Читать книгу The Rheology Handbook - Thomas Mezger - Страница 177

From a mineral oil is known: η1 = 2.00 Pas (at T1 = +50 °C = 323 K), and η2 = 1.00 Pas

(at T2 = +80 °C = 353 K). Desired is the viscosity value η3 at T3 = +60 °C (= 333 K).

1 Here is selected: Tref = T1 = 50 °C = 323 K

2 aT is calculated for T2 (as aT2): aT2 = η2 (T2) / η1 (Tref) = 1.00 Pas / 2.00 Pas = 0.5

3 EA is calculated with Tref = 323 K and T2 = 353 K:

ln (aT) = ([EA / RG] ⋅ [(T2)-1 – (Tref)-1]), therefore: EA = ([RG ⋅ ln (aT)] / [(T2)-1 – (Tref)-1])

EA = 8.314 ⋅ 10–3 (kJ/mol ⋅ K) ⋅ ln(0.5) / (2.83 ⋅ 10–3 – 3.10 ⋅ 10–3) 1/K = 21.3 kJ/mol

1 aT is calculated for T3 = 333 K (as aT3): aT3 = exp ([EA / RG] ⋅ [(T3)-1 – (Tref)-1]aT3 = exp ([21.3/8.314 ⋅ 10–3] ⋅ [3.00 ⋅ 10–3 – 3.10 ⋅ 10–3]) = exp (-0.256) = 1/e0.256 = 0.774

2 Result: η3 (T3) = aT3 ⋅ η1(Tref) = 0.774 ⋅ 2.00 Pas = 1.55 Pas

The already mentioned and a further calculated temperature-dependent viscosity value are presented in Table 3.5.

End of the Cleverly section