有界流体层中点涡偶极子的坍缩及胶体或尘埃等离子体系统中同电荷微粒相互吸引的流体力学机制
Collapse of Point Vortex Dipoles in a Bounded Fluid Layer and the Hydrodynamic Mechanism of Mutual Attraction of Like-Charged Micro-Particles in the Colloid or Dusty Plasma Systems
摘要：
得到了理想不可压缩流体动力学方程组在两固体边界平板内有限层中的新的精确弱解。该解决方案满足一个设计的非线性有限维哈密顿动力系统的坐标和兰姆脉冲的N点涡偶极子（PVD），即非常小的固体球形颗粒，相对于流体移动。当N=2时，给出了两个PVD坍缩（或在有限时间内收敛于一点）的必要条件。在此基础上，引入了两个相同半径的小球形粒子会聚的新的流体力学机制，并用于解释在胶体和尘埃等离子体系统中观察到的具有相同电荷符号的微粒子吸引的矛盾效应。两个物理气相沉积的坍缩条件与实验观测数据的一致性，其中只有当从上方和下方对流体层深度施加明确的必要限制时，才能观察到在流体层中运动的两个带相同电荷的微球的会聚（J.C. Crocker，D. G. Grier，1996）。我们还指出了在无界流体极限中两个PVD的崩溃条件与已知的数值结果之间的对应性的可能性，即两个有限尺寸的涡旋偶极子在无界流体中散射时实现共振键态（和相应的随机动力学区域）的碰撞参量阈值。V. Manakov，L. N. Shchur，1983; L. Tophoj，H. Aref，2008）。在这里，我们表明，在后一个过程中，偶极子的大小是不是那么重要，因为它被认为是以前。
英文摘要：
The new exact weak solution of the equations for the ideal incompressible fluid dynamics in the finite layer inside two plates with solid boundaries is obtained. The solution meets a devised non-linear finite dimension Hamiltonian dynamic system for the coordinates and the Lamb impulses of N point vortex dipoles (PVD), i.e. extremely small solid spherical particles, moving with respect to the fluid. For N=2 the necessary condition for the collapse (or the converging in one point during the finite time) of two PVD is stated. On the base of the proposed theory, the new hydrodynamic mechanism of converging for two small spherical particles (of the same radius) is introduced and used for interpreting the observed paradoxical effects of attraction for micro particles with the same sign of electrical charge in the colloid and dusty plasma systems. The correspondence of the condition for collapse of two PVD with the experimentally observed data where convergence of two like-charged micro-spheres moving in the fluid layer is observed only when definite necessary restrictions on the fluid layer depth are imposed from above and below (J. C. Crocker, D. G. Grier, 1996) is stated. We also state the possibility of correspondence between the obtained condition of collapse for two PVD in the limit of unbounded fluid and known numerical results on the threshold of the impact parameter for the realization of resonance bond state (and corresponding stochastic dynamic regime) for two finite size vortex dipoles during their scattering in unbounded fluid (S. V. Manakov, L. N. Shchur, 1983; L. Tophoj, H. Aref, 2008). Here we show that in the latter process the size of dipoles is not so important as it was thought before.
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