Soil Particle Concentrations and Size Analysis Using a Dielectric Method

1922). In this approach, solution, containing sediment particles, is directly sampled at a given depth and time, Limitations of traditional methods for particle-size analysis warrant and particle concentrations are measured by gravimetric the investigation of new techniques. An alternative method based on the difference between the dielectric constant of soil solids (≈4) and analysis. Because of its greater accuracy, the pipette dispersing solution (≈81) was developed. We determined changes in method is often used as a standard to which other partisuspended sediment concentrations (C ) using a coaxial probe placed cle-size methods are compared (Gee and Bauder, 1986). on the surface of a dispersed soil suspension by monitoring changes Standard instruments for the pipette and hydrometer in the apparent dielectric constant with time following complete mixmethods of soil particle-size analysis are not usually ing. A single-point calibration for each sample was obtained using automated to provide continuous readings of particle the known initial concentration. A refractive index (n ) model of the sizes. Continuous, or nearly continuous, measurements suspension dielectric properties gave the slope of a C vs. n curve for of particle-size analysis include scattering techniques changes in silt-size (0.002–0.05 mm) particles. A magnetic stirring rod (light, neutron, and x-ray), size exclusion and hydrodywas used to homogenize the dispersion, and temperature changes were namic chromatography, field flow fractionation, electrominimized given the rapid measurement time. Using the dielectric method, particle-size distributions were measured on a 1to 2-g sample zone sensing, sedimentation and centrifugation, sieving with 400-s settling time because the effective depth of measurement and filtration, ultrasonic measurements, aerosol timewas only 1.5 mm. Wet sieving was used to remove the sand fraction. of-flight measurements, and electric bifringence tranComparisons between the silt and clay fractions obtained using the sient measurements (Barth and Flippen, 1995). Correladielectric and pipette methods were in agreement. The combination tive studies between the pipette technique and more of speed, automation, small sample size, and nearly continuous data automated means of particle-size analysis (e.g., Penshould be balanced against the higher cost of the equipment necessary nington and Lewis, 1979; Konert and Vandenberghe, for the dielectric method. 1997) show that the clay fraction (,2 mm) is either occasionally or systematically underreported by as much as 30 to 66%, most likely related to assumptions regardF many years, sedimentation methods have been ing shape factors for nonspherical particles inherent in used for measuring soil particle-size distributions. each method, including sedimentation. It has been arIn the hydrometer method, first described by Bouyoucos gued (Syvitski et al., 1991) that particle-size analyzers (1925), the floatation depth of a hydrometer is measured should no longer have their results compared with classias a function of time, providing an indication of the cal techniques such as sieving and pipetting. However, solution density. Soil particles, being denser than the since soil size fractions are classically defined in terms aqueous solution in which they are dispersed, tend to of equivalent spheres with regard to Stokes’ law, accepsettle with time and the fraction of particles remaining tance of techniques other than sedimentation may repin suspension at a given measurement depth is estimated resent a break with methods in use in soil science for from the fluid density. An analysis involving Stokes’ more than 60 yr. Interestingly, recent developments in law (Casagrande, 1934), which states that the terminal soil particle-size analysis include the use of a sedimentavelocity of a particle is proportional to the square of tion and gamma attenuation approach (Oliveira et al., particle radius, is used to estimate the particle-size distri1997) to yield nearly continuous measurements, albution. A more accurate approach using the same theory though these involve expensive and hazardous is the pipette method, which apparently was developed equipment. more or less simultaneously by three different research We will describe here a rapid radio-wave electronic groups (Jennings et al., 1922; Krauss, 1923; Robinson, system for continuously monitoring particle concentration in a settling soil dispersion, which we believe to G.C. Starr, USDA-ARS Southwest Watershed Research Center, P.O. be a novel application of well-established principles. Box 213, Tombstone, AZ 85638; P. Barak, B. Lowery, and M. AvilaSegura, Dep. of Soil Science, Univ. of Wisconsin, 1525 Observatory Differences in apparent dielectric constant of soil partiDr., Madison, WI 53706-1299. Research supported by USDAcles (≈4), soil air (≈1), and water (≈81) have been used CSREES-NRI, Univ. of Wisconsin-Madison College of Agricultural for years as the basis of in situ determination of the and Life Sciences, and USDA-ARS. Received 22 Mar. 1999. *Correamount of soil water in a matrix of soil particles by time sponding author ([email protected]). Abbreviations: TDR, time domain reflectometry. Published in Soil Sci. Soc. Am. J. 64:858–866 (2000). STARR ET AL.: DIELECTRIC METHOD FOR PARTICLE-SIZE ANALYSIS 859 domain reflectometry (TDR; Topp et al., 1980). We constituents. This model was extended and applied to solutions composed of solvent mixtures in Starr et al. propose using differences in the dielectric constant to measure the concentration of dispersed soil particles (2000), where agreement between model and measured refractive index was about 6 0.2. Predictive equations settling in a solution of sodium polymetaphosphate by measuring the refractive index (the square root of apof the model were determined by equating the refractive index (n) measured in composite dispersion with the parent dielectric constant) with a coaxial probe dielectric water content sensor and interpreting the combined sum of the refractive indices of each component weighted by the respective component volume fraction. effects of soil solids, bound water, and dispersing solution on the refractive index measured in solution using Although this model was introduced (Whalley, 1993) with little more than an intuitive theoretical underpinan extension of the refractive index model presented by Whalley, (1993) that was applied to the soil matrix. ning and to our knowledge has not been derived from first principles of electromagnetic physics, it does lead Our objective is to describe the new method and the theory on which it relies. to linear and closed-form equations, as will be shown. In our model of soil dispersion, the volume fractions were converted to a mass per unit volume, or concentraTHEORY tion (C), using the density (r) of the respective constitThe time (t) required for a particle of diameter (d) uent (2.65 kg L21 for soil solids and 1 kg L21 for water) to settle a distance (h) traveling at its terminal velocity resulting in Eq. [2]: (given by Stokes’ law) depends on the density of the n 5 oiniCi/ri [2] particle (rp), the density of the liquid (rl), and the viscosity of the liquid (h). It is typically assumed (Gee and The sum across all constituents (i) could include free Bauder, 1986) that all particles with diameters .d will water, soil separates, organic matter, and bound water. be absent (settled out) and those with diameters ,d Thus, a more specific equation to represent soil disperwill be present in their initial concentration after a time sion can be written where the refractive index of the given by: composite dispersion equals a sum of terms specific to each constituent: t 5 18hh/[g(rp 2 r1)d 2] [1] n 5 nsaCsa/rsa 1 nsiCsi/rsi 1 ncCc/rc where g is the gravitational constant (9.8 m s22). Thus, by measuring the soil concentration at some calculated 1 nomCom/rom 1 nbCb/rb 1 nwCw/rw [3] time and given depth, a measure is made of the concenIn Eq. [3] n, r, and C have the following subscripts: sa, tration of particles with diameters less than a given si, c, om, b, and w, defining the sand, silt, clay, organic diameter. Such a measure of the clay fraction (d , 2 matter, bound water, and free water constituents, remm) for a typical depth of 10 cm has an associated spectively. The n of soil separates can be assumed to settling period on the order of 8 h, but if the depth of be 2 (apparent dielectric constant of 4) and their density sampling is reduced to 1.5 mm, this time is reduced to can be assigned a value of 2.65 kg L21, whereas free ≈400 s. Such a shallow depth of measurement is not water has an n of 9 and a density of 1 kg L21. To obtain feasible with any method of measurement previously complete dispersion (Gee and Bauder, 1986) of soils described in the literature, but is possible with the with appreciable organic matter, destruction or removal method presented here. of the organic matter is necessary and the organic matter The method employs a measurement of refractive term will, therefore, be negligible. In a settling experiindex (the square root of apparent dielectric constant) ment, the concentration of soil separates, Cs, is a paramin solution as a function of time during settling. As the eter that must be determined and it is described by the soil particles with a low refractive index (n 5 2) settle following equation: out of the measurement volume and are replaced with water (n 5 9), the refractive index increases. Changes in Cs 5 Csa 1 Csi 1 Cc [4] refractive index can be used to determine concentration It is desirable to consider changes in concentration changes based on the refractive index of particles setas they relate to refractive index changes in a settling tling out of solution. Further, if the initial concentration dispersion because changes in refractive index may be is known and initial refractive index is measured, then much more accurately measured and because this allows a known point (calibration) is obtained and only relative for simplification of the model, as will be shown. Prior measurements of refractive index are needed. In an to the time when clay begins to settle out of the measureideal Stokes’ model of particle settling, throughout the ment volume, Cc and Cb are invariant. If, in addition, period when silt settles out of the measurement volume, sand has been removed from the dispersion by sieving the clay concentration does not change. Thus, the poorly and organic matter has been destroyed (as is typical understood dielectric properties of clay and associated with the pipette method) then the rate of change of bound water (Hilhorst and Dirksen, 1994) are approxirefractive index with concentration when silt is settling mately a constant throughout the duration of the excan be derived by differentiating Eq. [3]: periment. The approach taken by Whalley (1993) modeling ]n/]Csi 5 (nsi/rsi) 1 (nw/rw)]Cw/]Csi [5] TDR measurements of soil water content was based on the refractive indices and volume fractions of soil It is also straightforward to show that for silt settling: 860 SOIL SCI. SOC. AM. J., VOL. 64, MAY–JUNE 2000 n(0)] can be measured as a function of time during settling, the initial concentration Cs(0) is known or can be determined by oven drying, and the density and refractive indices of the silt and water are contstants that can be accurately estimated. Water is bound to the clay fraction and both the density of this bound water and its refractive index may be variable, depending among other things, on how tightly the water is bound. For simplicity, the bound water may be assumed to have a refractive index of 2 and a density of 1 kg L21. The concentration of bound water can be assumed proportional to the concentration of clay because the bound water is integrally associated with clay in a lattice type structure. The constant of proportionality, here termed the bound water fraction, h, can be expressed by the equation: