Oscillations of small bubbles and medium yielding in elastoviscoplastic fluids

Abstract

We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluids and driven by an acoustic pressure field. We model the rheological behavior of the yield-stress fluid using the recently developed elasto-visco-plastic (EVP) constitutive equation that takes into account the elastic and visco-plastic deformations of the material [P. Saramito, J. NonNewton. Fluid Mech.158 (1-3) (2009) pp. 154161]. Assuming that the bubble remains spherical during the pressure driving, we reduce the problem to a set of ODEs and an integrodifferential equation, which we solve numerically for the case of two yield stress fluids, a soft Carbopol gel and a stiffer Kaolin suspension.We find that, depending on the amplitude and frequency of the pressure field, the radial oscillations of the bubble produce elastic stresses that may or may not suffice to yield the surrounding material.We evaluate the critical amplitude of the acoustic pressure required to achieve yielding and we find a good agreement between numerical simulations and an analytical formula derived under the assumption of linear deformations. Finally, we examine the bubble oscillation amplitude for a very wide range of applied pressures both below and above the critical value to assess the impact of yielding on the bubble dynamics. This analysis could be used to identify a signature of yielding in experiments where the radial dynamics of a bubble is measured. More generally, these results can be used to rationalize the optimal conditions for pressure-induced bubble release from yield-stress fluids, which is relevant to various biomedical and industrial applications, including oil industry and food processing.

Acoustic bubble dynamics in a yield-stress fluid

“…While the shape of the yielded region has been investigated in great detail for passive bubble rise, 9,18 the case of oscillating bubbles has only been examined very recently. 19,20 Building upon the progress in modelling both bubble dynamics in soft materials 13 and the rheology of yield-stress fluids, 21 these articles confirm that bubble rise is indeed possible for bubbles below R c ; 19 they also compute the minimum oscillation amplitude required to initiate yielding. 20 To the best of our knowledge, these numerical and theoretical results have not yet been compared to experiments: experimental articles so far have focused on the case of bubble removal in a shear-thinning, viscoelastic surrounding fluid 22 and removal in yield-stress fluids for bubbles already close to the static rise radius at rest, R c .…”

“…19,20 Building upon the progress in modelling both bubble dynamics in soft materials 13 and the rheology of yield-stress fluids, 21 these articles confirm that bubble rise is indeed possible for bubbles below R c ; 19 they also compute the minimum oscillation amplitude required to initiate yielding. 20 To the best of our knowledge, these numerical and theoretical results have not yet been compared to experiments: experimental articles so far have focused on the case of bubble removal in a shear-thinning, viscoelastic surrounding fluid 22 and removal in yield-stress fluids for bubbles already close to the static rise radius at rest, R c . 3 In this article, we conduct experiments to test the criterion for medium yielding and bubble removal that we previously derived, 20 using a Carbopol microgel as a model yield-stress fluid.…”

“…We extract the viscosity and linear elastic modulus of the material, and compare these measurements to the predictions of the model. 20 We finally conclude on the efficiency of bubble removal through bubble oscillation in yield-stress fluids.…”

“…We briefly recall here the physics of the linear oscillations of a spherical bubble in a yield-stress fluid we derived in a previous article. 20 We will show in Section 3.4 that the assumptions of spherical bubble and linear dynamics are reasonable given the size of the bubbles and the rheological properties of the fluid that we use in the experiments.…”

“…20 To the best of our knowledge, these numerical and theoretical results have not yet been compared to experiments: experimental articles so far have focused on the case of bubble removal in a shear-thinning, viscoelastic surrounding fluid 22 and removal in yield-stress fluids for bubbles already close to the static rise radius at rest, R c . 3 In this article, we conduct experiments to test the criterion for medium yielding and bubble removal that we previously derived, 20 using a Carbopol microgel as a model yield-stress fluid. We investigate the oscillation dynamics of initially spherical bubbles (100-200 mm) excited by a standing-wave ultrasound field with controlled frequency (19-30 kHz), acoustic pressure amplitude, and spatial distribution of pressure gradients.…”