Electrical voltage by electron spin-vorticity coupling in laminar ducts

TL;DR

This paper demonstrates a linear relationship between electrical voltage and pressure drop in laminar duct flows, driven by spin hydrodynamic generation, with experimental validation across various duct geometries.

Contribution

It introduces a universal linear scaling law for spin hydrodynamic voltage generation in laminar ducts, validated analytically and experimentally across different geometries.

Findings

Good agreement between experimental results and the analytical scaling law.

Efficiency of spin hydrodynamic generators is similar for circular pipes and square ducts.

Micro-channels with square cross-sections are optimal for such generators.

Abstract

We report a linear scaling law for an electrical voltage as a function of the pressure drop in capillary pipes and ducts. This voltage is generated by a process which is termed spin hydrodynamic generation (SHDG), a result of the collective electron spin--coupling to the vorticity field in the laminar flow in combination with an inverse spin-Hall effect. We study this phenomenon in laminar duct flows with different width-to-height aspect ratios ranging from 1 (square ducts) to infinite (two dimensional channels). First, we analytically solve the governing Valet-Fert spin diffusion equations for the SHDG by means of the method of small parameters together with proper boundary conditions for the set of inhomogeneous elliptic partial differential equations. Secondly, the proposed linear scaling law is validated through a series of experiments using capillary tubes with rectangular and square cross-sections. The experimental results show a very good agreement to the analytically found scaling law. A subsequent substitution of the bulk velocity of the laminar wall-bounded flows by the pressure drop reveals a universal scaling law for the electrical voltage that incorporates all pipe and duct geometries which we could study in our experiments. Finally, the efficiency of the system is estimated for circular pipes, rectangular and square ducts. This study shows that the efficiency of a spin hydrodynamic generator is the same for a circular pipe and a square duct with the same diameter and height, respectively. Hence, due to the ease of manufacturing and the possibility to scale the experiments up to parallel settings in a compact form, micro-channels with a square cross-section seem to be the optimum for a spin hydrodynamic generator.