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<p>In this study, the nonlinear oscillatory dynamics of encapsulated microbubbles in Oldroyd-B viscoelastic fluids were investigated using a reduced dynamical systems framework. Unlike previous reduced Oldroyd-B models that neglect encapsulation, both interfacial elasticity and surface dilatational viscosity were incorporated in this study, enabling a unified treatment of shell-polymer coupling. Starting from the Rayleigh-Plesset equation augmented by viscoelastic and interfacial stress balances, a closed system of nonlinear ordinary differential equations was derived and non-dimensionalized in terms of the Reynolds, Weber, Deborah, and shell elasticity parameters. Bifurcation analysis revealed rich nonlinear behavior, including period-doubling cascades, multistability, and chaotic oscillations under acoustic forcing. Systematic parameter sweeps demonstrated that encapsulation fundamentally reorganizes the transition thresholds: the first period-doubling bifurcation shifts from approximately 1.0&#xa0;MPa in the uncoated Oldroyd-B case to approximately 1.8&#xa0;MPa when shell elasticity is included, corresponding to an 80% increase in the critical excitation threshold. Two-parameter regime maps further demonstrated that shell elasticity reorganizes the global bifurcation structure. Energy budget analysis provided physical insights into this behavior. Shell elasticity redistributes the elastic energy storage between the interface and bulk polymeric stresses, thereby modifying the effective restoration dynamics and influencing the subharmonic amplification. These results demonstrate that encapsulation fundamentally modifies the nonlinear response of viscoelastic bubbles and must be considered in the predictive modeling of ultrasound contrast agents and acoustically driven microbubble systems.</p>

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Shell–polymer coupling reorganizes nonlinear bifurcation thresholds of ultrasound-driven encapsulated microbubbles in Oldroyd-B fluids

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Ahmed K. Abu-Nab,
  • Tetsuya Kanagawa,
  • Yuri V. Fedorov

摘要

In this study, the nonlinear oscillatory dynamics of encapsulated microbubbles in Oldroyd-B viscoelastic fluids were investigated using a reduced dynamical systems framework. Unlike previous reduced Oldroyd-B models that neglect encapsulation, both interfacial elasticity and surface dilatational viscosity were incorporated in this study, enabling a unified treatment of shell-polymer coupling. Starting from the Rayleigh-Plesset equation augmented by viscoelastic and interfacial stress balances, a closed system of nonlinear ordinary differential equations was derived and non-dimensionalized in terms of the Reynolds, Weber, Deborah, and shell elasticity parameters. Bifurcation analysis revealed rich nonlinear behavior, including period-doubling cascades, multistability, and chaotic oscillations under acoustic forcing. Systematic parameter sweeps demonstrated that encapsulation fundamentally reorganizes the transition thresholds: the first period-doubling bifurcation shifts from approximately 1.0 MPa in the uncoated Oldroyd-B case to approximately 1.8 MPa when shell elasticity is included, corresponding to an 80% increase in the critical excitation threshold. Two-parameter regime maps further demonstrated that shell elasticity reorganizes the global bifurcation structure. Energy budget analysis provided physical insights into this behavior. Shell elasticity redistributes the elastic energy storage between the interface and bulk polymeric stresses, thereby modifying the effective restoration dynamics and influencing the subharmonic amplification. These results demonstrate that encapsulation fundamentally modifies the nonlinear response of viscoelastic bubbles and must be considered in the predictive modeling of ultrasound contrast agents and acoustically driven microbubble systems.