Viscometric Determination of Moisture in Honey F. C. OPPEN’ AND H. A. SCHUETTE, University of Wisconsin, Madison, Wis.
E
XPERIENCE has shown that, despite the fundamental accuracy of the vacuum-drying method (3) for the determination of moisture in honey, there is need for a rapid, accurate physical method to supplement it in routine testing. Studies have been made to meet this need by densimetric (7, 9), refractometric (4, 6, 8), and viscometric (8) means. The evident inaccuracies of the hydrometer, when used in highly viscous sirups, seemed to place the densimetric method outside the scope of the present investigation. Exploratory experiments made in this laboratory on a series of representative types showed a very poor degree of correlation between the refractive index of a honey and its moisture content as determined by the “official” procedure (8) Furthermore, many samples of this group were found to show such a blurred field in the Abbe refractometer as to render accurate readings impossible. The relative viscosities of these samples, on the other hand, showed a very high degree of correlation with their moisture contents. A thorough investigation of this phase of the problem was accordingly undertaken, and the results are summarized below.
ther assumed that the per cent variation in time of fall resulting from a fixed per cent variation in tube size depends only upon the values of the ratio d / D and not upon the actual values of either d or D; in other words, that observations using a 0.15-cm. ball in a 2.1-cm. tube would be subject to TABLEI. RELATION OF WALLEFFECT TO TIMEOF FALL Diameter of Tube Cm. 0.85 1.14 2.10 3.50 4.54
I
~~
1
Sec.
25.2 21.8 18.8 17.7 17.4
d/D 0.1870 0.1395 0.0757 0.0454 0.0350
~~~
the same percentage error as those using a 1.5-cm. ball in a 21-cm. tube, should each tube vary 1 per cent in diameter. If this be granted, then it can be shown graphically from these data that viscosity determinations using apparatus according to Chataway’s specifications are subject to errors upwards of 8 per cent from the normal variations (A0.5 mm. in 25-mm. tubing) present in different lots of glass tubing, while the probable errors from the same cause, using the apparatus of Gibson and Jacobs ( l l ) ,are of the order of 1 per cent. Besides the indispensable factors just mentioned, several other desiderata enter into the design of a satisfactory falling-sphere viscometer. These are a means for freeing the sphere of e n t r a i n e d air p 3 r n r n , /nferno/ Dlam. bubbles, and for i n t r o d u c i n g it i n t o t h e exact center of the tube, a fixed acceleration zone above the zone of measurement, wherein : the sphere may acquire uniform /l n i e r v o l/ f o r velocity, a n d a Acce /ersfion 0 constant height of liquid to eliminate the effect of hydrostatic pressure. ? The viscometer of Gibson and Jacobs ( F i g u r e 1 ) embodies these prin/nterva/ f o r ciples of design in Measuremen+ simple, practical form, a n d was therefore adopted for use i n t h i s 2 5 m m . Sfondord W o / /P y r e x T u b e study. The cali/nternd O Oh hm m .. /nternd b r a t i o n differs 2t.2 rnm. f 0.5 f r o m t h a t of Gibson and Jacobs (11) only in that the 15-cm. measuring zone is subFIGURE1. MODIFIED GIBSONdivided into three JACOBS VISCOMETER FOR DETERMIN5-cm. spaces. ING MOISTURE CONTENTOF HONEY
Design of Viscometer Chataway (8) was apparently first to point out the correlation between the relative viscosity of honey, measured by the falling-sphere method, and its moisture content. According to her method for determining viscosity, a glass tube filled with honey is supported vertically in a jar of water until thermal equilibrium is established. A steel ball is introduced at the top and its time of fall determined as the ball travels the distance between two marks on the side of the tube. Tables are provided for translating the time of fall thus obtained into moisture content. A comparison of Chataway’s apparatus and method with those of other workers (6, 11) reveals the desirability of certain modifications. The most important of these are the substitution of the smallest commercially available (0.16cm., 0.06-inch diameter) steel balls for the 0.475- and 0.23-cm. (0.19- and 0.094-inch) ball bearings employed by her, and the specification of 25-mm. standard-wall Pyrex tubing for the body of the viscometer, rather than the smaller size which was used by Chataway. These changes are vital because of the phenomenon of “wall effect.” It was early recognized (14) that the time of axial fall of a sphere through a viscous medium in a vertical cylindrical tube is greater than that calculated by Stokes (17) for a sphere falling in an infinite medium, and that the amount of divergence, or wall effect, is a function of the ratio d/D, in which d and D are the diameters of the sphere and cylinder, respectively. Without going into the mathematical treatment of this phenomenon, it will suffice to emphasize that an easily reproducible fallingsphere viscometer must have a small wall effect, hence a small ratio d/D. This is true, because, although steel ball bearings may be easily duplicated within close limits of tolerance, glass tubing varies considerably from lot to lot, and i t is important that such variations should not materially change the observed results. The effect upon time of fall of varying the diameter of the tube within wide limits is shown in Table I, due to Gibson and Jacobs (11). These data were obtained using a 0.16-cm. (0.06-inch) ball falling through castor oil at 20” C., and it may be safely assumed that about the same degree of variation would be encountered in substituting hbney for the oil. It may be fur-
Time of Fall for 15 Cm.
‘!j
,
.-.
Present address, Mollenhauer Laboratories, Green Bay, Wis.
130
MARCH 15, 1939
ANALYTICAL EDITION
131
With this viscometer the relative viscosities (time of fall in seconds through 15 cm.) were determined for 15 honeys of widely varying moisture contents, a t intervals of 5" from 30" to 50" C. As a result of this preliminary work, 40" was selected as a convenient standard temperature. A total of 30 honeys was measured a t this temperature. Before making readings, samples were carefully mixed, and allowed to remain in the tube until all the bubbles in the body of the liquid had risen to the top. Thermal equilibrium was assumed to have been reached when close checks (about 0.4 per cent of the total time of fall of the sphere) were obtained several minutes apart. Concurrently, the moisture content of these samples was determined by the official vacuum drying method (S), cooling the dishes for 3 hours instead of the prescribed short time.
Mathematical Analysis of Results The mathematical treatment of the data is a straight-forward application of elementary analytical geometry. Inasmuch as three interrelated variables are involved-moisture content, w, viscosity, V , and absolute temperature, T-the relation between any two is most conveniently ob-
3.0C
2.7:
2.JC
FIGURE 2. EFFECTOF TEMPERATURE UPON VISCOSITY OF INDIVIDUAL 2.2: HONEYS
Accurate temperature control is essential to viscometric work, because viscosity is an exponential function of temperature. In fact, observations could not be duplicated unless the temperature remained within *0.05' of the recorded value.
2.0c
>
-0 1.7: ul
Experimental Method The apparatus consisted essentially of the tube, calibrated as described, mounted vertically in a metal frame. The frame and tube were placed in a diffusely illuminated glass constant-temperature bath, provided with a stirrer and surrounded by insulation, in which an observation window was cut. Following the procedure of Gibson and Jacobs ( I I ) , the steel balls were introduced below the surface of the honey through the 3-mm. tube. This served to free the ball of air bubbles and to ensure its fall through the center of the viscometer tube, thus eliminating two of the common sources of error alluded to above. Uniform height of column was maintained by filling the viscometer tube with the thoroughly liquefied and well-mixed honey sample exactly to the highest calibration, while uniform conditions of fall were assured by adjusting the end of the 3-mm. tube to the mark 6 em. from the top. The 5-em. portion immediately below served to allow the ball to acquire velocity, while the last 15 cm. marked were used for the actual readings. When working with very viscous samples it was possible to measure the time of fall through the first and third 5-cm. subdivisions of the measuring zone, and, multiplying each value by 3 to convert to the standard 15-cm. distance, to obtain two measurements with the same ball.
LSC
1.25
I.0C
0.75
FIGURE3. VARIATION OF VISCOSITYWITH MOISTURE CONTENT AT VARIOUS TEMPERATURES
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VOL. 11, NO. 3
tion in w, P,, and T is obtained, from which w can be calculated for any values of V and T. This equation is an interesting and compact expression of the data reported, but becomes a bit awkward when applied to routine calculations. For this reason, a direct-reading graph was constructed which greatly simplifies the interpretation.
.59
m
Relation between Viscosity and Temperature with Per Cent Moisture Constant
/
SO
It was hoped that the equation log V T = a/T
A3
0401.25 /
A 130
1.75
2.25
2.56
+b
where a and 6 are empirical constants, reported by numerous investigators (1, 6, 10, 12, 13, 16, 16), would hold. Although a slight curvature resulted, as is general for associated liquids, when log V , was plotted against lo4 X 1/T, nevertheless, over
40
42
44
46
TEMPERATURE IN DECREES CENTIGRADE
FIGURE 5. DIRECT-READINO MOISTURE-VISCOSITY GRAPH
MARCH 15, 1939
ANALYTICAL EDITION
CONTENT OF HONEY TABLE 11. MOISTURE Sample
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
Viscosity, v40
Moisture Content B y ev& ora- From viscostion, o&cial ity graphio method Aethod
Difference
See.
%
%
%
37.0 23.2 36.0 50.7 68.1 26.9 20.4 19.3 18.7 47.9 42.9 32.8 62.0 238.5 119.6 22.3 18.9 19.1 35.4 29.6 21.8 29.4 15.8 209,4 310.3 58.6 23.7 167.6 40.8
16.52 17.85 16.59 15.90 15.16 18.05 18.69 18.52 18.64 15.70 16.16 16.46 15.56 12.39 13.76 18.21 18.82 18.99 16.96 17.09 18.02 17.59 19.73 13.04 12.31 15.86 18.12 13.64 16.56
16.7 18.2 16.8 15.8 15.2 17.6 18.5 18.8 18.9 16.0 16.3 16.6 15.3 12.7 13.9 18.3 18.8 18.8 16.8 17.4 18.3 17.4 19.5 12.9 12.3 15.5 18.1 13.3 16.4
+0.2 +0.3 +0.2 -0.1 0.0 -0.7 -0.1 +0.3 +0.3 +0.3 +o. 1 +O.l -0.3 10.3 +o. 1 +o. 1 0.0 -0.2 -0.2 +0.3 $0.3 -0.2 -0.2 -0.1 0.0 -0.4 0.0 -0.3 -0.2
is introduced merely for convenience. This equation may be .converted to the form log V T - log V T = ~ m ( l / T - TI) (1) in which V T ,is the viscosity a t any particular temperature 2'1, and m is the slope of the line. This may be rearranged, and adapted to the data of Figure 1 a t 40", by the introduction of the factor lo4,to yield 313 - T log Val3 = log VT - -X m From this can be calculated VSls (viscosity a t 40") knowing the viscosity at any other temperature-that is, Equation 2 can be used to correct the viscosity a t any other temperature to 40".
Relation between Viscosity and Moisture with Temperature Constant Trial showed that the reciprocal of per cent moisture yielded a straight line when plotted against log V for any one temperature (Figure 3). Since 40" has been selected as the standard, it is only necessary to know the equation a t this temperature for calculation of w, the per cent moisture, as values of V for any other temperature between 30" and 50' can be corrected to 40" with Equation 2. The viscositymoisture equation a t 40" was determined to be 42.8(16.00 - W ) 1.6,6 log V318 = (3) 16.00 w +
The correlation of points is not as good in Figure 3 as in Figure 2. This may be attributed both to the difficulty of obtaining uniform results with the A. 0. A. C, method (3) and to the fundamental lack of a closer correlation between viscosity and moisture content.
General Relation of Viscosity-MoistureTemperature
It was evident that Equations 2 and 3 would be more convenient if combined into one expression, because only one calculation would then be necessary for moisture determinations at temperatures other than 40". This combination
133
was effected as follows: The slopes, m, of the family of straight lines in Figure 2 were determined graphically and plotted against the values of log VSI~,corresponding to each value of m, resulting in the straight line of Figure 4. Its equation was determined to be m = 0.1460 log
+ 0.2175
(4) By substituting 4 in 2 and solving for Val3 there is obtained (0.0313 log V T 0.2175 T - 68.1 log Val8 = (5) 45.7 - 0.1147 T v 3 1 8
+
Finally, by equating the values of log V313 given in 3 and 5 there results, upon solving for w , the equation - 156.7 T w = T (log V 62,500 (6) , 1) - 2.287 (313 - T)
+
which gives w , as desired, in terms of V T and T.
Graphic Representation of Equation 6 Because of the realization that the solution of Equation 6 might be an obstacle in practice, it was decided to represent the material contained therein graphically for rapid and convenient reference. Accordingly, Figure 5 was constructed, from calculated values of rn and log Vs13 corresponding to even values of w , the scales being marked in terms of seconds, percentages, and Centigrade temperatures directly. In order to obtain the per cent moisture from this graph, it is necessary only to locate point p on the graph corresponding to the observed values of viscosity and temperature, and lay a straightedge through p in the mean direction of the adjacent "isomoisture" lines. At the point of intersection of the straightedge with the moisture scale, the per cent is read as closely as possible.
Summary The relative viscosity, as measured by the falling-sphere method under vigorously defined conditions, affords a rapid and practical method of determining the moisture content of honey. The results may be evaluated either by the use of empirical equations or, more simply, by the use of a specially constructed graph. A comparison of the results (Table 11) on 29 samples of honey of different floral types by the viscometric and official drying methods showed an average difference of 0.2 per cent. Literature Cited (1) Andrade, E. N. da C., Nature, 125, 309, 582 (1930). (2) Andrade, E. N. da C., Phil. Mag., [7]17, 692 (1934), (3) Assoc. Official Agr. Chem., Official and Tentative Methods, 4th ed., p. 462, 1935. (4) Auerbach, F.,and Borriee, G., 2. Untersuch. Nahr. Genussm., 47, 177 (1924). (5)Ibid., 48,272 (1924). (6) Bacon, L. R., J. Franklin Inst., 221, 251 (1936). (7) Chataway, H.D., Can. Bee J.,43,215 (1935). (8) Chataway, H.D.,Can. J . Research, 6,532 (1932). (9) Ibid., 8,435 (1933). (10) Dunn, J. S., Trans. Faraday SOC.,22, 401 (1926). and Jacobs, L. M., J . Chem. SOC.,117,473(1920). (11) Gibson, W. H., (12) Gueman, J. de, Anales SOC. espaa. 5 s . quim., 11, 353 (1913); J. Chem. SOC.,104,ii, 836 (1913). (13) Kendall, J., and Monroe, K. P., J . Am. Chem. Soc., 39, 1787 (1917). (14) Lorente, H.A.,Verslag. Akad. Wetenschappen Amsterdam, 5,168 (1896); Fortschr. Physik, 1896,I, 307. Phil. Mag., [6] 23,458 (1912). (15) Porter, A. W., (16) Sheppard, S.E., Nature, 125,489 (1930). (17) Stokes, G.G., Phil. Mag., [31 29, 60 (1846); Trans. Cambridge Phil. SOC.,8,287 (1850). RECEIVBD September 19, 1938. Presented before the Division of Agricultural and Food Chemistry at the 96th Meeting of the American Chemical Society, Milwaukee, Wis., September 5 to 9, 1938.
