On the shapes of natural sand grains

Digitized outlines of sand grains from a dozen locations, including deserts, beaches, and seabeds, have been acquired using an optical microscope linked to a desktop computer. Fourier analysis of the outlines returns the normalized power spectrum of each sample, averaged over several hundred grains. Regardless of the origin of the samples, these power spectra all exhibit essentially the same inverse power law dependence on the harmonic number, n, varying as n−10/3 for 2 ≤ n ≤ 20. This “universal” spectrum provides the basis of a numerical technique for synthesizing the irregular outline of a sand grain: The outline is represented as a random pulse train in which identically shaped microasperities, with normally distributed amplitudes, are randomly superimposed on the perimeter of a circle. By identifying the spectrum of the microasperities with the observed inverse power law dependence derived from the optical images, the synthetic outlines are constrained to show the same statistical properties as the outlines of the real grains. The synthesized and real outlines are qualitatively similar in that visually, it is difficult to distinguish between them. The new numerical technique for synthesizing irregular outlines of sand grains has potential for investigating the random packing of realistically rough particles through computer simulation.