Lifshitz theory for a wedge

TL;DR

This paper extends Lifshitz theory to analyze van der Waals forces in a dielectric wedge, revealing anisotropic stresses and inherent instability driven by quantum forces, with implications for crack propagation and contact line dynamics.

Contribution

It introduces a novel Lifshitz theory formulation for non-planar geometries, specifically a dielectric wedge, highlighting quantum effects on stress distribution and stability.

Findings

Stresses in the wedge are anisotropic.

The wedge configuration is inherently unstable.

Quantum forces dominate the behavior, unlike classical predictions.

Abstract

We develop the Lifshitz theory of van der Waals forces in a wedge of a dielectric material. The non-planar geometry of the problem requires determining point-wise distribution of stresses. The findings are relevant to a wide range of phenomena from crack propagation to contact line motion. First, the stresses prove to be anisotropic as opposed to the classical fluid mechanics treatment of the contact line problem. Second, the wedge configuration is always unstable with its angle tending either to collapse or unfold. The presented theory unequivocally demonstrates quantum nature of the forces dictating the wedge behavior, which cannot be accounted for with the classical methods.