functionDynamicViscosityWater

Information

1. Purpose of model

Pure function that computes the dynamic viscosity of ordinary (liquid) water as a function of temperature and density, following the IAPWS-R12-08 formulation. It provides the temperature- and density-dependent viscosity used by the aquifer flow models (ControlVolumeL4, DarcyFlow_horizontal/vertical) instead of a constant value.

2. Level of detail, physical effects considered, and physical insight

Purely mathematical component. Implements the first two factors of the IAPWS-R12-08 correlation:

• Zero-density (dilute-gas) limit term eta_0(T).
• Residual term eta_1(T, rho) accounting for the density dependence.

The critical enhancement factor eta_2 is set to 1 (neglected), so the function is not valid in the immediate vicinity of the critical point.

3. Limits of validity

- Not valid near the critical point (645.91 K < T < 650.77 K together with 245.8 kg/m³ < rho < 405.3 kg/m³), because the critical enhancement term of IAPWS-R12-08 is omitted.

- Valid for ordinary water (H2O) within the temperature/density range of the IAPWS-R12-08 industrial formulation.

- The density rho must be the actual water density consistent with the temperature (e.g. taken from a TILMedia property model).

- All coefficients are constants of the IAPWS-R12-08 release.

4. Interfaces

Inputs:

T — temperature of water [K]

rho — density of water [kg/m³]

Output:

eta — dynamic viscosity of water [Pa·s]

5. Nomenclature

	T	temperature of water [K]
	rho	density of water [kg/m³]
	eta	dynamic viscosity of water [Pa·s] (output)

Reference constants and auxiliary quantities (IAPWS-R12-08):

T_ref = 647.096 K, rho_ref = 322.0 kg/m³, eta_ref = 1×10^-6 Pa·s — reference temperature, density and viscosity

T_d = T / T_ref, rho_d = rho / rho_ref — reduced (dimensionless) temperature and density

eta_0 — viscosity in the zero-density (dilute-gas) limit [-]

eta_1 — residual viscosity contribution due to finite density [-]

H_0 ... H_3 — coefficients of the zero-density term [-]

C_ij — coefficients of the residual (density-dependent) term [-]

6. Governing Equations

Reduced variables:

T_d = T / T_ref,   rho_d = rho / rho_ref

Zero-density (dilute-gas) limit:

eta_0 = 100 · sqrt(T_d) / ( sum_i=0..3 H_i / T_dⁱ )

Residual (density-dependent) contribution:

eta_1 = exp( rho_d · sum_i=0..5 (1/T_d − 1)ⁱ · sum_j C_ij (rho_d − 1)^j )

Dynamic viscosity (critical enhancement factor eta_2 = 1 neglected):

eta = eta_0 · eta_1 · eta_ref

7. Remarks for Usage

Pure function (no side effects). Pass a density that is consistent with the temperature (e.g. from a TILMedia VLEFluid property record). The result is returned in Pa·s. Used inside ControlVolumeL4 to populate the temperature- and density-dependent viscosity fields f_eta / f_eta_v of the Darcy flow models.

8. Validation

Implements the industrial formulation of IAPWS-R12-08; reference values for verification are provided in the IAPWS-R12-08 release. The function is exercised within the ATES aquifer models (e.g. ATES.Validierung.Buoyancy.Val_homogenLayer).

9. References

[1] IAPWS (2008): Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance. International Association for the Properties of Water and Steam.

[2] Huber, M. L., Perkins, R. A., Laesecke, A., Friend, D. G., Sengers, J. V., et al. (2009): New International Formulation for the Viscosity of H2O. Journal of Physical and Chemical Reference Data, 38(2), 101–125. doi:10.1063/1.3088050.

10. Version History

Function created by Markus Gillner (markus.gillner@tuhh.de), May 2026

Documentation added by Markus Gillner (markus.gillner@tuhh.de), June 2026

Inputs

Outputs