Viscosity of the Metallic Liquids Model

This section provides details about calculating the dynamic and kinematic viscosities.

The viscosity of metallic liquid alloys is modeled as follows:

viscosity of metallic liquid alloys

where

  • dynamic (or shear) viscosity of the liquid is the dynamic (or shear) viscosity of the liquid,
  • viscosity at finite temperatures is the viscosity at finite temperatures,
  • activation energy is the activation energy in J/mole,
  • gas constant is the gas constant, and
  • absolute temperature is the absolute temperature.

The SI unit of viscosity is pascal.second (Pa.s). The viscosity parameters are expanded via Redlich-Kister polynomials.

For example, viscosity of a liquid A-B alloy is:

viscosity of a liquid A-B alloy

The two first terms are the contributions for the end-members, A and B elements and the last term accounts for the excess viscosity. Basically, the activation energies are optimized. parameter L0 that is optimized to fit the viscosity data and parameter L1 that is optimized to fit the viscosity dataetc. are the parameters that are optimized to fit the viscosity data.

The kinematic viscosity, kinematic viscosity, is the ratio of the dynamic viscosity, kinematic viscosity, to the density, density, of the alloy:

ratio of the dynamic viscosity to the density

The SI unit of kinematic viscosity is square meter per second (m2/s).

Both the dynamic viscosity and kinematic viscosity can be calculated, retrieved, shown, and plotted in Thermo‑Calc via the variables in Console Mode, using the quantity names in Graphical Mode, and also via the quantities in the SDKs.

The values for dynamic viscosity and kinematic viscosity in Console Mode are obtained with the variables DVIS (dynamic viscosity) and KVIS (kinematic viscosity). For example, once the equilibrium is calculated in Console Mode, you can get the viscosity value by show DVIS(LIQUID) or show KVIS(LIQUID).

On the Plot Renderer in Graphical Mode, the dynamic viscosity and kinematic viscosity each can be directly plotted when the variables are available to select.

The quantities of DVIS (dynamic viscosity) and KVIS (kinematic viscosity) can be retrieved, for a phase, e.g. DVIS(FCC_A1), or for a system, i.e. DVIS, via get_value_of() or get_values_of(), from most phase equilibrium calculations in these Software Development Kits (SDKs), for instance,

  • with_single_equilibrium_calculation(),
  • with_property_diagram_calculation() or
  • with_batch_equilibrium_calculation().

These can also be accessed in both ThermodynamicQuantity.kinematic_viscosity("LIQUID") or ThermodynamicQuantity.dynamic_viscosity("LIQUID").

There are two basic examples included with your software installation and that use demonstration (DEMO) databases.

Search the help (press F1 when in Thermo‑Calc) for brief descriptions of these examples, or browse to the examples located in your installation. From the main menu, Help→ Examples Files:

  • Graphical Mode T_12_Viscosity_in_Cr-Ni.tcu
  • Console Mode tcex55