Scale-independent model based on fractal theory for calculating the adhesion force between a particle and rough surfaces

Abstract

The elimination of the scale-dependent statistical parameters is a challenge in the estimation of the van der Waals force between a particle and rough surfaces. Herein, a scale-independent parameter, the fractal dimension, was introduced into the Rabinovich model to calculate the microadhesion force. First, a Weierstrass-Mandelbrot function is proposed to generate a random 2D contour, which has a simplified form and is more reasonable for spectrum analysis. And then, the roughness scale extraction method was employed to calculate the fractal-dimension value of the real aluminum (Al) surface. And last, the proposed scale-independent Rabinovich-Fractal model was used to calculate the adhesion forces, which are consistent with the results of the atomic force microscopy adhesion test. Aside from providing a more accurate estimation of the van der Waals forces, the proposed model is not influenced by the sampling scale of the surface roughness measurement, which eliminates the related error in van der Waals force estimation.