Temperature dependence of liquid viscosity
Encyclopedia
The temperature
dependence of liquid viscosity is the phenomenon by which liquid viscosity
tends to decrease (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:
where T is temperature and
and 
are coefficients. See first-order fluid and second-order fluid
.
This is an empirical model that usually works for a limited range of temperatures.
for molecular kinetics:
where T is temperature,
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.
The model is:
where T-temperature,
, 
, 
and 
are empiric parameters (only three of them are independent from each other).
If one selects the parameter
based on the glass transition temperature, then the parameters 
, 
become very similar for the wide class of polymer
s. Typically, if
is set to match the glass transition temperature 
, we get
17.44
and
K.
Van Krevelen recommends to choose
K, then
and
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.
the viscosity dependence of many liquids (refrigerants, hydrocarbons and lubricants) versus temperature and applies over a large temperature and viscosity range:
where T is absolute temperature in kelvins,
is the kinematic viscosity in centistokes, 
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:
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))
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
dependence of liquid viscosity is the phenomenon by which liquid viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
tends to decrease (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
where T is temperature and
and are coefficients. See first-order fluid and second-order fluidSecond-order fluid
An incompressible second-order fluid is the retarded-motion expansion terms through second order. The retarded motion expansion is one constitutive model to describe non-Newtonian fluids....
.
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 equationArrhenius equation
The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of the reaction rate constant, and therefore, rate of a chemical reaction. The equation was first proposed by the Dutch chemist J. H. van 't Hoff in 1884; five years later in 1889, the Swedish...
for molecular kinetics:
where T is temperature,
is a coefficient, E is the activation energyActivation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
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.
Williams-Landel-Ferry model
The Williams-Landel-Ferry model, or WLF for short, is usually used for polymer melts or other fluids that have a glass transition temperature.The model is:
where T-temperature,
, , and are empiric parameters (only three of them are independent from each other).If one selects the parameter
based on the glass transition temperature, then the parameters , become very similar for the wide class of polymerPolymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s. Typically, if
is set to match the glass transition temperature , we get17.44and
K.Van Krevelen recommends to choose
K, thenand
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.
Seeton Fit
The Seeton Fit is based on curve fittingCurve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function...
the viscosity dependence of many liquids (refrigerants, hydrocarbons and lubricants) versus temperature and applies over a large temperature and viscosity range:
where T is absolute temperature in kelvins,
is the kinematic viscosity in centistokes, 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:
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