Curvature Effects on the Regimes of the Lateral van der Waals Force

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 peak, valley, and intermediate regimes, respectively. In the present paper, we discuss how the curvature of the corrugated surface affects the occurrence of the mentioned regimes. For this, we calculate the vdW interaction between a polarizable particle and a grounded conducting corrugated cylinder. We consider the corrugations along the azimuthal (ϕ-direction) angle or along the cylinder axis (z-direction). We show that when the corrugation occurs in the z-direction, the curvature has a small effect on the occurrence of the valley regime. On the other hand, it inhibits the intermediate regimes up to a certain particle–surface distance above which it amplifies the occurrence of this regime. When the corrugation occurs in the ϕ-direction, we show that the curvature inhibits both the valley and intermediate regimes.