含少量气泡流体饱和孔隙介质中的弹性波  

Propagation of elastic waves in saturated porous medium containing a small amount of bubbly fluid

作　　者：王婷 崔志文[1] 刘金霞[1] 王克协[1] Wang Ting Cui;Zhi-Wen;Liu Jin-Xia;Wang Ke-Xie(School of Physics, Jilin University, Changchun 130012, China)

机构地区：[1]吉林大学物理学院,长春130012

出　　处：《物理学报》2018年第11期142-148,共7页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:41474098;11134011);吉林省科技发展计划(批准号:20180101282JC);声场声信息国家重点实验室开放基金资助的课题~~

摘　　要：考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.It is very important to understand the acoustical properties of porous medium. To study the relationship between acoustical and other physical properties of porous medium will help us to use acoustical tools for determining the physical properties of porous medium. Many researchers have paid much attention to the properties of acoustic wave propagation in the gassy marine sediments based on the Blot model which is popularly used to predict the dispersion and attenuation of sound in saturated porous medium. The patchy model which contains gas inside the spherical water predicts that the existence of gas just has little effect on the propagation of acoustic wave in porous medium when the gas content is very smaU. However, the presence of a small number of bubbles in a fluid saturated sediment will lead to different acoustic responses. As is well known, the bubble vibration theory proposed by Keller and Miksis shows that a small number of bubbles existing in the liquid will have a great influence on sound velocity and attenuation. Therefore, in order to study the effect of a small amount of gas existing in fluid saturated porous medium on the property of acoustic wave propagation, we investigate a bubbly liquid saturated porous medium and consider the case of the bubbles vibrating linearly under the action of sound waves. First, we derive the continuity equation of the seepage according to the mass conservation of the pore fluid and the relationship between porosity differentiation and pore fluid pressure differentiation. Then, the bubble linear vibration theory given by Commander is used to deal with the time derivative of gas volume fraction in the continuity equation of the seepage, The bubble linear vibration theory gives the relationship between instantaneous bubble radius and background pressure of the medium. Through this relationship, we obtain the equation of time derivative of gas volume fraction and time derivative of pore fluid pressure. Then, we combine the obtained equation with the continuity equation

关 键 词：孔隙介质 含气泡液体 BIOT理论 弹性波 

分 类 号：O357.3[理学—流体力学]