Abstract

A photosedimentation technique is used to analyze the size composition of soil samples. The number and size of the particles are determined, respectively, by the Stokes formula and the Beer–Lambert law, measuring time-of-flight and laser light attenuation simultaneously and hence evaluating solution turbidity. A simple software procedure has been developed to obtain fractional volume size distribution, taking into account the particle’s optical properties depending mainly on its size and refractive index. Laboratory measurements on calibrated particulates, showing their reproducibility and validation as well as a classification of ground samples, are presented. Size distribution data can then be utilized to obtain a textural classification of the soil samples for agricultural applications.

© 1998 Optical Society of America

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References

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  1. T Allen, Particle Size Measurements, 5th ed., Powder Technical Series, Brian Scarlet, ed. (Chapman & Hall, London, 1997), Secs. 3, 5.5.2, 9.8, 7, 7.8.
  2. F. J. Welcher, Standard Methods of Chemical Analysis, 6th ed. (Van Nostrand Reinhold, New Jersey, 1995), Vol. 3, Chap. 41.
  3. A. C. Groom, J. C. Anderson, “Measurement of size distribution of human erythrocytes by a sedimentation method,” J. Cell Physiol. 79, 127–138 (1971).
    [CrossRef]
  4. G. K. Batchelor, “Sedimentation in a dilute dispersion of spheres,” J. Fluid Mech. 52, 245–268 (1972).
    [CrossRef]
  5. M. Kerker, Scattering of Light and Other Electromagnetic Radiation, E. M. Loebl, ed. (Academic, New York, 1969).
  6. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).
  7. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).
  8. Dirk A. Tel, Myrna Hagarty, eds. International Institute of Tropical Agriculture (ITTA) and University of Guelph, Soil and Plant Analyses. Study guide for agricultural laboratory directors and technologists working in tropical regions, (International Institute for Tropical Agriculture, University of Guelph, Guelph, Canada, 1984).
  9. G. Casalicchio, G. Vianello, Elementi di Pedologia, (Cooperativa Libraria Universitaria Editrice Bologna, Bologna, Italy, 1979).
  10. L. Cavazza, Fisica del Terreno Agrario, (Unione Tipografico Editore Torinese, Torino, Italy, 1881).
  11. A. J. Koolen, H. N. Kuipers, Agricultural Soil Mechanics, (Springer-Verlag, Berlin, 1983).
    [CrossRef]
  12. R. C. Weast, ed. Handbook of Chemistry and Physics, 52nd ed. (CRC Press, Cleveland, Ohio, 1972).

1972

G. K. Batchelor, “Sedimentation in a dilute dispersion of spheres,” J. Fluid Mech. 52, 245–268 (1972).
[CrossRef]

1971

A. C. Groom, J. C. Anderson, “Measurement of size distribution of human erythrocytes by a sedimentation method,” J. Cell Physiol. 79, 127–138 (1971).
[CrossRef]

Allen, T

T Allen, Particle Size Measurements, 5th ed., Powder Technical Series, Brian Scarlet, ed. (Chapman & Hall, London, 1997), Secs. 3, 5.5.2, 9.8, 7, 7.8.

Anderson, J. C.

A. C. Groom, J. C. Anderson, “Measurement of size distribution of human erythrocytes by a sedimentation method,” J. Cell Physiol. 79, 127–138 (1971).
[CrossRef]

Batchelor, G. K.

G. K. Batchelor, “Sedimentation in a dilute dispersion of spheres,” J. Fluid Mech. 52, 245–268 (1972).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

Casalicchio, G.

G. Casalicchio, G. Vianello, Elementi di Pedologia, (Cooperativa Libraria Universitaria Editrice Bologna, Bologna, Italy, 1979).

Cavazza, L.

L. Cavazza, Fisica del Terreno Agrario, (Unione Tipografico Editore Torinese, Torino, Italy, 1881).

Groom, A. C.

A. C. Groom, J. C. Anderson, “Measurement of size distribution of human erythrocytes by a sedimentation method,” J. Cell Physiol. 79, 127–138 (1971).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).

Kerker, M.

M. Kerker, Scattering of Light and Other Electromagnetic Radiation, E. M. Loebl, ed. (Academic, New York, 1969).

Koolen, A. J.

A. J. Koolen, H. N. Kuipers, Agricultural Soil Mechanics, (Springer-Verlag, Berlin, 1983).
[CrossRef]

Kuipers, H. N.

A. J. Koolen, H. N. Kuipers, Agricultural Soil Mechanics, (Springer-Verlag, Berlin, 1983).
[CrossRef]

Vianello, G.

G. Casalicchio, G. Vianello, Elementi di Pedologia, (Cooperativa Libraria Universitaria Editrice Bologna, Bologna, Italy, 1979).

Welcher, F. J.

F. J. Welcher, Standard Methods of Chemical Analysis, 6th ed. (Van Nostrand Reinhold, New Jersey, 1995), Vol. 3, Chap. 41.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

J. Cell Physiol.

A. C. Groom, J. C. Anderson, “Measurement of size distribution of human erythrocytes by a sedimentation method,” J. Cell Physiol. 79, 127–138 (1971).
[CrossRef]

J. Fluid Mech.

G. K. Batchelor, “Sedimentation in a dilute dispersion of spheres,” J. Fluid Mech. 52, 245–268 (1972).
[CrossRef]

Other

M. Kerker, Scattering of Light and Other Electromagnetic Radiation, E. M. Loebl, ed. (Academic, New York, 1969).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles, (Wiley, New York, 1983).

Dirk A. Tel, Myrna Hagarty, eds. International Institute of Tropical Agriculture (ITTA) and University of Guelph, Soil and Plant Analyses. Study guide for agricultural laboratory directors and technologists working in tropical regions, (International Institute for Tropical Agriculture, University of Guelph, Guelph, Canada, 1984).

G. Casalicchio, G. Vianello, Elementi di Pedologia, (Cooperativa Libraria Universitaria Editrice Bologna, Bologna, Italy, 1979).

L. Cavazza, Fisica del Terreno Agrario, (Unione Tipografico Editore Torinese, Torino, Italy, 1881).

A. J. Koolen, H. N. Kuipers, Agricultural Soil Mechanics, (Springer-Verlag, Berlin, 1983).
[CrossRef]

R. C. Weast, ed. Handbook of Chemistry and Physics, 52nd ed. (CRC Press, Cleveland, Ohio, 1972).

T Allen, Particle Size Measurements, 5th ed., Powder Technical Series, Brian Scarlet, ed. (Chapman & Hall, London, 1997), Secs. 3, 5.5.2, 9.8, 7, 7.8.

F. J. Welcher, Standard Methods of Chemical Analysis, 6th ed. (Van Nostrand Reinhold, New Jersey, 1995), Vol. 3, Chap. 41.

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Figures (5)

Fig. 1
Fig. 1

Laboratory setup scheme distances: b = 1 mm, H = 40 cm, d = 5 cm, D = 2 m, and h lies between 3 and 10 cm.

Fig. 2
Fig. 2

Extinction efficiency Q ext(r) of aluminum oxide.

Fig. 3
Fig. 3

Fractional volume size distribution of calibrated particles (r = 3.0, 14.5, 25.0 μm). Curves labeled as mis 11 and mis 14 are vertically shifted by 15 and 30 units, respectively, keeping the same x axis.

Fig. 4
Fig. 4

Fractional volume size distribution of two ground samples.

Fig. 5
Fig. 5

Textural triangle8,10: 1, sand; 2, loamy sand; 3, sandy loam; 4, loam; 5, silt loam; 6, silt; 7, sandy clay loam; 8, clay loam; 9, silty clay loam; 10, sandy clay; 11, silty clay; 12, clay.

Tables (5)

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Table 1 Measurements on Calibrated Samples

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Table 2 Examples of the Sedimentation Measurements of Quartz Sanda

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Table 3 Examples of the Sedimentation Measurements of Quartz Silta

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Table 4 Examples of the Sedimentation Measurements of Kaolin Claya

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Table 5 Extinction Efficiency Qext for Sand/Silt/Clay

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

F g = 4 / 3 π r 3 ρ s - ρ g ,
F v = 6 π η ur .
u o = 2 9 ρ s - ρ g η   r 2 .
u = u o 1 - k ϕ ,
I / I o = exp - γ d ,
γ = π r 2 NQ ext ,
ln I / I o = π r 2 NQ ext d .
r t = 9 η h 2 ρ s - ρ g 1 / 2 t - 1 / 2 = Zt - 1 / 2 ,
Z = 9 2 η h ρ s - ρ g 1 / 2
ln I 1 / I o = d π N 1 Q 1 r 1 2 + N 2 Q 2 r 2 2 + + N n Q n r n 2 , ln I 2 / I o = d π N 1 Q 1 r 1 2 + N 2 Q 2 r 2 2 + + N n - 1 Q n - 1 r n - 1 2 , ln I 3 / I o = d π N 1 Q 1 r 1 2 + N 2 Q 2 r 2 2 + + N n - 2 Q n - 2 r n - 2 2 , ln I k / I o = d π N 1 Q 1 r 1 2 + N 2 Q 2 r 2 2 + + N n - k + 1 Q n - k + 1 r n - k + 1 2 , ln I n / I o = d π N 1 Q 1 r 1 2 ,
ln I / I o = π NQ ext dZ 2 1 / t .
L 1 = N 1 Q 1 / t 1 2 + N 2 Q 2 / t 2 2 + + N n Q n / t n 2 L 2 = N 1 Q 1 / t 1 2 + N 2 Q 2 / t 2 2 + + N n - 1 Q n - 1 / t n - 1 2 L 3 = N 1 Q 1 / t 1 2 + N 2 Q 2 / t 2 2 + + N n - 2 Q n - 2 / t n - 2 2 L k = N 1 Q 1 / t 1 2 + N 2 Q 2 / t 2 2 + + N n - k + 1 Q n - k + 1 / t n - k + 1 2 L n = N 1 Q 1 / t 1 2
Q k = Q ext k = C ext k π r k 2 = j = 1 2 / α k 2 2 j + 1 Re a j + b j .
Re = 2 r 3 ρ s - ρ ρ g 18 η 2 .
sample   m - 1 sample   m - 2       53 %   sand 18 %   sand         47 %   silt 49 %   silt         0 %   clay 33 %   clay

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