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Temperature dependence of liquid viscosity

From Biocrawler, the free encyclopedia.

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

Exponential model

$μ(T) = μ 0 exp( - b T)$ where T is temperature and $μ 0$ and $b$ a coefficients. See First-Order Fluid and Second order fluid. This is an empiric model that usually works for limited range of temperatures.

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Arrhenius model

The model is based on asumption of the fluid flow to obey Arrhenius equation for molecular kinetics:

$\mu(T)=\mu_0 \exp( \frac {E}{RT} )$

where T is temperature, $μ 0$ is a coefficient, E is the activation energy and R is the universal gas constant

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WLF model

Williams-Landel-Ferry model or WLF for short is usually used for polymer melts or other fluids that has Glass transition temperature.

The model is: $\mu(T)=\mu_0 \exp \left( \frac {C_1 (T-T_r)} {C_2+ T -T_r )} \right)$

where T-temperature, $C 1$ , $C 2$ , $T r$ and $m u 0$ are empiric parameters (only three of them are independent from each other).

If select parameter $T r$ based on glass transition temperature., then 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 allow to guess temperature dependence of a polymer by knowing viscosity only at one temperature.