- Temperature dependence of liquid viscosity
The
temperature dependence of liquid viscosity is the phenomenon by which liquidviscosity tends to fall (or, alternatively, its "fluidity" tends to increase) as its temperature increases. This can be observed, for example, by watching how cooking oil appears to move more fluidly upon a frying pan after being heated by a stove. It 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 andsecond-order fluid .This is anempirical 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 formolecular kinetics ::mu(T)=mu_0 exp( frac {E}{RT} )
where "T" is temperature, mu_0 is a coefficient, "E" is the
activation energy and "R" is theuniversal gas constant .A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature.Williams-Landel-Ferry model
The Williams-Landel-Ferry model, or WLF for short, is usually used for
polymer melt 's or other fluids that have aglass transition temperature .The model is:
:mu(T)=mu_0 exp left( frac {-C_1 (T-T_r)} {C_2+ T -T_r} ight)
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
polymer s. Typically, if T_r is set to match the glass transition temperature T_g, we get:C_1 approx17.44
and
:C_2 approx51.6 K.
Van Krevelen recommends to choose:T_r=T_g+43 K, then
:C_1 approx8.86
and
:C_2 approx101.6 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.
eeton Fit
The [http://www.springerlink.com/content/n20n33940mn3m213/?p=ce068239764c4feda3bc4176e8144163&pi=7 Seeton Fit] is based on
curve fitting the viscosity dependence of many liquids (refrigerants, hydrocarbons and lubricants) versus temperature and applies over a large temperature and viscosity range::ln left( {ln left( { u + 0.7 + e^{ - u } K_0 left( { u + 1.244067} ight)} ight)} ight) = A - B*ln left( T ight)
where "T" is absolute temperature in kelvins, u is the kinematic viscosity in centistokes, K_0 is the zero order modified Bessel function of the second kind, and "A" and "B" are liquid specific values. This form should not be applied to ammonia or water viscosity over a large temperature range.
For liquid metal viscosity as a function of temperature, Seeton proposed:
:ln left( {ln left( { u + 0.7 + e^{ - u } K_0 left( { u + 1.244067} ight)} ight)} ight) = A - {B over T}
Viscosity of water equation accurate to within 2.5% from 0 °C to 370 °C:
μ (Temp)= 2.414*10^-5 (N·s/m²) * 10^(247.8 K/(Temp - 140 K))
*N - newton
*s - second
*m - meter
*K - kelvin
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