Mathematical models for the van der Waals force and capillary force between a rough particle and surface.

The capability of predicting the adhesion forces between a rough particle and surface including the van der Waals force and capillary force is important for modeling various processes involving particle surface retention and resuspension. On the basis of the fractal theory describing the behavior of multiple roughness scales and the Gaussian roughness distribution, a set of mathematical models for the van der Waals force and capillary force is proposed. The proposed models provide the adhesion force predictions in good agreement with the existing experimental data and converge to the previous classical solutions of the adhesion forces between a smooth particle and surface as the roughness goes to zero. The influences of roughness for the combination of particle and surface, relative humidity (RH), contact angle, and Hurst exponent toward the adhesion forces are examined using the proposed models. The decline mode of the adhesion force with surface roughness and contact angle, as well as the increase mode with RH and the Hurst exponent are reasonably predicted by the proposed models. The comparison between the proposed models and those from the existing studies is also performed, which shows the similarities and differences between the proposed models and the existing models.