Hydrodynamic Metamaterial Cloak for Drag-Free Flow

Metamaterials engineered based on transformation optics have facilitated inaccessible manipulation of various physical phenomena. However, such metamaterials have not been introduced for flowing viscous matter. Here we propose a hydrodynamic metamaterial cloak that can conceal an object in two-dimensional creeping flow by guiding viscous forces. Coordinate transformation of fluidic space is implemented to calculate a tensoric viscosity based on a form invariance of Navier-Stokes equations. The hydrodynamic cloak with the viscosity tensor is numerically simulated to verify a fictitious fluidic empty space created in it. The corresponding metamaterial microstructure is systemically designed and fabricated in a microfluidic device. The experimental results reveal that a solid object amid the flow can be hydrodynamically hidden without entailing a disturbance in flow fields and experiencing a drag.

Figure 1

Conceptual illustration of the hydrodynamic cloak. (a) Fluid flow in the bare space. (b) Fluid flow in the space with the obstacle. The obstacle amid the flow is subject to hydrodynamic force. (c) Fluid flow when the obstacle is encircled by the hydrodynamic cloak mapped with tensoric viscosity. The yellow lines indicate the pressure contour.

Figure 2

Theoretical modeling of the hydrodynamic cloak. (a) Concept of coordinate transformation from virtual to physical spaces for cloaking a space. (b) Spatial profiles of the tensoric viscosity mapped on the cloaking shell in radial and azimuthal directions. Numerical simulation results of pressure (c)–(e) and velocity fields (f)–(h) simulated for the bare, obstacle, and cloak cases. The black lines in the images indicate the pressure contours (c)–(e) and streamlines (f)–(h), respectively.

Figure 3

Design and fabrication of the hydrodynamic metamaterial cloak. (a) Ten-layered structure of the multilayered cloak. (b) Discretized viscosity tensor in each layer along radial (left) and azimuthal (right) axes. The predicted pressure field (c) and velocity field (d) with the multilayered cloak. (e) Detailed configuration of the microstructured metamaterial.

Figure 4

Numerical and experimental validation of the hydrodynamic metamaterial cloak. Simulated pressure fields (a)–(c), velocity fields (d)–(f), and streamlines (g)–(i) for each microstructure. All the simulation results coincide with those from theoretical analyses shown in Fig. S4 [18]. Figures 4 are the experimentally captured streamlines for each case. The red dashed lines indicate the obstacle surface.