A self-consistent electrostatic electrified shallow water model for charged liquid surface dynamics

Suzuki, S. [Stanford University, CA (United States)] (ORCID:0009000245993926); Shneider, M. N. [Princeton University, NJ (United States)] (ORCID:0000000229257008); Hara, K. [Stanford University, CA (United States)] (ORCID:000000021816165X)

doi:10.1063/5.0287263

DOE OSTI · 3006376

A self-consistent electrostatic electrified shallow water model for charged liquid surface dynamics

Suzuki, S. [Stanford University, CA (United States)] (ORCID:0009000245993926)·Shneider, M. N. [Princeton University, NJ (United States)] (ORCID:0000000229257008)·Hara, K. [Stanford University, CA (United States)] (ORCID:000000021816165X)

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Abstract

The dynamics of an electrified liquid surface are investigated using a shallow water model that is self-consistently coupled with an electrostatic solver. To account for the spatiotemporal variation of a curved liquid surface, the electric field on curved surfaces is calculated by solving a two-dimensional electrostatic equation using the weighted least squares (WLSQ) interpolation method. First, the WLSQ implementation is verified with analytical theory obtained from a Laplace solution assuming a half-cylinder liquid surface profile. Then, the coupled electrified shallow water model is used to study the instability of liquid surface perturbation as a function of the potential drop between an electrode and conducting liquid, surface tension, and gravity. We present a linear dispersion theory of liquid surface instability for long-wavelength perturbations, including the effects of liquid viscosity. Furthermore, the effects of multiple sinusoidal surface perturbations on the electrified liquid surface instability are investigated.

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Capillary waves Electrostatics Interpolation Liquids Modulational instability Water model

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Suzuki, S. [Stanford University, CA (United States)] (ORCID:0009000245993926), Shneider, M. N. [Princeton University, NJ (United States)] (ORCID:0000000229257008), Hara, K. [Stanford University, CA (United States)] (ORCID:000000021816165X). 2025-11-14. A self-consistent electrostatic electrified shallow water model for charged liquid surface dynamics. https://doi.org/10.1063/5.0287263

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