Breakthrough in Zero-Drag Hydrodynamic Cloaking Technology

Academic Background

In modern microfluidics and nanoengineering, invisibility characteristics are crucial for ensuring interference-free interactions between intrusive objects and their surrounding environments. For instance, in microfluidic chips transporting biomolecules or precisely controlling drug release, invisibility characteristics significantly enhance operational accuracy and efficiency. Additionally, invisibility characteristics play a vital role in achieving hydrodynamic zero-drag performance, which is essential for alleviating the global energy crisis. However, the long-standing d’Alembert paradox and unresolved Navier-Stokes equations have hindered the development of zero-drag hydrodynamic cloaking technology. The d’Alembert paradox states that in ideal fluids, objects in motion experience no drag, whereas in real fluids, drag is always present. This paradox has made it exceptionally complex to achieve zero-drag hydrodynamic cloaking across a wide range of Reynolds numbers.

To address these challenges, Yao et al. published a research paper titled “On-demand zero-drag hydrodynamic cloaks resolve d’alembert paradox in viscous potential flows” in the journal Microsystems & Nanoengineering. The study proposes a zero-drag hydrodynamic cloaking technology based on isotropic and homogeneous viscosity, validated through experiments and numerical simulations, successfully resolving the d’Alembert paradox in viscous potential flows.

Source of the Paper

The paper was co-authored by Neng-Zhi Yao, Bin Wang, Hao Wang, Chen-Long Wu, Tien-Mo Shih, and Xuesheng Wang, affiliated with the School of Mechanical and Power Engineering at East China University of Science and Technology and the Department of Mechanical Engineering at the University of California, Berkeley. The paper was published in Microsystems & Nanoengineering in 2024.

Research Process

Theoretical Design

The study first proposed a theoretical framework based on Newton’s third law to achieve zero drag by eliminating mutual interference between objects and fluids. By simplifying the Navier-Stokes equations, the research team transformed them into Laplace-like equations and obtained analytical solutions for elliptical hydrodynamic cloaks using the variables separation method. The dynamic viscosity of the cloak was found to depend solely on geometric parameters and the background fluid’s dynamic viscosity, indicating its constant nature.

Experimental and Numerical Validation

To validate the proposed theory, the research team conducted experiments and numerical simulations. The experiments employed an easy-to-implement thermostatically controlled method, which accurately matched viscosity manipulations. Numerical simulations were performed using COMSOL Multiphysics software, modeling the classic viscous potential flow—Hele-Shaw flow. By calculating the drag experienced by objects with and without the cloak, the team demonstrated that the cloak exhibited zero-drag characteristics across a wide range of Reynolds numbers, successfully resolving the d’Alembert paradox.

Results and Discussion

The experimental and numerical results showed that the proposed elliptical hydrodynamic cloak exhibited zero-drag characteristics at Reynolds numbers below 1000 and maintained significant drag-reduction effects even at Reynolds numbers up to 3000. Additionally, the cloak could be switched on and off at will, enabling precise flow manipulation. The study also revealed that vorticity transport played a decisive role in the cloaking and drag-reduction effects, suggesting that vorticity control could be key to designing zero-drag hydrodynamic cloaks at higher Reynolds numbers.

Key Findings

1. Zero-Drag Characteristics: Experimental and numerical results demonstrated that the elliptical hydrodynamic cloak exhibited zero-drag characteristics across a wide range of Reynolds numbers, successfully resolving the d’Alembert paradox in viscous potential flows.
2. Drag-Reduction Effects: At Reynolds numbers up to 3000, the cloak maintained drag-reduction effects exceeding 96%, indicating its significant drag-reduction capability in high-speed flows.
3. Vorticity Control: The study found that vorticity transport was decisive for cloaking and drag-reduction effects, suggesting that vorticity control could be pivotal for designing zero-drag hydrodynamic cloaks at higher Reynolds numbers.

Conclusion and Significance

The study proposed a zero-drag hydrodynamic cloaking technology based on isotropic and homogeneous viscosity, validated through experiments and numerical simulations. The research not only resolved the d’Alembert paradox in viscous potential flows but also provided new insights for drag-reduction technologies in microfluidics, biofluidics, and hypervelocity transportation. Furthermore, the study highlighted the critical role of vorticity control in achieving zero-drag hydrodynamic cloaking, offering a theoretical foundation for designing cloaks at higher Reynolds numbers.

Research Highlights

1. Resolving the d’Alembert Paradox: The study successfully resolved the d’Alembert paradox in viscous potential flows, challenging the conventional belief in the impossibility of zero drag.
2. Zero-Drag Hydrodynamic Cloak: The research proposed a zero-drag hydrodynamic cloak based on isotropic and homogeneous viscosity, capable of achieving zero-drag characteristics across a wide range of Reynolds numbers.
3. Vorticity Control: The study revealed that vorticity transport is decisive for cloaking and drag-reduction effects, providing a new perspective for designing cloaks at higher Reynolds numbers.

Additional Valuable Information

The study was supported by the National Natural Science Foundation of China and the Shanghai Science and Technology Development Fund. Research data are available from the corresponding author upon reasonable request.

Through this research, Yao et al. not only advanced the field of fluid mechanics but also provided new possibilities for drag-reduction technologies in microfluidics, biofluidics, and hypervelocity transportation. Future research could further explore the potential of achieving zero-drag hydrodynamic cloaking at higher Reynolds numbers and in turbulent flows, integrating interdisciplinary technologies such as optofluidics, magnetohydrodynamics, and electroosmotic flows to expand the applications of cloaking technology.