Studies in Newtonian Flow. I. The Dependence of the Viscosity of Liquids on Temperature

Abstract

It is shown that the Walther and Andrade equations, while very satisfactory for moderate ranges of temperature, are not adequate to define the dependence of the viscosity of liquid normal paraffins on temperature over extended ranges. One method of developing a viscosity-temperature relationship is presented that gives equations defining this dependence with satisfactory validity. The purpose of this paper is to show that the precise dependence of the viscosity of liquids on temperature is complicated. This is in contrast to the relatively simple relation for the precise dependence of the viscosity of liquids on free-space which will be presented in subsequent papers.

Using 20-million-year-old amber to test the super-Arrhenius behaviour of glass-forming systems

“…Once the equilibrium line is crossed, as temperature increases further, the glass is in a state of lower volume or enthalpy than the equilibrium value (HoH eq ). As a result, the relaxation times for these points should be longer than the equilibrium values of relaxation time owing to the high density 29 -hence they are upper bounds to the equilibrium value.…”

“…However, as shown in the figure, as temperature is increased the volume (or enthalpy H) increases and eventually intersects with the equilibrium liquidstate extrapolated parameter. At temperatures below this intersection (H4H eq ), the relaxation times measured should be shorter than the equilibrium times owing to the excess of volume or enthalpy relative to the equilibrium state 29 . Once the equilibrium line is crossed, as temperature increases further, the glass is in a state of lower volume or enthalpy than the equilibrium value (HoH eq ).…”

Free volume dependence of polymer viscosity

“…In earlier publications on the relationships between shear viscosity and a measure of free volume (Batchinski 1913;Doolittle 1951aDoolittle ,b, 1952Doolittle and Doolittle 1957;Utracki 1974Utracki , 1983aUtracki -c, 1985Utracki , 1986) the liquids of interests were low molecular weight solvents or oils. For these substances, the zero-shear viscosity, η 0 , followed the empirical equations relating it to density, ρ=1/V=ρ(P, T), as proposed by Batchinski and by Doolittle, or to the hole fraction, h, computed from the PVT surface.…”

“…Thus, the total specific volume of a given liquid is: V ¼ V 0 þ V f , and the free volume fraction: Batchinski (1913) showed that zero-shear viscosity (η 0 ) of low molecular weight liquids at different T and P changes with the density (ρ), i.e., with f: η 0 òρ. Four decades later Doolittle (1951aDoolittle ( ,b, 1952Doolittle ( , 1954Doolittle and Doolittle 1957) correlated viscosities with redefined free volume [f D ≡V f /V 0 =f/(1−f )]:…”

Rheology of Polymers with Nanofillers

“…Doolittle modified Eq. (16.34) to read [Doolittle 1951a[Doolittle , b, 1952[Doolittle , 1954Doolittle and Doolittle, 1957] ln η 0,P,…”