Computations of Lifshitz–van der Waals interaction energies between irregular particles and surfaces at all separations for resuspension modelling

Abstract

The phenomenon of particle resuspension plays a vital role in numerous fields. Among many aspects of particle resuspension dynamics, a dominant concern is the accurate description and formulation of the van der Waals (vdW) interactions between the particle and substrate. Current models treat adhesion by incorporating a material-dependent Hamaker's constant which relies on the heuristic Hamaker's two-body interactions. However, this assumption of pairwise summation of interaction energies can lead to significant errors in condensed matter as it does not take into account the many-body interaction and retardation effects. To address these issues, an approach based on Lifshitz continuum theory of vdW interactions has been developed to calculate the principal many-body interactions between arbitrary geometries at all separation distances to a high degree of accuracy through Lifshitz's theory. We have applied this numerical implementation to calculate the many-body vdW interactions between spherical particles and surfaces with sinusoidally varying roughness profile and also to non-spherical particles (cubes, cylinders, tetrahedron etc) orientated differently with respect to the surface. Our calculations revealed that increasing the surface roughness amplitude decreases the adhesion force and non-spherical particles adhere to the surfaces more strongly when their flatter sides are oriented towards the surface. Such practical shapes and structures of particle–surface systems have not been previously considered in resuspension models and this rigorous treatment of vdW interactions provides more realistic adhesion forces between the particle and the surface which can then be coupled with computational fluid dynamics models to improve the predictive capabilities of particle resuspension dynamics.