Radial oscillation and translational motion of an encapsulated bubble in a zero-order Bessel standing wave field

• Radial and translational response investigated for coated bubble in Bessel wave. • Radial oscillation reaches maximum at resonance and weakened with growing χ and κ s . • On-axial Bubbles move toward pressure antinode at f ≤ f res and toward pressure node at . f > f res • More cycles required for off-axial bubble to reach new equilibrium in z direction. • Axial & transverse motions depend on frequency, off-axial distance, shell material. The dynamic response is investigated for a gas-filled microbubble encapsulated by a thin lipid shell subjected to a zero-order Bessel standing wave. Based on the Marmottant model and the force analysis, dynamic equations are derived for the encapsulated bubble with the axial and transverse motions coupled with each other. The resulting equations are solved numerically for an encapsulated bubble exerted by a zero-order Bessel standing wave. The dependence of the bubble dynamics on the elastic modulus and surface dilatational viscosity of the coating shell, the driving frequency of the incident wave as well as the axial and transverse coordinates of the encapsulated bubble is also explored. The radial oscillation, which reaches its maximum amplitude under resonance frequency, will be weakened with the increase of the elastic modulus and surface dilatational viscosity of the shell. The encapsulated bubble settles around the pressure antinode when driven below or at resonance and the pressure node when driven above resonance. The axial and transverse moving directions are influenced by the off-axial distance, the driving frequency and the shell material. The obtained results may assist in understanding the dynamic response for encapsulated bubbles in non-plane wave fields.