Summary
In this paper, several methods of measuringσ 2 have been compared for the four systems reported in Part 1 (1). These are a 1% solution of polyacrylamide in a water/glycerol mixture, a solution of polyisobutylene in oil (Paratac), 0.05 M/0.05M solution of cetyltrimethyl ammonium bromide (CTAB) and toluene sulphonic acid (TSA), and a 16% tetradecyldimethyl ammonio propane sulphonate (DMH)/4% sodium dodecyl sulphate (SDS).
Total thrusts were measured in three geometries for all four systems and pressure profiles in a coneand-plate configuration were measured for the polyacrylamide and CTAB/TSA solutions. The sources of errors arising from edge effects or experimental spread in the determination of thrusts at various gaps were examined comprehensively and a working range for obtaining reliable estimates ofσ 2 was established. Both the Paratac and CTAB/TSA gave negative values which compared well with the generally accepted values in the literature (refs 4, 5, 9, 32–40). The polyacrylamide system gave a small positiveσ 2 while for DMH/SDS,σ 2 was positive at low shear-rates, and became negative as the shear-rate increased. These latter results appear to be a true manifestation of the systems and cannot be explained by errors in the techniques.
Zusammenfassung
Es wurden in dieser Mitteilung einige Methoden für die Messung vonσ 2 für die vier in Teil 1 angegebenen Systeme verglichen. Dies sind eine 1%-Lösung von Polyacrylamid in einem Wasser-Glyzerin-Gemisch, eine Lösung von Polyisobutylen in Öl (Paratac), eine 0.05 M/0.05 M-Lösung von Cetyltrimethylammoniumbromid (CTAB) resp. Toluolsulfonsäure (TSS), sowie eine 16%-Lösung von Tetradecyldimethylammoniopropansulfonat (DMH)/4% Natriumdodecylsulfat (NaDS).
Es wurden die Gesamtschubwerte in drei Geometrien für alle vier Systeme und Druckprofile in einer Konusund-Platte-Konfiguration für die Polyacrylamid- und CTAB/TSS-Lösungen gemessen. Die Fehlerquellen, die von Randeffekten oder von versuchsbedingten Streuungen bei der Bestimmung von Schubwerten an verschiedenen Spalten stammen, wurden umfassend untersucht, sowie ein Arbeitsbereich, um verläßliche Schätzungen vonσ 2 zu bekommen, festgestellt. Die Paratac- sowie auch die CTAB/TSS-Lösungen zeigten negative Werte, die in guter Übereinstimmung mit den allgemein angenommenen Literaturwerten waren (4, 5, 9, 32–40). Das Polyacrylamidsystem zeigte einen kleinen positivenσ 2-Wert, während bei DMH/NaDSσ 2 positiv wurde bei niedrigen Schubgeschwindigkeiten, er wurde negativ mit steigenden Schubgeschwindigkeiten. Diese Resultate geben anscheinend eine wahre Eigenschaft der Systeme wieder und sind durch Fehler in der Arbeitsweise zu erklären.
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Abbreviations
- \(\dot \gamma \) :
-
shear rate
- \(\dot \gamma _R \) :
-
shear rate at edge of gap
- σ 1 :
-
first normal stress difference
- σ 2 :
-
second normal stress difference
- σ *2 :
-
point value ofσ 2
- ρ :
-
density
- Ω :
-
rotational speed
- ψ 0 :
-
cone angle
- C :
-
centre gap between platens
- d :
-
edge separation
- f :
-
thrust per unit area of platens
- f 1 :
-
thrust per unit area of platens due toσ 1
- g :
-
acceleration due to gravity
- P 22 :
-
2-2 component of stress tensor
- P′ 22 :
-
P 22 corrected for hole pressure
- P H :
-
hole pressure
- R :
-
radius of platen
- r 0 :
-
radius at whichP 22 = 0
- h :
-
rise height of fluid in manometer platen
- p(r) :
-
pressure on plate at distantr from axis of rotation\(\bar p - p_a \)
- p a :
-
atmospheric pressure
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Barnes, H.A., Eastwood, A.R. & Yates, B. A comparison of the rheology of two polymeric and two micellar systems. Part II: Second normal stress difference. Rheol Acta 14, 61–70 (1975). https://doi.org/10.1007/BF01527213
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DOI: https://doi.org/10.1007/BF01527213