Viscosity is a measure of the resistance of a fluid system against flow, i.e., forces of mechanical deformation. This resistance is caused by the internal friction within a liquid and is apparent when such forces of deformation are applied to it [1, 2, 3].
Viscosity is expressed in Pascal × second [Pa × s].
In the past, the unit Poise was used. The following relationship exists between the two:
1 Pascal × second is equal to the dynamic viscosity between two layers of a homogenous, laminarly flowing fluid moving in parallel along a horizontal plane at a vertical distance of 1 m from one other, with a velocity difference of 1 m/s, between which the shear stress of 1 Pa exists:
1 Pa × s = 1 N × s/m² = 1 kg/m × s
The rheological behavior of substances is dependent upon temperature, concentration, particle size and particle charge, among other things. With ideally viscous fluids, also known as Newtonian fluids, the shear stress increases proportionally to the shear velocity and to the viscosity. Only with these fluids is the viscosity relatively simple to quantify.
To facilitate comparison of the results from either wort or beer, it is necessary to adjust the values to a defined extract content or original gravity, respectively. As wort and beer are diluted, the change in viscosity is not proportional but rather follows a hyperbolic function. The viscosity of the wort samples (adjusted to an extract content 8.6 % or 12.0 %) and viscosity of beer samples (adjusted to an original gravity of 12 %) are calculated with the help of tabulated values recorded by KOLBACH [4] or the trigonometric function developed by ZÜRCHER [5]. The viscosity can be determined quickly by using a computer to calculate the ZÜRCHER function.
The equations are as follows:
\(η_{\text{dissolved substances}} = \text{dynamic viscosity}_{\text{measured}} \space– \space1.002\)
\(a = {ln \hspace{0.2em} η_{gel.} + \sqrt{η_{gel.}^2+1} \over c^{1.20}}\)
\(\text{Dynamic viscosity η}_{\text{standardized}} = {{e^{a \hspace{0.2em} × \hspace{0.2em} x^{1.20}}} – \hspace{0.2em} {e^{-a \hspace{0.2em} × \hspace{0.2em} x^{1.20}}} \over 2}+1.002\)
\(\text{Kinematic viscosity 𝝂} = {η \over 𝝆}={Pa \hspace{0.2em} × \hspace{0.2em} s \over kg \hspace{0.2em} × \hspace{0.2em} m^3} = {m^2 \over s} = {10^6 \hspace{0.2em} mm^2\over s}\)
| a |
= |
constant, dependent upon the composition of the wort or the beer |
| x |
= |
standardized extract content in percent (% w/w): For beer and cast-out wort samples adjusted to 12 % Plato, for congress wort adjusted to 8.6 % |
| η |
= |
dissolved substances = dynamic viscosity measured for a given extract or original gravity reduced by 1.002 |
| c |
= |
extract content or original gravity measured for the sample percent in percent (% w/w) |
| ρ |
= |
density of the sample in kg ×m3 |
The calculation may also be performed using the slide rule developed by Zürcher [6].
Devices for measuring viscosity can be calibrated using freshly double-distilled water (1.002 mPa × s at 20.0 °C), a 20 % w/w sucrose solution (1.941 mPa × s at 20.0 °C) as well as with Newtonian oil reference standards (e.g., oil no. 2A) from the Physikalisch-Technischer Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany.
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E. Krüger, H. J. Bielig, Betriebs- und Qualitätskontrolle in Brauerei und alkoholfreier Getränkeindustrie, Verlag Parey, Berlin und Hamburg, 142, 1976
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M. Heidinger, Messung rheologischer Eigenschaften, ed. Contraves AG, CH-8052 Zürich
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DIN und DIN-ISO-Normen (Viskosität), Beuth Verlag GmbH, D-10787 Berlin
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P. Kolbach, MB 13, 21, 1960
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Ch. Zürcher, MB 26, 242 und 258, 1973
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Ch. Zürcher, MB 27, 127, 1974