响应粒子间非线性流体动力学相互作用的对称性
Symmetry properties of nonlinear hydrodynamic interactions between responsive particles
摘要：
两个相同的粒子在相同的稳定力的驱动下通过粘性流体，由于流体动力学的相互作用，可以相对于彼此移动。这种相对平移的存在与否对由许多粒子组成的受驱动悬浮液的动力学有着深远的影响。我们考虑一对粒子，在力的线性顺序，不相互作用流体动力学。如果系统具有受外力影响的固有性质（例如粒子的形状、它们相对于边界的位置或边界的形状），则可能出现非线性地依赖于力的流体动力学相互作用。我们研究了这种非线性响应的一般性质。通过分析粒子交换和力反转下的对称性，得出了关于相对平移和运动时间可逆性的一般结论。我们证明了三个具体的例子中的结论的适用性：（a）两个球驱动平行的墙壁;（b）两个可变形的物体驱动平行于它们的连接线;（c）两个球驱动沿弯曲的路径。时间可逆性的打破表明可能使用的非线性流体动力学相互作用分散或组装粒子的交变力。
英文摘要：
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of a driven suspension consisting of many particles. We consider a pair of particles which, to linear order in the force, do not interact hydrodynamically. If the system possesses an intrinsic property (such as the shape of the particles, their position with respect to a boundary, or the shape of the boundary) which is affected by the external forcing, hydrodynamic interactions that depend nonlinearly on the force may emerge. We study the general properties of such nonlinear response. Analysis of the symmetries under particle exchange and under force reversal leads to general conclusions concerning the appearance of relative translation and the motion's time-reversibility. We demonstrate the applicability of the conclusions in three specific examples: (a) two spheres driven parallel to a wall; (b) two deformable objects driven parallel to their connecting line; and (c) two spheres driven along a curved path. The breaking of time-reversibility suggests a possible use of nonlinear hydrodynamic interactions to disperse or assemble particles by an alternating force.
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