论文标题
转化流体动力学非材料：关于形式不变性和结构化设计的严格论证，具有空间差异
Transformation hydrodynamic metamaterials: Rigorous arguments on form invariance and structured design with spatial variance
论文作者
论文摘要
如果管理方程式在坐标转换下正式不变，则转换光学的方法一直是操纵物理场的强大工具。然而，由于缺乏对各种流体类别的转化理论的验证的严格论证，流体动力学的调节仍然远非令人满意。在本文中，我们系统地研究了转化光学对流体力学的适用性。我们发现，stokes方程和Navier-Stokes方程分别描述了Stokes流量和一般流，将在曲线转换下改变其形式。相反，以浅色几何形状的特征的Hele-shaw流刚性地保留了其在任意转换下的管理方程式的形式。基于派生的转换规则，我们提出了具有空间变化的细胞深度的多层结构的设计，而不是工程级别2剪切粘度张量，以实现所需的转化转化性动态Hele-Shaw水力动力学交流材料。这项工作中揭示的理论认证和制造方法可能可以用人工结构设计概念来精确控制流量分布的途径。
The method of transformation optics has been a powerful tool to manipulate physical fields if governing equations are formally invariant under coordinate transformations. However, regulation of hydrodynamics is still far from satisfactory due to the lack of rigorous arguments on the validation of transformation theory for various categories of fluids. In this paper, we systematically investigate the applicability of transformation optics to fluid mechanics. We find that the Stokes equation and the Navier-Stokes equations, respectively describing the Stokes flow and general flow, will alter their forms under curvilinear transformations. On the contrary, the Hele-Shaw flow characterized with shallow geometries rigidly retain the form of its governing equation under arbitrary transformations. Based on the derived transformation rules, we propose the design of multilayered structures with spatially varying cell depth, instead of engineering the rank-2 shear viscosity tensor, to realize the required anisotropy of transformation Hele-Shaw hydrodynamic metamaterials. The theoretical certify and fabrication method revealed in this work may pave an avenue for precisely controlling flow distribution with the concept of artificial structure design.
