives rise to cavitation bubbles, which undergo high-frequency eigenmodes. The aim of the present study is to determine the parameters of the bubble natural oscillations. To this end, a theory is developed that describes the pulsation of a spherical bubble located at the center of a spherical cavity surrounded by an infinite solid medium. It is assumed that the medium inside the bubble is a gas-vapor mixture, the cavity is filled with a compressible viscous liquid, and the medium surrounding the cavity behaves as a viscoelastic solid. The theoretical solution takes into account the outgoing acoustic wave produced by the bubble pulsation, the incoming wave caused by reflection from the liquid-solid boundary, and the outgoing wave propagating in the solid. A dispersion equation for the calculation of complex wavenumbers of the bubble eigenmodes is derived. Approximate analytical solutions to the dispersion equation are found. Numerical simulations are performed to reveal the effect of different physical parameters on the resonance frequency and the attenuation coefficient of the bubble oscillations.

Optimal subharmonic emission of stable bubble oscillations in a tube

“…Figure 6 shows the temporal evolution of the bubble radius for D/R 0 ≈ 19, K = 6.5 × 10 −4 ( kD ≈ 1.68), P a = 4, and We = 7. We observe that the amplitude of the oscillation is indeed larger than the results from DNS in an unbounded domain, indicating the appearance of local resonance established between the bubble and the tube wall similar to the one reported in previous works of bubbles in closed pores [39].…”

Radial oscillation and translational motion of a gas bubble in a micro-cavity

“…Bubble dynamics has been investigated for many years, and various models have been developed to describe the motion of bubbles in aqueous media [10] , [11] , [12] , near a rigid/elastic surface [13] , and in a tube [14] , [15] . In recent years, cavitation phenomena that occur in fully confined liquids has received more attention [16] , [17] , [18] , [19] , [20] , and models have been developed to understand the motion of fully confined bubbles in a liquid cavity, and the medium surrounding the cavity is considered to be an elastic/viscoelastic solid [21] , [22] , [23] , [24] , [25] , [26] , [27] . It is motivated mainly by applications in biology.…”

“…Sap cavitation occurs when the tree’s pumping system is operating under a negative pressure less than the threshold pressure [19] , [20] . For this interesting phenomenon, theoretical models of a bubble locate at the center of a spherical liquid cavity surrounded by solid medium were developed to investigate the behaviors of the bubble, such as the vibration frequency and attenuation of acoustic emissions related to cavitation bubbles inside trees [22] , [23] , [24] . In these researches, the breathing mode of cavitation bubbles is considered be the dominant mode, and it was found that the natural frequency of the bubble oscillation increases with the bubble radius, which is different from the case of unbounded liquid.…”

Accelerated Formation of H2 Nanobubbles from a Surface Nanodroplet Reaction

“…45,46 In particular, the formation of bubbles within confined nano/micro-fluids is a growing field which has largely only been discussed theoretically. [47][48][49][50][51][52] Experimentally, the cavitation of bubbles has been explored in droplets of the order ∼ 20-150 µm. [53][54][55] It is unclear how the droplet size influences the evolution of gas nanobubbles produced from a droplet reaction.…”