Curvature effects on the regimes of the lateral van der Waals force
Alexandre P. Costa, Lucas Queiroz, Danilo T. Alves
TL;DR
Curvature effects on lateral van der Waals forces for a neutral anisotropic polarizable particle near a corrugated, grounded cylinder are investigated. The authors generalize a perturbative, beyond-PFA approach from planar corrugations to cylindrical geometry by deriving the electrostatic Green's function for Poisson's equation with a corrugated boundary described by $\rho=a+h(\theta,z)$ and use it to obtain the vdW interaction. They apply the method to a general corrugation and specialize to a sinusoidal profile to study curvature-induced changes in the peak, valley, and intermediate regimes. The work provides a geometry-tuned framework for nonadditive vdW forces on curved surfaces, with implications for nanoscale control and device design.
Abstract
Recently, it has been shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated plane, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak but also to a valley or an intermediate point between a peak and a valley, with such behaviors called the peak, valley, and intermediate regimes, respectively. In the present paper, we calculate the vdW interaction between a polarizable particle and a grounded conducting corrugated cylinder, and investigate how the effects of the curvature of the cylinder affect the occurrence of the mentioned regimes.