Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11974232, 11727813)
Received Date:20 May 2020
Accepted Date:20 July 2020
Available Online:28 November 2020
Published Online:05 December 2020
Abstract:A theory is developed to model the dynamic of bubble and particle inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim of this work is to study how the outer elastic medium affects the interaction between bubble and particle. Starting from the theory of velocity potential distribution, combined with Lagrangian equations, the motion equations of bubbles and particles in the cavity are obtained. The resonance frequency of the bubbles and influence of the interaction between particle and bubble on the translational behavior under the action of sound waves are analyzed. The results show that the properties of medium elasticity and density can change the resonance frequency of the bubble in the cavity. As the radius of the spherical cavity increases, the resonance frequency of the bubble has a tendency to first decrease and then increase, and gradually tends to the resonance frequency of a single bubble in an unbounded liquid. The translation of bubble and particle in the spherical liquid cavity is affected by factors such as acoustic field parameters, the characteristics of the outer elastic medium, and the characteristics of the bubble and particle themselves. The overall characteristic is that the particle has a tendency to move to the cavity wall, and the translation of bubble is closely related to the interaction characteristics between bubble and particle. Keywords:bubble/ particle/ radial vibration and translation/ spherical liquid cavity
气泡的初始半径不同, 声场中气泡的振动行为也不同. 为分析气泡半径对粒子和气泡系统平动的影响, 选取初始半径分别为2, 3, 4, 5 μm气泡做数值分析, 如图3所示. 在气泡和粒子中心间距不变的条件下, 当气泡半径为2 μm时, 气泡和粒子均向腔壁平动; 随着气泡半径的增大, 气泡向液体腔中心跳跃式平动而粒子向腔壁运动且其路径有起伏跳跃特征, 且在气泡半径为4 μm时相互作用力最强. Wu等[21]发现无界液体中气泡和粒子间相互作用强弱与气泡的初始半径相关并表现为互相吸引. 由于液体腔外层的弹性介质会对气泡与粒子间相互作用产生影响, 从而使得液体腔中的气泡和粒子与无界液体中的气泡和粒子的运动趋势不同, 并在气泡半径不同时表现出相互吸引或排斥的特征. 图 3 气泡初始半径对气泡和粒子的平动的影响 Figure3. The effect of initial radius of bubble on the translation of bubble and particle.
液体腔体内气泡和粒子动力学模型可用于分析超声植物提取、生物组织空化等, 应用领域不同, 选用的声波频率范围不同. 为探索频率的影响, 利用(37)式计算了5 μm气泡的共振频率约为0.72 MHz并选取频率分别为0.7, 1.0, 1.5 MHz的声波分析液体腔内气泡和粒子的平动, 如图4所示. 当频率为0.7 MHz接近气泡的共振频率时, 气泡和粒子间相互作用最强, 且表现为气泡向腔中心平动, 而粒子向腔壁运动. 随着频率的增加, 气泡的径向振动行为相对逐渐减弱, 二者之间的相互作用也减弱, 在驱动声波频率为1.5 MHz时, 气泡和粒子间仅有轻微的相互远离运动特征. 图 4 驱动声波频率对气泡和粒子的平动的影响 Figure4. The influence of driving sound frequency on the translation of bubble and particle.
声波频率一定时, 驱动声压大小决定气泡振动强弱, 进而影响气泡与粒子的平动特征, 图5中曲线对应声压幅值分别为0.5, 1.0, 1.5, 3.0 atm. 在同样的声场条件下, 粒子相较气泡而言其平动更显著, 主要原因在于气泡的膨胀推动粒子向腔壁运动. 随着驱动声压幅值的增加, 气泡的径向振动越强, 推动粒子向腔壁运动的位移越大. 在声压幅值小于1.5 atm时气泡进发生较小的平动位移, 而当声压幅值增大到3.0 atm时, 气泡向液体腔中心运动. Vincent等[13]在实验中观察到凝胶中的液体腔内气泡由于外层弹性介质的影响将向中心位置运动, 而在声波作用下, 气泡和粒子间的相互作用在一定程度上能够平衡外层弹性介质的影响, 但当驱动声压较高时, 二者相互作用增强, 将表现为更为复杂的相互吸引和排斥的特征. 图 5 驱动声压幅值对气泡和粒子的平动的影响 Figure5. The influence of sound pressure amplitude on the translation of bubble and particle.
液体腔的大小对密闭腔内气泡的运动状态有着显著影响, 为更进一步分析影响特征, 改变内腔半径分别为100, 300, 500 μm分析粒子和气泡的平动, 如图6所示. 在不同尺度的液体腔内的粒子和气泡在声波作用下的运动行为表现为: 粒子朝腔壁运动且随着内腔半径的增大粒子的运动位移变大; 对于气泡而言, 在内腔半径较小时, 外层弹性介质对气泡的振动行为的影响更为显著, 因此, 在一定程度影响可调节粒子和气泡相互吸引或排斥的状态, 表现为腔内径100 μm时气泡向着腔壁远离粒子运动; 随着内腔半径的增大, 粒子向腔壁运动的位移变大, 声波作用下气泡则朝向球腔中心有小的位移变化. 图 6 腔体大小对气泡和粒子平动的影响 Figure6. The influence of cavity size on the translation of bubble and particle.
液体腔内由于粒子的存在影响气泡的径向振动和平动. 为更进一步分析粒子密度对密闭腔内气泡的运动状态的影响, 比较粒子密度ρp分别为0.5ρ, ρ和1.5ρ时粒子和气泡的平动状态变化, 如图7所示. 随着粒子密度的增大, 粒子向腔壁运动的位移逐渐减小, 原因在于重粒子平动状态发生变化需要更大的推力作用. 对气泡而言, 粒子密度越大气泡向着球腔中心运动位移也越小, 因此气泡和粒子间的相互作用同时影响二者的平动行为. 图 7 粒子密度对气泡和粒子平动的影响 Figure7. The influence of particle density on the translation of bubble and particle.