Temperature dependence of liquid viscosity

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The temperature dependence of liquid viscosity is usually expressed by one of the following models:

Exponential model

[\mu(T)=\mu_0 \exp(-bT) ]

where T is temperature and [\mu_0] and [b] are coefficients. See first-order fluid and second-order fluid. This is an empirical model that usually works for a limited range of temperatures.

Arrhenius model

The model is based on the assumption that the fluid flow obeys the Arrhenius equation for molecular kinetics:

[\mu(T)=\mu_0 \exp( \frac ) ]

where T is temperature, [\mu_0] is a coefficient, E is the activation energy and R is the universal gas constant. A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature.

WLF model

The Williams-Landel-Ferry model or WLF for short is usually used for polymer melt's or other fluids that have a glass transition temperature.

The model is:

[\mu(T)=\mu_0 \exp \left( \frac \right)]

where T-temperature, [C_1], [C_2], [T_r] and [\mu_0] are empiric parameters (only three of them are independent from each other).

If one selects the parameter [T_r] based on the glass transition temperature, then the parameters [C_1], [C_2] become very similar for the wide class of polymers. Typically, if [T_r] is set to match the glass transition temperature [T_g], we get

[C_1 \approx]17.44

and

[C_2 \approx]51.6 K.

Van Krevelen recommends to choose

[T_r=T_g+43] K, then

[C_1 \approx]8.86

and

[C_2 \approx]101.6 K.

Using such universal parameters allows one to guess the temperature dependence of a polymer by knowing the viscosity at a single temperature.

In reality the universal parameters are not that universal, and it is much better to fit the WLF parameters from the experimental data.

 

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