Nonlinear ultrasonic waves in bubbly liquids with nonhomogeneous bubble distribution: Numerical experiments

Abstract

This paper deals with the nonlinear propagation of ultrasonic waves in mixtures of air bubbles in water, but for which the bubble distribution is nonhomogeneous. The problem is modelled by means of a set of differential equations which describes the coupling of the acoustic field and bubbles vibration, and solved in the time domain via the use and adaptation of the SNOW-BL code. The attenuation and nonlinear effects are assumed to be due to the bubbles exclusively. The nonhomogeneity of the bubble distribution is introduced by the presence of bubble layers (or clouds) which can act as acoustic screens, and alters the behaviour of the ultrasonic waves. The effect of the spatial distribution of bubbles on the nonlinearity of the acoustic field is analyzed. Depending on the bubble density, dimension, shape, and position of the layers, its effects on the acoustic field change. Effects such as shielding and resonance of the bubbly layers are especially studied. The numerical experiments are carried out in two configurations: linear and nonlinear, i.e. for low and high excitation pressure amplitude, respectively, and the features of the phenomenon are compared. The parameters of the medium are chosen such as to reproduce air bubbly water involved in the stable cavitation process.

Sonochemical Treatment of Water Polluted by Chlorinated Organocompounds. A Review

“…The predictions are in reasonable agreement with the experimental results of Mark et al [93]. Other interpretations are linked to the self-attenuation of the acoustic field near the sonotrode tip: larger excitations produce more numerous and violently oscillating bubbles, which may act as a screen for the acoustic waves [94], and dissipate a larger energy [95].…”

Two-dimensional Numerical Simulations of Nonlinear Ultrasonic Propagation in Bubbly Liquids

“…This fact has already been observed by the authors in other numerical and experimental works referred to bubbly media [16,9], in particular when waves interferences occur [17,10,13]. The nonlinear bubble vibration strongly affects the distribution of energy in the frequency domain but not the distribution of energy in space, which remains highly concentrated at the focus.…”

“…The differential system is solved following the 2-D finite-differences scheme given in [14], except for boundary conditions (2), and included in the SNOW-BL code [9,15,10,13]. In this case the dimensionless variables are X = x/X fl , Y = y/, and Τ = co f t, where λ β =c 0l / f is the wavelength in the liquid at the driving frequency.…”

“…The presence of bubbles changes the behavior of the acoustic field [9][10][11]8], In this framework, numerical models for simulating the propagation of acoustic waves in liquids with oscillating bubbles which account for dissipation, dispersion, and nonlinearity are necessary to understand the acoustic phenomenon and its effects. The presence of bubbles changes the behavior of the acoustic field [9][10][11]8], In this framework, numerical models for simulating the propagation of acoustic waves in liquids with oscillating bubbles which account for dissipation, dispersion, and nonlinearity are necessary to understand the acoustic phenomenon and its effects.…”

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density

“…Correct wave equations are thereby essential for a sufficient understanding of the physics governing the wave behavior. A number of theoretical studies have intensively been performed (Kuznetsov et al, 1978;Commander and Prosperetti, 1989;Nigmatulin, 1991;Gumerov, 1992;Nakoryakov et al, 1993;Akhatov et al, 1996;Khismatullin and Akhatov, 2001;Liang et al, 2008;Vanhille and Campos-Pozuelo, 2009;Ando et al, 2011;Leroy et al, 2011;Grandjean et al, 2012;Louisnard, 2012;Sinelshchikov, 2013, 2014, to name a few), and various nonlinear wave equations describing weakly nonlinear phenomena were submitted. The KdVB equation (e.g., van Wijngaarden, 1968van Wijngaarden, , 1972 and the nonlinear Schr€ odinger (NLS) equation (e.g., Gumerov, 1992;Akhatov et al, 1996) are two well-known nonlinear equations for plane waves in uniform bubbly liquids.…”