Theory

The program uses Sutherland's law (Sutherland, 1893) in the reference form of equation (1). It converts this to the two-constant form of equation (2), which OpenFOAM's sutherland transport model requires (OpenFOAM user guide, 2026): $A_s$ from equation (3) and $T_s = S$ . The same law provides the viscosity for:

the incompressible solution (at the Material step's temperature);
the heat-transfer correlations;
the acoustic packing and perforate models.

$S = 0$ makes the viscosity grow as $T^{1/2}$ (hard spheres). The packing flow resistivity, which is measured with room-temperature air, is scaled with the viscosity of this gas relative to that of air at 20 °C.

Equations

\mu(T) = \mu_\mathrm{ref}\left(\frac{T}{T_\mathrm{ref}}\right)^{3/2}\frac{T_\mathrm{ref} + S}{T + S}

(1)

\mu(T) = \frac{A_s\,T^{3/2}}{T + T_s}

(2)

A_s = \mu_\mathrm{ref}\,\frac{T_\mathrm{ref} + S}{T_\mathrm{ref}^{3/2}}, \qquad T_s = S

(3)

where	meaning	unit
$\mu$	Dynamic viscosity	Pa s
$\mu_\mathrm{ref}$	Viscosity at the reference temperature (entered in µPa s)	Pa s
$T_\mathrm{ref}$	Reference temperature	K
$S$	Sutherland temperature	K
$A_s$	Sutherland coefficient	kg/(m s K^0.5)
$T_s$	Sutherland temperature of the solver	K
$T$	Temperature	K

Default and rule

Default: 17.16 µPa s at 273.15 K, S = 110.4 K (air)
Rule: A new material starts with the values for air: 17.16 µPa s at 273.15 K, $S$ = 110.4 K ( $A_s$ = 1.458e-6).
Source: Sutherland's law (Sutherland, 1893) in the two-constant form of OpenFOAM's sutherland transport model (OpenFOAM user guide, 2026).

Valid range mu_ref > 0; T_ref > 0; 0 <= S <= 5000 K

Typical S

Air 110.4 K, N₂ 111 K, CO₂ 240 K, helium about 79 K.

Fit range

Sutherland's law with one reference point is accurate over a few hundred kelvin around that point; choose the reference near the temperature of the run.

Viscosity (custom gas)

Theory

Equations

Default and rule

Valid range mu_ref > 0; T_ref > 0; 0 <= S <= 5000 K

References 2

Theory

Equations

Default and rule

Valid range mu_ref > 0; T_ref > 0; 0 <= S <= 5000 K

Related 4

References 2