Note on the symmetries of certain material tensors for a particle in Stokes flow
Note on the symmetries of certain material tensors for a particle in Stokes flow
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注意斯托克斯流中粒子的某些材料张量的对称性
DOI：
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发表时间：
1972
影响因子：
3.7
通讯作者：
E. Hinch
中科院分区：
文献类型：
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作者：
E. Hinch
考虑在粘性流体中运动的任意形状的单个刚性粒子。物体的给定点0的速度为u，物体的角速度为0。远离粒子的不受干扰的流动是匀速u和由涡量2S2和纯应变e组成的一般线性流动。粒子对流体施加一个力F，一对力L和一个相对于0指定的应力S。应力是一个二阶张量，由Batchelor （1970, p. 562）定义为粒子的力偶极子强度的对称部分，并且是粒子对体应力张量的对称部分的贡献。应该注意的是，平移速度、耦合和应力的值将取决于物体点0的任意选择。让运动足够慢，以使蠕变流动方程得到服从（低雷诺数）。然后，从控制方程的线性和边界条件F， L和S在U U， S2 w和e中必须是线性的。乍一看，这些关系的表达式似乎需要九个不同等级的不同材料张量，这些张量都取决于粒子的形状方向和点0的位置：（$=pk ' A P ' R '）。问:)。(% E:)。
Consider a single rigid particle of arbitrary shape moving in a viscous fluid. A given point 0 of the body has velocity u and the angular velocity of the body is o. The undisturbed flow far from the particle is a uniform velocity U together with a general linear flow composed of a vorticity 2S2 and a pure strain E. The particle exerts on the fluid a force F, and a couple L and a stresslet S specified relative to 0. The stresslet is a second-order tensor defined by Batchelor (1970, p. 562) as the symmetric part of the force dipole strength for the particle and is the particle contribution to the symmetric part of the bulk stress tensor. It should be noted that the values of the translational velocity, the couple and the stresslet will depend on the arbitrary choice of the point 0 of the body. Let the motion be sufficiently slow for the creeping flow equations to be obeyed (low Reynolds numbers). Then from the linearity of the governing equations and boundary conditions F, L and S must each be linear in U u, S2 w and E. At first sight an expression of these relationships might appear to require nine different material tensors of various ranks which all depend on the particle’s shape orientation and the position of the point 0: ($=pk’ A P’ R”. Q’ :).(%E:).