# Viscosity-temperature Dependence Models

New viscosity-temperature coupling (viscTempCoupling) has been introduced into the nanoFluidX code as an option. Three models were implemented: polynomial, Sutherland, and power law.

The polynomial dependency can be specified by five coefficients (4th order polynomial), such that the dynamic viscosity is given by:(1)
$\mu ={C}_{0}+{C}_{1}T+{C}_{2}{T}^{2}+{C}_{3}{T}^{3}+{C}_{4}{T}^{4}$
With $T$ of course being the temperature of the particle and ${C}_{n}$ being the coefficients. For air the viscosity can be approximated by a linear function, with ${C}_{1}=5×{10}^{-8}$ . The second option is the Sutherland law, which abides the following expression:(2)
$\mu =\frac{{\mu }_{0}{\left(\frac{T}{{T}_{0}}\right)}^{\frac{3}{2}}\left({T}_{0}+S\right)}{T+S}$
Where,
${\mu }_{0}$
Is the reference viscosity.
${T}_{0}$
Is the reference temperature.
$S$
Is the Sutherland coefficient.

For air, these values are: ${\mu }_{0}$ = 1.72 x 10-5Pas, ${T}_{0}$ = 273.15 K and S = 110.4.

The last option is the power law, which is defined by:(3)
$\mu ={\mu }_{0}{\left(\frac{T}{{T}_{0}}\right)}^{n}$

With $n$ being the exponent. For air, the power law values are: ${\mu }_{0}$ = 1.72 x 10-5 Pas, ${T}_{0}$ = 273.15 K and $n$ = 0.66.

First thing that needs to be specified is the viscTempCoupling switch in the Simulation parameters section.

Since the viscosity field is updated after establishing the time step, reference viscosity has to be specified in the domain parameter section as: ref_visc. The reference viscosity should be the highest expected viscosity during the simulation.

After the reference viscosity has been set, the viscosity-temperature coupling parameter section needs to be defined: see Viscosity-temperature Coupling Parameters.

Important to note is that if the viscTempCoupling is turned on, then all the fluid phase viscosities in the case have to be defined through the Viscosity-temperature coupling parameters section.