Estimation of Fractal Dimension of Suspended Sediments from Two Mexican Rivers

Abstract

Sampling programs for suspended sediment were carried out in the Usumacinta River and its tributary Grijalva River in Mexico during the years 2016 and 2017. Suspended sediment samples collected during these sampling programs were analyzed in the laboratory using a Rotating Annular Flume (RAF) fitted with a Particle Tracking Velocimetry (PTV) to obtain the 2D images of the suspended sediment particles as they were undergoing floc reconstruction, and subsequently using a glass settling column fitted with inline digital holography set up to obtain 3D holograms of the fully flocculated sediment particles. From these high-resolution hologram images, the fractal dimension of the flocculated sediment particles was obtained using the classical box-counting method and an improved Triangular box-counting method. The estimated fractal dimension of flocculated sediment, which is a measure of floc compactness and structure that control the settling velocity of flocculated sediment was used to validate two empirical models to estimate the fractal dimension in terms of the floc sizes of suspended sediments of these two rivers. It is shown in this study that the floc characteristic can be analyzed in laboratory experiments after floc reconstruction with the use of an RAF and it offers a viable alternative to the costly in-situ sampling that is often carried out in ocean research. The digital holography method employed in this research offers an efficient methodology to obtain the floc fractal dimension. Regarding the innovative aspects and new contribution to science, we can say that we have developed a laboratory protocol to test river waters to establish floc properties such as fractal dimensions of flocs in this research which will help to test river waters on a routine basis with manageable costs. We can also say that we have developed models to predict the relationship between floc fractal dimension and floc size, which did not exist before.