Effect of direct bubble-bubble interactions on linear-wave propagation in bubbly liquids

Abstract

We study the influence of bubble-bubble interactions on the propagation of linear acoustic waves in bubbly liquids. Using the full model proposed by Fuster and Colonius [J. Fluid Mech. 688, 253 (2011)], numerical simulations reveal that direct bubble-bubble interactions have an appreciable effect for frequencies above the natural resonance frequency of the average size bubble. Based on the new results, a modification of the classical wave propagation theory is proposed. The results obtained are in good agreement with previously reported experimental data where the classical linear theory systematically overpredicts the effective attenuation and phase velocity.

Nonlinear acoustic propagation in bubbly liquids: Multiple scattering, softening and hardening phenomena

“…As expected, high-frequency waves propagate more quickly than lowfrequency waves. This is a well-known behaviour already observed numerically and experimentally [12,20,25]. By comparing two different time steps, one can observe low frequency oscillations due to the local effect of the bubble dynamics (typically on the interval x = [0, 2]mm).…”

“…Many physical phenomena can play a role on bubble dynamic response and the propagation of waves through bubbly liquids: heat and mass transfer effects [17], direct bubble-bubble interactions, fragmentation, or polydispersity are some examples of complex processes that should be correctly modeled for real applications [18,19,20]. Here, in order to investigate the influence of weakly nonlinear bubble oscillations on the propagation of waves, we choose the simplest model able to reproduce these effects.…”

A Review of Models for Bubble Clusters in Cavitating Flows

“…General solutions accounting for frequency effects have been reviewed by Commander & Prosperetti [38] finding good agreement between previously reported experimental results and theoretical predictions for the case of pure gas bubbles. This limiting solution can be used to validate numerical codes [8,69,70,57]. Extensions of the theory to account for the effect of direct bubblebubble interactions have been numerical reported in [70].…”

“…This limiting solution can be used to validate numerical codes [8,69,70,57]. Extensions of the theory to account for the effect of direct bubblebubble interactions have been numerical reported in [70].…”

Optimal subharmonic emission of stable bubble oscillations in a tube

“…Supposing that (i) the bubble radius is small in comparison with the wavelength of the external driving pressure and (ii) the averaged distance between the bubbles is small compared to the wavelength, the interaction term is usually calculated taking advantage of the incompressible assumption in the bubble near field [23][24][25][26]. This approach is problematic when the number of bubbles is large because the interaction term diverges [27,28] and one needs to introduce a cutoff distance within which bubble-bubble interactions effectively occur [29]. An alternative physical approach to resolve the paradox is to account for liquid compressibility [30].…”