Anomalous pressure-density relations and speed of sound in bubbly water systems

Jesse L Prelesnik; Jingyi L Chen; Krishnan Mahesh; J Ilja Siepmann

doi:10.1063/5.0235457

Anomalous pressure-density relations and speed of sound in bubbly water systems

J Chem Phys. 2024 Nov 28;161(20):204501. doi: 10.1063/5.0235457.

Authors

Jesse L Prelesnik¹, Jingyi L Chen¹, Krishnan Mahesh², J Ilja Siepmann^{1

3}

Affiliations

¹ Department of Chemistry and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, USA.
² Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union Street SE, Minneapolis, Minnesota 55455-0153, USA.
³ Department of Chemical Engineering and Materials Science, University of Minnesota, 412 Washington Avenue SE, Minneapolis, Minnesota 55455-0132, USA.

PMID: 39575738
DOI: 10.1063/5.0235457

Abstract

The speed of sound in bubbly water is an important parameter in the wave equations governing pressure-density relations for turbulent multi-phase flow simulations. Recent molecular simulation results indicate that, for bubbles that are thermodynamically stable at finite volume conditions, the derivative of total pressure P with density ρ has a negative sign, complicating the interpretation of the speed of sound. We show that such a negative compressibility is thermodynamically consistent in a single-component two-phase model at finite volume, and identify an empirically derived equation of state to illustrate that this observation is not an artifact of small simulation length scales. To reconcile this thermodynamic relation with measurements of sound propagation, we decompose the derivative ∂P/∂ρ for bubbly water into its constituent phases to identify absorptive and transmissive contributors, both with an equation of state and using molecular simulations. We find that the speed of sound in the liquid phase remains real-valued while the bubble attenuates sound, giving a negative system compressibility. The inclusion of N2 molecules in molecular simulations illustrates that these observations are robust and hold also for mixtures. From these simulations, we also compute scattering functions for bubbly systems to identify oscillations associated with the speed of sound. Finally, the spherical harmonic modes of bubble oscillations are analyzed in the context of resonance with propagating waves.