无界流体中球体诱导的速度场和压力场
Velocity and Pressure Fields Induced by Spheres in an Unbounded Fluid
摘要：
本文提出了一种求解无界不可压缩粘性流体在任意数目的球体在其中运动和旋转所产生的外力场中的速度场和压力场以及流体对质点所施加的力和力矩的方法。在完全线性化的计划，我们表示的速度和压力场的流体中的诱导表面力密度和推导出明确的形式包含在这些关系中的所有数量不施加任何额外的限制粒子的大小，它们之间的距离，和频率范围。我们显示了不正确的类似的结果得到了几个作者，因为这些结果表示在不存在的逆张量。我们解释了导致这种情况的原因，并提出了消除发散量的程序。在静止的情况下，使用所提出的程序，我们得到的平移，旋转，耦合摩擦和流动张量的系统包含任意数量的球体，分别为第二，第四，和第三阶的无量纲参数等于一个典型的半径的一个球的两个球之间的典型距离的比率。在各种特殊情况下，本文所得结果与其它方法所得的结果一致。
英文摘要：
We propose a procedure for the determination of the time-dependent velocity and pressure fields of an unbounded incompressible viscous fluid in an external force field induced by an arbitrary number of spheres moving and rotating in it as well as the forces and torques exerted by the fluid on the particles. Within the completely linearized scheme, we express the velocity and pressure fields of the fluid in terms of induced surface force densities and derive the explicit form for all quantities contained in these relations not imposing any additional restrictions on the size of particles, distances between them, and the frequency range. We show the incorrectness of similar results obtained earlier by several authors because these results are expressed in terms of nonexistent inverse tensors. We explain the reasons leading to this and propose a procedure for the elimination of divergent quantities. In the stationary case, using the proposed procedure, we obtained the translational, rotational, and coupled friction and mobility tensors for a system containing an arbitrary number of spheres up to, respectively, the second, forth, and third orders in the dimensionless parameter equal to the ratio of a typical radius of a sphere to a typical distance between two spheres. In various particular cases, the results obtained in the present paper agree with the well-known results derived by other methods.
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