Theory of the Maxwell Pressure Tensor and the Tension in a Water Bridge

TL;DR

This paper develops a theoretical framework for understanding the tension in a water bridge using the Maxwell pressure tensor, linking electric fields, dielectric fluid properties, and fluid dynamics.

Contribution

It provides a detailed calculation of water bridge tension based on the Maxwell pressure tensor and explores dielectric fluid Bernoulli flows in electric fields.

Findings

Derivation of water bridge tension from Maxwell pressure tensor

Discussion of dielectric fluid pressure tensor properties

Analogies between dielectric fluid flows and superfluid quantum flows

Abstract

A water bridge refers to an experimental "flexible cable" made up of pure deionized water which can hang across two supports maintained with a sufficiently large voltage difference. The resulting electric fields within the deionized water flexible cable, maintain a tension which sustains the water against the downward force of gravity. A detailed calculation of the water bridge tension will be provided in terms of the Maxwell pressure tensor in a dielectric fluid medium. General properties of the dielectric liquid pressure tensor are discussed along with unusual features of dielectric fluid Bernoulli flows in an electric field. Analogies between dielectric fluid Bernoulli flows in strong electric fields and quantum Bernoulli flows in superfluids are explored.