  Dispersion forces (van der Waals force and Casimir force) originating from
quantum fluctuations are crucial in the cohesion of microscale and nanoscale
particles. In reality, these particles have a variety of irregular shapes that
differ considerably from any idealized geometry. Previous experiments have
demonstrated that dispersion forces strongly depend on the geometry. Because of
the nonadditivity of these forces, commonly used numerical additive methods,
such as the Hamaker and Derjaguin approximations, are not suitable for
calculations with complex geometries. Moreover, experimental studies are
difficult to identify the contributions of the dispersion force from the many
forces that constitute the cohesion. Therefore, no general law about the
influence of particle geometry on dispersion forces has been established. Thus,
in this paper, the fluctuating surface current (FSC) technique, an exact
scattering theory-based nonadditive algorithm, was used to study this
influence. To characterize complex geometries, a data-adaptive spatial
filtering method was introduced to perform scale decomposition, and descriptors
at three observation levels (global, local, and surface) were used. Based on
the advanced geometric analyses and accurate numerical calculations, the
influence of multiscale surface fluctuations on dispersion forces was
determined. Furthermore, a convenient formula for predicting the dispersion
forces between particles with complex shapes from the exact Lifshitz solution
was established via multistage corrections.
