A Fractal Approach to Model Specific Surface Area of Soils: Probing Molecule Size Effect.

It is not only the particle-size distribution that may be fractal; surfaces of individual particles may also have that property. We propose a new fractal approach that makes the surface area a function of probing-molecule size, porosity, solid phase and surface fractal dimensions as well as maximum and minimum particle radii to model specific surface area in porous media. To evaluate the developed model, 20 soil samples were used, each of which included 16 measured points for particle-size distribution. The specific surface area (SSA) values were measured by retention of ethylene glycol monoethyl ether (EGME). We calculated the fractal dimension of the solid phase directly from the log-space slope of cumulative particle mass versus particle size. These plots were also used to identify maximum and minimum particle radii. The surface fractal dimension was determined by directly fitting the de Gennes (1985) model to the measured soil water retention curve. We assumed a probing molecule covering particles surface with a size of 2×10^-9 m (2 nm). Comparison of the measured SSA with the estimated one rendered a slope of 0.77.