Читать книгу The Rheology Handbook - Thomas Mezger - Страница 179

The following holds for the viscosity/pressure shift factor ap in general:

Equation 3.11

ap = η(p) / η(pref)

The dimensionless factor ap is the ratio of the two viscosity values at the pressure p and at the reference pressure pref. For polymers, this relation is only valid for the values of the zero-shear viscosity η0. The viscosity/pressure coefficient αp is defined as follows:

Equation 3.12

ap = exp (αp ⋅ Δp)

with αp in [1/MPa = MPa-1], at the pressure difference Δp = p - pref [MPa]

Typical values of αp for liquids are in between +0.005 and +0.05 MPa-1

(or 5 ⋅ 10-3 MPa-1 ≤ αp ≤ 50 ⋅ 10-3 MPa-1). For water at T < +32 °C, the value of αp is negative, since viscosity decreases with increasing pressure as explained above; for T > +32 °C, αp is

positive, i. e. viscosity increases now with increasing pressure.

In order to estimate viscosity values at pressures at which no measuring values are available, proceed as follows:

1 Select pref (i. e. a pressure, at which an η-value is available), usually is selected:pref = 0.1 MPa (= 1 bar).

2 Calculate the shift factor ap for another available η(p)-value (using Equation 3.11).

3 Calculate the coefficient αp (using Equation 3.12).

4 Calculate the shift factor ap for the desired η(p)-value (using Equation 3.12).

5 Result: Calculate the desired η(p)-value (using Equation 3.11).