Abstract
An electronic current driven through a conductor can induce a current in another conductor through the famous Coulomb drag effect. Similar phenomena have been reported at the interface between a moving fluid and a conductor, but their interpretation has remained elusive. Here, we develop a quantum-mechanical theory of the intertwined fluid and electronic flows, taking advantage of the nonequilibrium Keldysh framework. We predict that a globally neutral liquid can generate an electronic current in the solid wall along which it flows. This hydrodynamic Coulomb drag originates from both the Coulomb interactions between the liquid’s charge fluctuations and the solid’s charge carriers and the liquid-electron interaction mediated by the solid’s phonons. We derive explicitly the Coulomb drag current in terms of the solid’s electronic and phononic properties, as well as the liquid’s dielectric response, a result which quantitatively agrees with recent experiments at the liquid-graphene interface. Furthermore, we show that the current generation counteracts momentum transfer from the liquid to the solid, leading to a reduction of the hydrodynamic friction coefficient through a quantum feedback mechanism. Our results provide a roadmap for controlling nanoscale liquid flows at the quantum level and suggest strategies for designing materials with low hydrodynamic friction.
- Received 16 May 2022
- Revised 18 January 2023
- Accepted 20 January 2023
DOI:https://doi.org/10.1103/PhysRevX.13.011019
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
There is not much mystery in how water flows through a garden hose. But make the garden hose times narrower: Will the water flow according to the same laws of physics? There is no definitive answer to this question, and yet, nanometer-scale pipes are everywhere, from biological ion channels to pores in large-scale desalination membranes. In this study, we focus very closely on the interface between a liquid and a solid wall, thanks to a new quantum-mechanical theory. We discover that the wall is not just an inert boundary, like in the garden hose. In fact, the liquid “pulls” on the electrons inside the wall, so that an electric current is generated in response to a liquid flow. Surprisingly, this current can in turn accelerate the liquid, through a mechanism that we call quantum feedback.
The key messengers in this mechanism are the solid’s phonons—sound vibrations of its atomic lattice. As the liquid flows along the surface, it launches sound waves along the flow direction, and these set the electronic cloud in motion, generating an electric current. But because of how fast sound travels within the solid, the electrons end up going faster than the flow. Ultimately, the electrons pull on the liquid (thanks to an effect called quantum friction), so that it experiences less resistance when flowing along the surface.
Our results provide a recipe for designing materials with quantum feedback, which might help reduce friction and save energy in membrane-based filtration processes. They also show how unusual the laws of physics can be for liquids flowing in tiny pipes: Doing plumbing at the nanoscale requires quantum mechanics.
