Quantification of the surface roughness of quartz sand using optical interferometry

In comparison to the description of particle size and shape, the surface roughness, which mainly affects the inter-particle friction, is more difficult to measure and quantify. One difficulty arises from the variability between particles and the heterogeneity of roughness within one particle. In this study, optical interferometry, which has the advantage of non-contact measurements of the particle surface, was adopted to measure the surface roughness of a quartzitic sand (Leighton Buzzard sand–LBS). The roughness was determined as the root mean square deviation (RMSf) of the surface from the mean plane over a field of view of 106.6 * 106.6 μm2. This size of field of view is limited compared to the whole surface area of one particle. Three fractions of LBS particles were used to study the effect of particle size on the surface roughness and the roughness was measured at different points across the surface of coarse particles to assess the number of measurement points required for surface roughness quantification. The measurements revealed the followings. (1) The roughness of LBS can be measured by optical interferometry, mainly due to the high reflectivity of the quartz and the rounded particle shape. (2) RMSf of LBS with different particle sizes increases with the size of field of view first and tends to converge at larger sizes. (3) Surfaces of medium size (1.18–2.36 mm) particles are the smoothest. (4) Roughness of one particle varies at different measurement points, with no correlation between the mean value of RMSf and the number of points measured, while the standard deviation reaches a constant value only after a specific number of measurement points, 3 for 1.18–2.36 mm particles and 5 for 2.36–5 mm particles.