Nonlinear dynamics of lipid‐encapsulated acoustic microbubbles under ultrasound effect: Modelling and numerical investigations

Abstract The nonlinear dynamic behaviour of lipid‐encapsulated microbubbles under ultrasonic fields is examined in this study; this field is gaining attention because of its potential uses in targeted medicine delivery and ultrasonography. The aim of the study is to create a mathematical model that faithfully represents the behaviour of microbubbles while taking into account the intricate mechanical characteristics of the lipid shell, including surface elasticity, surface tension, and viscosity. The present paper highlights a theoretical, mathematical modelling and numerical study for the behaviour of lipid‐encapsulated microbubbles based on the study of the nonlinear dynamics of acoustic microbubbles under the influence of ultrasound frequencies in viscoelastic medium. The proposed model is based on the Gilmore model with the effect of enthalpy, which is solved numerically via a finite difference technique to determine the lipid‐encapsulated acoustic microbubble behaviour and its properties. Effects of initial encapsulated microbubble radius, polytropic exponent, and applied pressure source are studied. Additionally, this work focuses on knowing the effect of surface tension, which plays the pivotal role in lipid‐coated acoustic microbubbles where the current work studies the three states of surface tension as effect of zero surface tension, and effect of constant surface tension and variable surface tension. The impacts of the different types of materials such as lipid, polymer, and albumin that encapsulated acoustic microbubbles are applied on the processes of growth and departure for the microbubble's radius. From our analysis, it is obtained that the behaviour of lipid‐encapsulated microbubbles is more significantly affected with these significant physical parameters such as initial radius, polytropic exponent, and frequency respectively, and taken the highest values with the increasing of initial radius, polytropic exponent, and ultrasound frequency. Additionally, the dynamic behaviour of lipid‐coated acoustic microbubbles has its highest value in the case of influence of zero surface tension and its lowest values in the case of constant and variable surface tension. Furthermore, the phase portrait of the encapsulated microbubble radius and radial velocity under the influence of different values of both the initial micro cavitation radius and frequencies are investigated. Finally, the proposed model is validated to study the behaviour of lipid‐coated acoustic microbubbles, and we found that obtained results give a good agreement with previous theoretical works.