Simulating the electrostatic patch force in experimental geometries

TL;DR

This paper develops a finite-element model to accurately simulate electrostatic patch forces in complex 3D geometries, including rough surfaces, aiding precision force measurements in experiments like Casimir and gravitational wave detection.

Contribution

It introduces a versatile finite-element approach to evaluate patch forces in realistic experimental geometries with roughness and curvature, surpassing analytical limitations.

Findings

Model matches known solutions for simple geometries.

Effective in complex geometries with rough surfaces.

Provides estimates of patch forces relevant to high-precision experiments.

Abstract

Potential patches are responsible for a force between closely-spaced objects that forms a parasitic contribution to sensitive force measurements. Existing analytical models cannot account for the patch force in the 3D geometries of real experiments. Here, we present a finite-element method model to evaluate the impact of patches in geometries with roughness, edges, and curvature. First, we test our model against the plate-plate and sphere-plate geometries, for which the exact solutions are known. Then, we apply it to more complicated geometries for which analytical solution are challenging, and finally we extend it to handle AFM-measured rough surfaces. Patch textures are generated as a Voronoi diagram representing crystalline grains, or may be imported from potentials measured in Kelvin Probe Force Microscopy experiments. This work provides a reliable estimation of the parasitic contribution from random potential patches in realistic experimental geometries, which may be of relevance to Casimir force measurements or gravitational wave interferometers.