Abstract
We investigate the radial oscillations of small gas bubbles trapped in yield-stress fluid 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.154-161]. 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 sot 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.
Highlights
Yield-stress fluids encompass a large variety of soft materials, e.g., pastes, slurries, emulsions, and microgels, which possess a characteristic stress τy below which they stop flowing and behave as solids [1,2]
To explore the transition to the nonlinear regime, we report in Fig. 2(a) the dynamics of a 100 μm bubble driven at its resonance frequency, ω = ω0, in the Carbopol gel
We have investigated the dynamics of a bubble driven by an oscillating pressure field in an incompressible and elastic yield-stress fluid using numerical simulations and an approximate linear theory
Summary
Yield-stress fluids encompass a large variety of soft materials, e.g., pastes, slurries, emulsions, and microgels, which possess a characteristic stress τy below which they stop flowing and behave as solids [1,2]. The Bingham and Herschel-Bulkley models implicitly assume that the unyielded material cannot deform, even if the yield surface may adjust to flow, especially in time-dependent problems, and leave undetermined the stress field there. While this problem is not critical for the case of bubble rise, bubble oscillation prescribes a nonzero strain field everywhere in the fluid. The theoretical and numerical framework developed in this paper can be applied to validate constitutive equations for yield-stress fluids by comparing with experiments performed under controlled extensional deformation imparted via bubble oscillation
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