Assessing surface roughness for correlation with particulate deposition

The textures of carpets are measured and the roughness is characterized with relative area, area-scale complexity and average texture depth. Particle depositions are measured on the carpets. The relative areas and the complexity (change in relative area with scale) are both capable of discriminating the different carpets with better than 90% confidence. The strongest regression coefficients (R) between particulate deposition and relative area are -0.81 at a scale of about 0.5mm ². At the coarser scales the regressions are positive. The regression coefficient between particulate deposition and complexity also exceeds -0.8 at scales of about 3mm ² and then, for some particulate diameters, R rises with decreasing scale through zero eventually reaching 0.95 at scales below approximately 0.001mm ². The scale of the carpet roughness and the size of the particles, both influence the correlations. The characterization of the carpet roughness, particularly scale sensitivity, is important for finding correlations.