Simulation of sediment particle surface morphology and element distribution by the concept of mathematical sand

•We present a concept of mathematical sand.•The mathematical sand is represented mathematically by a Fourier series.•Mathematical sand can address the complex surface morphology of various particles.•Elemental distribution of phosphorus on the surface of mathematical sand is proposed.•It is a novel method to explore the relation between sediment particles and containments.

Transport of contaminants with sediment is closely connected with the complex surface morphology of particles in the hydro-environment. Based on a large number of experimental results of sediment morphology, we present the concept of mathematical sand which can address the complex surface morphology of suspended sediment. The sand particle can be represented mathematically by a Fourier series that can simulate the shape and size of real particles. The parameters of Fourier series were determined by around 1036 sediment images obtained by a scanning electron microscopy (SEM). Moreover, the distribution of phosphorus on the surface of a mathematical sand particle was proposed based on the statistical results of measured particle's surface element distribution. The study provided a novel method to explore the relation between the sediment particles and the contaminants.