Exact solutions for the evolution of ellipsoidal inclusions in porous media
Exact solutions for the evolution of ellipsoidal inclusions in porous media
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多孔介质中椭圆体包裹体演化的精确解
DOI：
10.1093/qjmam/hbn005
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Buchak P
中科院分区：
文献类型：
--
作者：
Buchak P
本文导出了当远场存在线性应变流时多孔介质中单个椭球体包体随时间演化的精确数学解。这是一个两相自由边界问题。结果表明，初始椭球形包裹体在演化过程中仍保持椭球形。利用椭球谐波理论确定了控制椭球包体几何参数的常微分方程组。
This paper derives exact mathematical solutions for the time-dependent evolution of a single ellipsoidal inclusion in a porous medium when a linear straining flow is active in the far field. This represents a two-phase free boundary problem. It is shown that the dynamics is such that an initially ellipsoidal inclusion remains ellipsoidal under evolution. The theory of ellipsoidal harmonics is used to determine the system of ordinary differential equations governing the geometrical parameters of the ellipsoidal inclusion.