匀强磁场对水中气泡运动的影响

Effect of magnetic field on single-bubble in water

基于Rayleigh-Plesset方程,考虑极性水分子在均匀磁场运动受到磁场力作用,根据能量守恒建立了外磁场作用下单气泡运动的控制方程,并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析.结果表明:随磁场强度的增强,附加压强线性增大,气泡膨胀率降低,最大半径减小,气泡坍缩速度下降;外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.

In this paper, we extend the Rayleigh-Plesset model by considering the effect of a magnetic field on the nonlinear response of an oscillating spherical air bubble in water. Water molecules in motion, derived by a time varying ultrasound pressure field, suffer a torque from the magnetic field by Lorentz force. The rotational energy and the translational energy together constitute the kinetic energy of the water molecule. The work done by the pressure during the contraction and expansion of bubble is equal to the total kinetic energy of the water molecule in liquid. According to energy conservation, we establish a modified control equation of the bubble motion under the action of an applied external magnetic field. The integration of the nonlinear differential equation governing the bubble motion is performed analYtically by using a regular expansion, and is solved numerically by using a fourth-order Runge-Kutta method. It is shown that the variation of ambient pressure changes the bubble dynamics when the magnetic field is off. The ambient pressure is increased due to the effect of external magnetic field. The pressure induced by magnetic field increases linearly with the increase of magnetic field intensity and the coefficient is about 10^3 times. The bubble expansion rate, maximum radius, and the velocity of the collapsing bubble decrease as the magnetic field increases. It is predicted that the applying of a magnetic field can widen the pressure range and modify bubble dynamics.