Richard A. Dobbins and G. Stephen Jizmagian, "Particle Size Measurements Based on Use of Mean Scattering Cross Sections*," J. Opt. Soc. Am. 56, 1351-1354 (1966)

Two methods for the determination of the mean size of polydispersions may be based on measurement of optical scattering cross section. The first requires a single spectral transmittance together with a knowledge of particle concentration obtained independently. This method is applicable for any ratio of particle size to wavelength. Both mean size and concentration can be measured by a spectrophotometric method, which is based on measurement of spectral transmittance at two suitably selected wavelengths. The spectrophotometric method is applicable to the measurement of mean particle size of either stationary or moving polydispersions and is particularly useful for the immediate evaluation of the mean size of a polydispersion which is inaccessible except to optical observation. These two methods of size measurement are demonstrated on polydispersions of known mean diameter in an aqueous suspension.

K_{th} is the theoretical value of scattering coefficient as determined by interpolation between tabulated values listed in Ref. 3. K_{ex} is obtained from Eq. (2) with measured values of C_{v}, D, T, and l.

Table III

Comparison of experimental and theoretical mean scattering coefficients of polydispersions.

${\overline{K}}_{p}$ is found by interpolation from Table II of Ref. 1. ${\overline{K}}_{m}$ is found from Eq. (5) of Ref. 1 with values of K from a tabulation of results of Mie theory given in Ref. 3 for m=1.20 and the known concentrations of the particles of the various discrete sizes. ${\overline{K}}_{ex}$ is found from Eq. (6) of Ref. 1 using measured values of C_{v}, D_{32}, T, and l.

Table IV

Comparison of actual particle size and size computed from one transmittance measurement of a polydispersion of known concentration.

C_{v}×10^{+5}

λ′ (μ)

D_{32} (μ)

(D_{32})_{ex} (μ)

2.15

0.436

0.903

1.02

0.375

0.436

1.02

1.02

0.75

0.436

1.02

1.03

1.25

0.436

1.02

1.03

2.50

0.436

1.02

1.04

2.50

0.365

1.02

1.13

2.50

0.656

1.02

1.08

2.50

1.01

1.02

1.19

2.63

0.365

1.13

1.14

Table V

Particle size and concentration as determined by spectrophotometric tests.

Tests made with apparatus as shown in Fig. 1.
Tests made with spectrophotometer designed to permit simultaneous measurement of spectral transmission at two wavelengths of light.

K_{th} is the theoretical value of scattering coefficient as determined by interpolation between tabulated values listed in Ref. 3. K_{ex} is obtained from Eq. (2) with measured values of C_{v}, D, T, and l.

Table III

Comparison of experimental and theoretical mean scattering coefficients of polydispersions.

${\overline{K}}_{p}$ is found by interpolation from Table II of Ref. 1. ${\overline{K}}_{m}$ is found from Eq. (5) of Ref. 1 with values of K from a tabulation of results of Mie theory given in Ref. 3 for m=1.20 and the known concentrations of the particles of the various discrete sizes. ${\overline{K}}_{ex}$ is found from Eq. (6) of Ref. 1 using measured values of C_{v}, D_{32}, T, and l.

Table IV

Comparison of actual particle size and size computed from one transmittance measurement of a polydispersion of known concentration.

C_{v}×10^{+5}

λ′ (μ)

D_{32} (μ)

(D_{32})_{ex} (μ)

2.15

0.436

0.903

1.02

0.375

0.436

1.02

1.02

0.75

0.436

1.02

1.03

1.25

0.436

1.02

1.03

2.50

0.436

1.02

1.04

2.50

0.365

1.02

1.13

2.50

0.656

1.02

1.08

2.50

1.01

1.02

1.19

2.63

0.365

1.13

1.14

Table V

Particle size and concentration as determined by spectrophotometric tests.

Tests made with apparatus as shown in Fig. 1.
Tests made with spectrophotometer designed to permit simultaneous measurement of spectral transmission at two wavelengths of light.