T H E EFFECT OF TEMPERATURE ON T H E BASIC VISCOSITY OF ICE-CREAM MIXES BY ALAN LEIGHTON AND OWEN E. WILLIAMS*
This paper shows that under normal temperature conditions the basic viscosity of ice cream mixes varies inversely with the temperature. In a previous paper' it was shown that ice-cream mixes exhibit a true basic viscosity or, in other words, that when an ice-cream mix is stirred with sufficient vigor the viscosity drops to a certain value beyond which it is not lowered by continued stirring, at least under conditions encountered in the usual type of commercial ice-cream freezer. The change in value of this basic viscosity with variation in water concentration at constant temperature was shown to follow closely a slight modificationof the empirical equation given by Arrhenius.2 The modified form of the equation which is that of a straight line is log? = 8 C K (Equation I ) in which equation, 7 is the viscosity in centipoises, C is the concentration in part solids to I O O parts water, and 8 and K are constants. It was further pointed out that when C becomes zero, log 7 = K, or the antilogarithm of K should equal the viscosity value of water at the temperature at which the measurements are made. The true viscosity value of water at oo C. was only approximated in those experiments. The variation was attributed to errors arising from the fact that the concentration (C) was expressed in terms of parts solids in IOO parts water instead of in terms of molecular concentration. When freshly prepared ice-cream mixes are allowed to stand at low temperatures they show a marked increase in viscosity. In commercial practice, freshly prepared mixes are usually held for a period of at least twenty-four hours before being frozen as it is the common belief that this increased viscosity is desirable. This procedure is known technically as ripening and is sometimes called aging. Since this increased viscosity was found to be destroyed by mechanical stirring, it was pointed out that the increase must be due to the formation of a mechanical structure in the mix rather than to the hydration of the protein molecules, as it is difficult to see how hydrated water could be removed by mechanical force. The above mentioned experiments were carried out at a temperature of oo C. with three mixes of different basic concentrations. This paper gives the results obtained by determining the basic viscosity of different water concentrations of two mixes of essentially the same basic composition through a
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'Alan Leighton and 0. E. Williams: The Basic Viscosity of Ice Cream Mixes. J. Phys.Chem.,31, 596 (19zj). Svante Arrhenius: Viscosity and Hydration of Colloid Eo:utions. Medd. Wobel Inst. 3 (13), 1-20 (1916).
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ALAN LEIGHTOX AND OWEN E. WILLIAMS
temperature range of 8°C. to - I O C. The temperature range, which is near freezing, permits the temperature curve for each concentration to be extrapolated to the freezing temperature of that particular concentration. The viscosity value at the freezing temperature will then be the viscosity value of the unfrozen portion of the basic mix when this temperature IS reached in the freezer. This point will be discussed later. The data of these two experiments are reported because they are more nearly complete than the data of a number of others carried out with mixes of different basic concentrations. However, the existence of the same viscosity relationships is shown in all cases. As in the previous work, four concentrations of the basic mix were made up for this experiment. The highest concentration was prepared directly from cream, condensed skim milk, sugar, and gelatin. The basic viscosity of this mass was determined through the chosen temperature range. The mix was then diluted to the next concentration by the addition of cold water, the measurements repeated, and the work further repeated through the lower concentrations. Each complete series of temperature-concentration-viscosity measurements extended over periods of from three to four days. For the determination of the basic viscosity, the laboratory, horizontal, brine-cooled, six-gallon ice-cream freezer was completely filled with the mix so that air could not be whipped in, and the dashers rotated at a speed of 175 R.P.M., the normal speed of the freezer. The temperature in the freezer was controlled manually. At frequent intervals samples were drawn from the freezer into small flasks, packed in shaved ice and carried to the viscometer which was immersed in a constant temperature bath adjusted to the temperature of the experiment. Two entirely separate batches of a normal icecream mix were used as the basis of the series of experiments here reported. Their basic composition was: Fat Sugar Milk solids not fat Gelatin
12.00
14.00 IO.00
.30 36.30 Water 63.70 Measurements of mix No. I were made at concentrations of 57.0, 70.0, 83.0,and 100.0parts total solids to I O O parts water; and of mix No. 2 at concentrations of 56.99, 78.26, and 99.53 parts total solids to I O O parts water. In the latter series it was found impossible to get consistent measurements at concentrations of I 2 0 parts total solids to I O O parts water. This was due, apparently, to the progressive precipitation of lactose from the mix. It should be pointed out here that the basic mix of normal concentration is practically saturated to lactose a t a temperature of oo C. This means that in nearly all of this work solutions supersaturated with lactose are being dealt with. Were it not for the unusual ability of lactose to form highly supersaturated solutions it would be practically impossible to get consistent results in these series of experiments.
BASIC VISCOSITY O F ICE-CREAM hlIXES
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Table I shows the viscosities for both series of experiments at four temperatures, also the calculated values of 8 and K. I n Fig. I are given the straight-line curves obtained by plotting logarithmically against concentration the viscosity values at different temperatures for both series of experiments.
Although there is a slight variation in the value of 8 for the different series of measurements at the different temperatures, in each experiment this value can without any serious error be considered as a constant. The value of the constant K does, however, vary with the temperature. Since 8 gives the slope of the lines and is constant, it follows that the lines are parallel. The values of K determine the relative positions of the lines at the different temperatures. A direct plotting of the antilogarithms of K against temperature gives a straight line in both experiments, Fig. 2 . This means that within the temperature range of these experiments the viscosity value bears an inverse straight-line relationship to the temperature. A calculation of the value of K in terms of temperature gives the following relationships, ForexperimentNo. I , K = log(2.3746 - .08233 T) For experiment Xo. 2 , K = log (2.5016 - ,0635 j T ) T is expressed in degrees Centigrade. By substituting in equation I , (log q = 0 C K), the values of K deteritlined empirically above, the following results are obtained: For experiment No. I , log q = .02006c log (2.3746 - .08237T) (Eq. 2) For experimentxo. 2 , log q = .01860c log (2.j016 - .063 j5T) (Eq. 3)
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ALAN LEIGHTON AND OWEN E. WILLIAMS
N 3
P
P
$ 2
uuuu 0
m
0
0
I O N
0 3
I
@
2
suuu 0
m
0 0 0 r 0 N 3
I
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BASIC VISCOSITY O F ICE-CREAM MIXES
These equations give the viscosity values of the two experimental mixes in terms of concentration and temperature. As with any water solution ice separates from a liquid ice-cream mix when the temperature is lowered to the proper point. Further cooling causes a continued ice separation and a progressive concentration of the milk solids in the unfrozen portion of the mix. The freezing-point-concentration relationships of the experimental mixes can also be calculated empirically.' Taking into consideration these data and
V A L U E S OF K (Ant.\.g8r\tnmc )
FIG.2 The Variation with Temperature of the Antilogarithms of K
FIG.3 The Increase in Viscosity of the Unfrozen Portions of Mixes I and I1 with Lowering Temperature during the Freezing Process
the measured viscosity-temperature-concentration relationships expressed in equations 2 and 3, and assuming that there is 1ittle.or no supercooling, the change can be shown in the value of the viscosity of the unfrozen portions of the experimental mixes with the lowering of the temperature during the freezing process. Since the experimental mixes Nos. I and z have identical basic composition they will have the same ice curve. Experiments have shown, however, that their viscosity values are different. Table I1 and Fig. 3 give the results of the calculations made to show the change of viscosity in the unfrozen portions of such mixes with change in temperature during the freezing process. 'Alan Leighton: On the Calculation of the Freezing Point of Ice Cream Mixes.
J. Dairy Sci., 10, 333 (192;).
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ALAN LEIGHTON AND OWEN E. WILLIAMS
TABLE I1 Freezing Points and Corresponding Viscosity Values of Four Concentrations of Nos. I and 2 Mixes CON CENTRATION
57 Pts. to IOO HrO
Temp. Visc. I Visc. 2
57 Pts. t o 100 H'O
oOc 33.02
-2.25'F.P. 35.60
28,74
30.38
7 0 Pts. to IOO H10
-276"F.P. 65.98 53.65
83 Pts. to IOO H O -3.28"F.P. 122.3
94.79
to
IO0 Pts. IOO H:O
-3.96'F.P. 273.9 199.4
The great increase in the viscosity of the unfrozen portion of the mix in the ice-cream freezer during the freezing process is t'hus shown. Conclusions: The experiments reported show that viscosity in ice-cream mixes bears an inverse linear relationship to temperature. These relationships of temperature] concentration, and viscosity have been expressed by simple empirical equations. The increase in the viscosit,y of the unfrozen portion of the ice-cream mix during the freezing process has been demonstrated. During the freezing process the lowering of the temperature results in an increase in the concentration of the milk solids and sugar in the liquid phase. This progressive concentration increase in the liquid phase increases its viscosity. The viscosity is simultaneously further increased by the effect of the temperature lowering itself. The combined effect of both temperature and concentration is shown.
