Sign inversion in the lateral van der Waals force

Sign inversion in the lateral van der Waals force between an anisotropic particle and a plane with a hemispherical protuberance: an exact calculation

“…In the present paper, we use the same calculation technique but focus our attention specifically on the lateral vdW force. This enables us to confirm, now via an exact calculation, the sign inversion predicted in [13] in the context of a perturbative approach. Moreover, while such perturbative approach consider that the height of the protuberance is very small when compared to the distance between the particle and the plane, the exact calculation discussed here enables us to study the lateral vdW force with no restriction on the particle position and on the size of the hemisphere.…”

“…As an example, it was predicted the presence of regimes in the behavior of the lateral vdW force when an anisotropic polarizable particle interacts with a periodic corrugated surface [11,12]. In addition, recently it was predicted that, for an anisotropic particle interacting with a conducting plane with a protuberance, a sign inversion in the lateral vdW force can occur, in the sense that, instead of pointing to the protuberance, in certain situations the force points to the opposite direction [13].…”

“…The prediction discussed in [13] was based on the application of a formula proposed by Eberlein and Zietal in [14] to compute the vdW interaction between a neutral polarizable particle and a perfectly conducting surface of arbitrary shape. This formula is written in terms of the homogeneous part of the Green's function of the Laplacian operator, where it is stored the information about the geometry of the surface.…”

“…This formula is written in terms of the homogeneous part of the Green's function of the Laplacian operator, where it is stored the information about the geometry of the surface. In [13], it was considered a perturbative analytical solution for the Green's function for the case of a perfectly conducting plane with a protuberance and, using it in the Eberlein-Zietal formula, it was predicted the mentioned sign inversion in the lateral vdW force up to first perturbative order in the ratio a/z 0 ≪ 1 (z 0 is the distance from the particle to the plane, and a is the height of the protuberance).…”

“…The paper is organized as follows. In section 2, we make a brief review of the perturbative predictions made in [13]. In section 3, we present the exact calculation made to write the formulas for interaction between a neutral polarizable particle and a conducting plane with a hemisphere.…”