Theory of water and charged liquid bridges

TL;DR

This paper develops a theoretical framework for understanding water and charged liquid bridges, presenting new solutions for their stability, shape, and flow dynamics, aligning well with experimental observations.

Contribution

It introduces a novel solution for the charged catenary and analyzes stability, shape, and flow of charged liquid bridges, advancing the theoretical understanding of these phenomena.

Findings

Derived stability conditions for charged liquid bridges

Calculated asymmetric bridge profiles consistent with observations

Modeled flow combining charge transport and neutral mass flow

Abstract

The phenomena of liquid bridge formation due to an applied electric field is investigated. A new solution for the charged catenary is presented which allows to determine the static and dynamical stability conditions where charged liquid bridges are possible. The creeping height, the bridge radius and length as well as the shape of the bridge is calculated showing an asymmetric profile in agreement with observations. The flow profile is calculated from the Navier Stokes equation leading to a mean velocity which combines charge transport with neutral mass flow and which describes recent experiments on water bridges.