Vibrational behavior of coated microbubble in finite tube under magneto-acoustic composite field

Abstract

The dynamic behavior of coated microbubble in a magneto-acoustic field is very significant for its application to therapy. In this paper, the radial vibration equation of microbubble is derived by placing the coated-microbubbles in a tube filled with magnetic fluid and considering the magnetic pressure on the magnetic fluid under the magneto-acoustic field. The dynamic equation is nondimensionalized by using characteristic quantities such as Weber number and Reynolds number. The effects of magnetic-acoustic field parameters and magnetofluid characteristics on the vibration behavior of the vibration system are analyzed by the Runge-Kutta method. The results show that the magnetic field can prevent the collapse and make bubble oscillate stably. When the acoustic field is constant, the magnetic field can stabilize the oscillation of the microbubble and increase the equilibrium radius of the oscillating microbubble. The stronger the magnetic field is, the more obvious the influence of magnetofluid magnetisability <i>χ</i>_m on the vibration of the microbubble is and the stronger the nonlinear of the transient response of the microbubble is when the magnetic field is larger. In addition, the larger acoustic field parameters will enhance the response of oscillating microbubble to magnetic field. The larger the magnetic field is, the weaker the influence of acoustic parameters on the oscillations of microbubble is. Also, the transient response of microbubble is obviously nonlinear, but the steady-state response keeps the reciprocating oscillation with small amplitude. It can be seen that the adjusting of the magneto-acoustic field is beneficial to realizing the stable oscillation of microbubble in the blood vessel and avoiding collapse.