单个蛋白质气泡的振动特性分析

Vibration performance of single protein bubble

根据粘弹性材料有限变形的应变能密度函数、Maxwell模型的松弛函数及气泡的变形梯度张量,推导出蛋白质气泡有限变形的应力方程。并结合气泡的动力学方程,得到气泡在内外压力差、弹性有限变形应力及粘性耗散应力共同作用下内径的非线性振动方程。利用该方程,通过数值模拟方法,对蛋白质气泡有限变形时的振动特性进行了分析,研究了气泡内外压力差、膜的厚度、膜的粘性以及气泡大小对气泡振动特性的影响。结果表明,蛋白质气泡的振动具有非线性特性,当初始压力差不同时,气泡的振动频率、振幅、速度的变化是不同的,停止振动时的大小也不相同;增加膜的厚度和膜的粘性会抑制气泡的振动,增强气泡承受载荷的能力;对于大小不同的气泡,尺寸较小的气泡振动频率高,速度衰减慢。

According to the strain energy density function for finite deformation of viscoelastic material, the relaxation function of Maxwell mode and the deformation gradient tensor of bubble, a stress equation for finite deformation of protein bubble is derived. By using the stress equation and dynamics equation of bubble, the nonlinear vibration equation of inner radius which is produced by the pressure difference, elastic stress and dissipation shear stress in finite deformation is developed. Based on this equation, the method of numeric simulation is used to analyze the effect of the pressure difference, the thickness and the viscosity of film and the size of bubble on the vibration of bubble. The results show that the vibration of bubble is nonlinear. The trend of frequency, amplitude and velocity is not identical, and the balance size of bubble is also different under the action of different initial pressure difference. Increasing the thickness and the viscosity of protein film can prohibit the vibration of bubble wall and thus can enhance the load-bearing capacity of protein bubble; The bubble with smaller size has the higher vibration frequency, and the decrement of velocity is more slowly in the finite deformation of bubble.