Particle size distribution (PSD) in soil is one of the more interesting soil physical properties. The information provided by PSD are often used to infer soil functioning and use. The traditional method of characterizing particle sizes in soils is to divide the array of possible particle sizes into three arbitrary separable size ranges: sand, silt and clay. An alternative to this approach is to measure and display the complete distribution of particle sizes. Sieves can be used to separate and determine the content of the relatively large particles of sand and coarse silt. However the common source of PSD data is the process of sedimentation of particles in water and the most popular techniques are the hydrometer method and the pipet method. Both methods are based on the Stoke’s law and employ the relationship among time, travel distance, and the diameter of a sphere subject to sedimentation in a viscous liquid.

In an earlier study (Tyler SW & SW Wheatcraft, 1992. Soil Sci Soc Am J 56:362-369) cumulative PSD have been analyzed with a power-law function relating mass of particles vs. radius: M(r<R)/M_T=BR^(3-D), where M is mass, D is the fragmentation fractal dimension, and B is a constant. More recently, a mass-time scaling model was proposed (Filgueira RR, Pachepsky Ya & LL Fournier, 2003. Soil Sci Soc Am J 67: 1703-1706) assuming a fractal mass-size distribution for particles settling in a liquid: M(r<R)/M_T=At^(D-3)/2, where M is mass, D is the fragmentation fractal dimension, and A is a constant.

The objective of this study was to test the agreement between the mass-time and the mass-radius relations in soil particle distributions settling in water, and to estimate the range of particle size where power-law scaling is applicable.

Five soils from Argentina, with different textures, where sampled and used in the measurements. The particle size analysis was done with a standard Bouyoucos hydrometer, following standard procedures to disperse aggregates. The readings of density of the suspensions were made between 40 seconds and 24 hours.

The following results were obtained: soil 1 (49.6% silt, 18.3% clay) D = 2.62 (estimated from time-mass scaling) and D = 2.60 (estimated from diameter-mass scaling), with determination coefficient R² = 0,98 in both cases; soil 2 (35.2% silt, 14.8% clay) D = 2.63 (estimated from time-mass scaling) and D = 2.62 (estimated from diameter-mass scaling), with determination coefficient R² = 0,98 in both cases; soil 3 (81.1% silt, 12.8% clay) D = 2.41 (estimated from time-mass scaling) and D = 2.38 (estimated from diameter-mass scaling), with determination coefficient R² = 0,99 in both cases; soil 4 (78.2% silt, 17.6% clay) D = 2.48 (estimated from time-mass scaling) and D = 2.45 (estimated from diameter-mass scaling), with determination coefficient R² = 0,99 in both cases; soil 5 (53.1% silt, 16.5% clay) D = 2.57 (estimated from time-mass scaling) and D = 2.55 (estimated from diameter-mass scaling), with determination coefficient R² = 0,99 in both cases. The diameter range of particles studied was from 1 to 50 micrometers, approximately.

Both models could fit data sets with a high determination coefficient and the resulting fractal dimension values, for each soil, were similar within 1% of variation.