Describing the dynamics of a nonlinear viscoelastic shelled microbubble with an interface energy model

Abstract

The present work introduces an interesting revamp to the recently proposed interface energy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022)] for gas-filled encapsulated bubbles (EBs) suspended in a viscous fluid. Here, the elastic and viscous parts of the viscoelastic shell material are described by the Gent hyperelastic material model and a polymer solute following upper-convected Maxwell (UCM) constitutive relations, respectively. Using the aforementioned framework, the integrodifferential type governing equation has been derived, and the physical features of the radial dynamics of the EB model are studied in detail using numerical simulations. The nonlinear behavior and the underlying implications of the newly introduced interface energy model for EBs are also investigated. It was observed that the interface parameters arising from the interface energy formulation and the Gent material model collectively introduce a stiffening effect into the EB model and the extension limit parameter at its lower values affects the radial dynamics of the bubble. Analysis has been carried out at different relaxation time scales, where the viscoelastic shell material resembles a fluid-like or solid-like behavior. The UCM-type viscous part of the viscoelastic shell material introduces strong nonlinear effects into the bubble model and significantly influences the EB’s behavior. For the present model, a detailed study has been conducted to capture the dynamic behavior of the bubble through the time series curves, phase space analysis, and the nonlinear frequency response of the bubble.