To calculate Cand N from R and -log T, eq. 93 is solved for varying values of C, which is the (-log T)-Rf(C)/a term, and a tabulation of corresponding f(C) values is thus obtained. The substitution of these C and f(C) values at specified increments of R in eq 93 yields a table from which C may be found for any pair of -log T and R values. Practically, C is found from curves based on the table, and N is obtained by subtraction from -log T. A graph covering the entire range of C, -log T, and R values of raw sugar is shown in figure 82.

FIGURE 82. Zerban and Sattler's curves for finding -log T and R.

-log T, absorbancy; C, concentration of coloring matter expressed as -log T; R relative turbidity Full range for white and raw sugars.

More exact results may be obtained if interpolation for R is carried out by means of table 41 on the basis of the approximate value of C read from the graph. The use of the table is explained by the following example:

A raw-sugar sample gave log T=0.57807, and R-917.1 for the green filter. On the graph, C is found to lie between 0.25 and 0.30. The value of Rf(C)/a for 1 R at C=0.25 is 0.0003351; hence that for 917.1 R is 0.0003351X917.1-0.30732, which, added to 0.25 c, gives

-log T=0.55732. Similarly the value of Rf(C)/a for 1 R at C=0.30, is 0.0003847, and that for R=917.1 is 0.35280, which, added to 0.30, gives log T=0.65280. The difference, x, between the required value of C and the value 0.25 is found from the equation

(x-0.25):(0.30-0.25)=(0.57807-0.55732):(0.65280–0.55732).

The result for x is 0.0109, which, added to 0.25, gives a value of 0.2609 for C. N equals 0.57807-0.2609, or 0.3172.

TABLE 41.-Zerban and Sattler table for finding C and f(C) from -log T and R

The absolute turbidity can also be calculated by means of table 41 and the Sauer equation

S=Af(k)Dt,

where S is the absolute turbidity, A is the relative Tyndall beamintensity as measured with the turbidimeter and equals 0.01 R in the Zerban and Sattler system. D is a factor varying with the thickness of the absorption cell, and t is the absolute turbidity of the standard glass block. By interpolation of column 2 in this table, the ƒ (C) for C(kd) equal to 0.2609 is found to be 2.0630. By substituting this figure in eq 90 along with A(0.01 R)=9.171, D=6.6395 (for the

2.455-mm cells used) and t=0.00282, the absolute turbidity found is 0.3542.

For products which are low in both color and turbidity the graph shown in figure 83 is used. If the scale is such that C and -log T are

FIGURE 83. Enlarged graph of lower portion of figure 82 for products low in both color and turbidity.

01100

+09000

ว

$2000

0.0010

0.0000k

plotted at 50 mm 0.001 unit, it is possible

to read C and -log T

values accurately to the fourth decimal place. Values of log T and of R, determined at one thickness, may be converted into corresponding values at another thickness, or Tinto log t. Over a wide range of thickness, the absorbancy is not directly proportional to the depth, b, in the turbid solutions, but is a power function of it, according to the equation

log

(c) PROCEDURE OF LANDT AND WITTE

Landt and Witte [10], employing a Zeiss-Pulfrich turbidimeter, studied the turbidity in 45-Brix sugar solutions which had been filtered through paper. Only the practical application of their method is given

here.

The procedure in making measurements is similar to that of Sauer [3], as described above, in that the turbid solution is first compared in brightness with an arbitrary glass turbidity standard to give the relative turbidity. From this value is deducted the turbidity value of the water surrounding the sample cell, giving a value called the corrected relative turbidity. This value is divided by the brightness of the calibrated turbidity standard, H, of the instrument relative to the turbidity brightness of the arbitrary standard used, thus giving the value A, or A corr. rel. turb./H. The value A is next multiplied by f(k), which, according to Landt and Witte, is found by the Sauer formula, applying only to the plane parallel cells:

=

f(k) =

kd(√2-1)2.303
10−k(d+m+n)[1—10—kd(√2—1) ]

(94)

Here k is a factor depending upon the extinction coefficient and dis the thickness of layer. For cylindrical beakers, account is taken of the fact that the primary as well as the scattered light suffers a weakening in passage through layers of solution on two sides of the actual Tyndall pencil. These factors are designated, respectively, m and n, and formula 94 becomes for the 26- and 36-mm beakers:

Values of k and ƒ (k), as calculated for various sizes of plane parallel cells are given in table 42, and for the 26-mm and 36-mm beakers, in table 43.

TABLE 42. Values of k and f(k) for plane parallel cells of various thicknesses (Landt and Witte)

TABLE 43.-Values of k and f(k) for cylindrical beakers 26 mm and 36 mm in diameter (Landt and Witte)

Next, in order to obtain strict comparison with other plane parallel cells or for calculation to absolute turbidity Af(k) must be multiplied by the factor, D, which is the ratio of the layer thickness of the calibrated standard to the layer thickness of the plane parallel cell. Finally, to reduce the results to terms of absolute turbidity, the whole is multiplied by t, the turbidity of the calibrated standard. The formula is therefore:

Absolute turbidity, T=Af(k)Dt.

3. REFERENCES

[1] R. T. Balch, Ind. Eng. Chem., Anal. Ed. 3, 124 (1931).

[2] H. Sauer, Z. Instrumentenk. 51, 408 (1931).

[3] H. Sauer, Z. tech. Physik. 12, 148 (1931).

[4] F. W. Zerban and L. Sattler, Ind. Eng. Chem., Anal. Ed. 3, 326 (1931). [5] F. W. Zerban and L. Sattler, Ind. Eng. Chem., Anal. Ed. 7, 157 (1935). [6] F. W. Zerban and L. Sattler, Ind. Eng., Chem., Anal. Ed. 8, 168 (1936). [7] F. W. Zerban and L. Sattler, Ind. Eng. Chem., Anal. Ed. 9, 229 (1937). [8] F. W. Zerban and L. Sattler, Ind. Eng. Chem., Anal. Ed. 10, 9 (1939). [9] F. W. Zerban, L. Sattler and I. Lorge, Ind. Eng. Chem., Anal. Ed. 6, 178 (1934).

[10] E. Landt and H. Witte, Z. Ver. deut. Zucker-Ind. 84, 450 (1934). [11] Zeiss Nephelometer, Advertising booklet (Carl Zeiss, Inc., 485 Fifth Ave., New York, N. Y.)

XXI. VISCOSITY OF SUGAR SOLUTIONS

1. THEORETICAL

Viscosity is the property of homogeneous fluids that causes them to offer resistance to flow. It is expressed mathematically by the constant of proportionality between shearing stress and rate of shear. It has the dimensional formula ML-1T-1, and is generally expressed as 7. In the cgs system, the unit of viscosity is the poise. The onehundredth part of this unit (the centipoise) is frequently used in practice. The viscosity of water at 20° C is often taken as 1.005 centipoises. The ratio of viscosity to density is called the kinematic viscosity, and the cgs unit is called the stoke, poises/(g/cm3). The reciprocal of viscosity is fluidity. The cgs unit of fluidity is the rhe.

An extensive investigation of the flow in capillary tubes was first undertaken by Poiseuille about 1838. He found that the rate of discharge was directly proportional to the first power of the pressure difference and to the fourth power of the diameter and inversely proportional to the length of the capillary tubes. This relationship, which is known as Poiseuille's law, expressed mathematically, is