# Transport Properties

Source: https://help.sim-flow.com/documentation/panels/transport-properties
Last updated: 2026-10-14

## Introduction

![img 5959e8f2c2287](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959e8f2c2287.png)

In the **Transport Properties** panel, you can define transport properties for materials used in incompressible simulations. Here you also define properties of each phase in a multiphase simulation, as well as interactions between those phases.

## Standard Material Properties

Depending on the selected solver, the set of properties you need to define will vary. In general, you will have to specify a subset of available properties:

- **\(\beta [\frac{1}{K}]\)** - thermal expansion
- **\(D_T[\frac{m^2}{s}]\)** - thermal diffusion coefficient
- **\(\rho[\frac{kg}{m^3}]\)** - density
- **\(\nu[\frac{m^2}{s}]\)** - kinematic viscosity
- **\(\mu[Pa \cdot s]\)** - dynamic viscosity
- **\(\kappa[\frac{W}{m \cdot K}]\)** - thermal conductivity
- **\(C_p[\frac{J}{kg \cdot K}]\)** - specific heat under constant pressure
- **\(C_v[\frac{J}{kg \cdot K}]\)** - specific heat under constant volume
- **\(R[\frac{J}{kg \cdot K}]\)** - specific gas constant
- **\(H_f[\frac{J}{kg}]\)** - enthalpy of formation
- **\(S_f[\frac{J}{kg \cdot K}]\)** - standard state entropy
- **\(M[\frac{g}{mol}]\)** - molar mass
- **\(Pr[-]\)** - Prandtl number
- **\(Pr_t[-]\)** - turbulent Prandtl number
- **\(T_{ref}[K]\)** - reference temperature
- **\(p_{ref}[Pa]\)** - reference pressure
- **\(\rho_{ref}[\frac{kg}{m^3}]\)** - reference density
- **\(C_{p,ref}[\frac{J}{kg \cdot K}]\)** - reference specific heat
- **\(A_S[\frac{kg}{m \cdot s \cdot K^{0.5}}]\)** - Sutherland coefficient
- **\(T_S[K]\)** - Sutherland temperature
- **\(T_{low}[K]\)** - low Janaf temperature limit
- **\(T_{high}[K]\)** - high Janaf temperature limit
- **\(T_{common}[K]\)** - common Janaf temperature
- **\(p_{v,sat}[Pa]\)** - saturation pressure
- **\(\rho_{v,sat}[\frac{kg}{m^3}]\)** - vapor saturation density
- **\(\rho_{l,sat}[\frac{kg}{m^3}]\)** - liquid saturation density
- **\(\Psi_v[\frac{s^2}{m^2}]\)** - kinematic vapor compressibility
- **\(\Psi_l[\frac{s^2}{m^2}]\)** - kinematic liquid compressibility

## Transport Model

![img 5959e9ff88f6b](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959e9ff88f6b.png)

Most incompressible flow solvers require you to specify the **Transport Model** . The transport model specifies how viscosity depends on shear rate \(\dot \gamma\).

**Available Transport Models:**

- **Newtonian**
- **Power Law**
- **Cross-Power Law**
- **Bird-Carreau**
- **Herschel-Bulkley**
- **Casson**

### Newtonian Model

![img 5959ea5c69d54](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ea5c69d54.png)

The **Newtonian** model describes the viscosity of a [Newtonian fluid](https://en.wikipedia.org/wiki/Newtonian_fluid) , which means that viscosity does not depend on shear rate.

**Inputs:**

- **\(\nu [\frac{m^2}{s}]\)** - kinematic viscosity

### Power Law Model

![img 5959ea8e346a6](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ea8e346a6.png)

The **Power Law** model describes the viscosity of a [power-law fluid](https://en.wikipedia.org/wiki/Power-law_fluid) defined as:

\(\nu=k \cdot \dot \gamma^{n-1}\)

where:

- **\(k\)** - flow consistency index
- **\(n\)** - flow behavior index

The implementation of this model is additionally constrained, so that the computed viscosity is bounded between the specified minimum and maximum values.

**Inputs:**

- **\(\nu_{min} [m^2/s]\)** - minimum kinematic viscosity
- **\(\nu_{max} [m^2/s]\)** - maximum kinematic viscosity
- **\(k [m^2/s^{1-n}]\)** - flow consistency index
- **\(n[-]\)** - flow behavior index

### Cross-Power Law Model

![img 5959eb4e4464e](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959eb4e4464e.png)

The **Cross-Power Law** model describes the viscosity of a [Cross fluid](https://en.wikipedia.org/wiki/Cross_fluid) defined as:

\(\nu=\nu_\infty + \frac{\nu_0 - \nu_\infty}{1+(m \cdot \dot \gamma)^n}\)

where:

- **\(\nu_0\)** - viscosity at zero shear rate
- **\(\nu_\infty\)** - viscosity at infinite shear rate
- **\(m\)** - relaxation time
- **\(n\)** - power index

**Inputs:**

- **\(\nu_0 [m^2/s]\)** - kinematic viscosity at zero shear rate
- **\(\nu_\infty [m^2/s]\)** - kinematic viscosity at infinite shear rate
- **\(m [s]\)** - relaxation time
- **\(n[-]\)** - power index

### Bird-Carreau Model

![img 5959ebe75fba7](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ebe75fba7.png)

The **Bird-Carreau** model describes the viscosity of a [Carreau fluid](https://en.wikipedia.org/wiki/Carreau_fluid) using the Bird-Carreau-Yasuda formulation:

\(\nu=\nu_\infty + \frac{\nu_0 - \nu_\infty}{(1+(k \cdot \dot \gamma)^a )^{\frac{n-1}{a}}}\)

where:

- **\(\nu_0\)** - viscosity at zero shear rate
- **\(\nu_\infty\)** - viscosity at infinite shear rate
- **\(m\)** - relaxation time
- **\(n\)** - power index
- **\(a[-]\)** - Yasuda coefficient, determines how quickly viscosity transitions from \(\nu_0\) to \(\nu_\infty\)

**Inputs:**

- **\(\nu_0 [m^2/s]\)** - kinematic viscosity at zero shear rate
- **\(\nu_\infty [m^2/s]\)** - kinematic viscosity at infinite shear rate
- **\(m [s]\)** - relaxation time
- **\(n[-]\)** - power index
- **\(a[-]\)** - Yasuda coefficient

### Herschel-Bulkley Model

![img 5959ec805bca6](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ec805bca6.png)

The **Herschel-Bulkley** model represents the viscosity of a [Herschel-Bulkley fluid](https://en.wikipedia.org/wiki/Herschel%E2%80%93Bulkley_fluid) described by:

\(\nu = \{ \begin{matrix} \nu_0 & \dot \gamma \leq \dot \gamma_0 \\ k\cdot |\dot\gamma| ^{n-1}+\tau_0\cdot |\dot\gamma| ^{n} & \dot \gamma > \dot \gamma_0 \end{matrix}\)

where:

- **\(\nu_0\)** - viscosity at zero shear rate
- **\(\tau_0\)** - yield stress
- **\(k\)** - flow consistency index
- **\(n\)** - flow behavior index
- **\(\dot\gamma_0\)** - critical shear rate

**Inputs:**

- **\(\nu_0[m^2/s]\)** - kinematic viscosity at zero shear rate
- **\(\tau_0[m^2/s^2]\)** - kinematic yield stress
- **\(k[m^2/s^{1-n}]\)** - consistency index
- **\(n[-]\)** - flow index

### Casson Model

![casson model](https://help.sim-flow.com/documentation/panels/images/transport-properties/casson-model.png)

The Casson model specifies minimum and maximum viscosities. Beyond the yield stress \(\tau_0\), the viscosity is described by a relationship:

\(\nu = (\sqrt{\frac{\tau_0}{\dot \gamma}} + \sqrt{m})^2\)

**Inputs:**

- **\( m[m^2/s]\)** - consistency index
- **\(\tau_0[m^2/s^2]\)** - kinematic yield stress
- **\(\nu_{min}[m^2/s]\)** - the minimum value of viscosity
- **\(\nu_{max}[m^2/s]\)** - the maximum value of viscosity

## Phase Properties

![img 5959ed4876985](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ed4876985.png)

When you select a multiphase solver, in the **Transport** panel, a list of current phases will be displayed. When you select a phase in the list, transport properties for this phase will be displayed below.

### Phase Interactions

For multiphase solvers, besides properties for each individual phase, you will have to define interactions between the phases. Each solver models phase interactions in a different manner and therefore requires a different set of inputs.

#### Drift Flux Foam Solver

![img 5959ee4d55f83](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ee4d55f83.png)

When you select the **Drift Flux** solver, you will have to define a model for relative velocity between the continuous and dispersed phases.

**Relative Velocity Models:**

- **Simple**
- **General**

##### Simple Model

![img 5959ee9c06cbf](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ee9c06cbf.png)

The **Simple** relative velocity model calculates dispersed diffusion velocity using the formula:

\(U_d=\frac{\rho_c}{\rho}\cdot V_0 \cdot 10^{-a \alpha_d}\)

where:

- **\(V_0\)** - drift velocity
- **\(\rho_c\)** - continuous phase density
- **\(\rho\)** - mixture density
- **\(\alpha_d\)** - dispersed phase fraction
- **\(a\)** - model constant

**Inputs:**

- **\(V_0 [m/s]\)** - drift velocity
- **\(a [-]\)** - model constant
- **\(\alpha_{residual} [-]\)** - minimum dispersed phase fraction for the model to be applied

##### General Model

![img 5959eed1bdf00](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959eed1bdf00.png)

The **General** relative velocity model calculates dispersed diffusion velocity using the formula:

\(U_d=\frac{\rho_c}{\rho}\cdot V_0 (e^{a \alpha_d}-e^{a_1 \alpha_d})\)

where:

- **\(V_0\)** - drift velocity
- **\(\rho_c\)** - continuous phase density
- **\(\rho\)** - mixture density
- **\(a_d\)** - dispersed phase fraction
- **\(a\)** - model constant
- **\(a_1\)** - model constant

**Inputs:**

- **\(V_0 [m/s]\)** - drift velocity
- **\(a [-]\)** - model constant
- **\(a_1 [-]\)** - model constant
- **\(a_{residual} [-]\)** - minimum dispersed phase fraction for the model to be applied

#### Inter Solver

![img 5959eefe3cfac](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959eefe3cfac.png)

The **Inter** family of solvers requires you to specify the surface tension between the two phases.

**Inputs:**

- **\(\sigma [N/m]\)** - surface tension between phases

#### Inter Mixing Solver

![img 5959ef1927ba7](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ef1927ba7.png)

The **Inter Mixing** solver requires you to specify the surface tension and diffusion coefficient between the three phases.

**Inputs:**

- **\(\sigma_{12} [N/m]\)** - surface tension between first and second phase
- **\(\sigma_{13} [N/m]\)** - surface tension between first and third phase
- **\(D_{23} [m^2/s]\)** - diffusion coefficient between second and third phase

#### Inter Phase Change Solver

![img 5959ef2f6891b](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ef2f6891b.png)

The **Inter Phase Change** solver is used to model phase transition due to cavitation.

**Inputs:**

- **\(\sigma [N/m]\)** - surface tension between phases
- **\(p_{sat} [Pa]\)** - saturation pressure

Additionally, you will have to specify a **Phase Change Model** .

**Available phase change models:**

- **Schnerr-Sauer**
- **Merkle**
- **Kunz**

##### Schnerr-Sauer Model

![img 5959ef48ebc5a](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ef48ebc5a.png)

Schnerr-Sauer cavitation model.

**Reference:**

*Schnerr, G. H., And Sauer, J.,
"Physical and Numerical Modeling of Unsteady Cavitation Dynamics",
Proc. 4th International Conference on Multiphase Flow,
New Orleans, U.S.A., 2001.*

**Inputs:**

- **\(n [1/m^3]\)** - bubble number density
- **\(d_{nuc} [m]\)** - nucleation site diameter
- **\(C_c [-]\)** - condensation rate coefficient
- **\(C_v [-]\)** - vaporization rate coefficient

##### Merkle Model

![img 5959ef7e17ade](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ef7e17ade.png)

Merkle cavitation model.

**Reference:**

*C. L. Merkle, J. Feng, and P. E. O. Buelow,
"Computational modeling of the dynamics of sheet cavitation",
in Proceedings Third International Symposium on Cavitation
Grenoble, France 1998.*

**Inputs:**

- **\(U_{\infty} [m/s]\)** - characteristic velocity of the flow
- **\(t_{\infty} [s]\)** - characteristic time scale of the flow
- **\(C_c [-]\)** - condensation rate coefficient
- **\(C_v [-]\)** - vaporization rate coefficient

##### Kunz Model

![img 5959ef930d0f2](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959ef930d0f2.png)

Modified version of the Kunz cavitation model, where the condensation term is switched off when the pressure is less than the saturation pressure.

**Reference:**

*Kunz, R.F., Boger, D.A., Stinebring, D.R., Chyczewski, Lindau. J.W., Gibeling, H.J., Venkateswaran, S., Govindan, T.R.,
"A Preconditioned Implicit Method for Two-Phase Flows with Application to Cavitation Prediction,"
Computers and Fluids, 29(8):849-875, 2000.*

**Inputs:**

- **\(U_{\infty} [m/s]\)** - characteristic velocity of the flow
- **\(t_{\infty} [s]\)** - characteristic time scale of the flow
- **\(C_c [-]\)** - condensation rate coefficient
- **\(C_v [-]\)** - vaporization rate coefficient

#### Solvers with variable number of phases

![img 5959efb804f8e](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959efb804f8e.png)

Certain solvers allow you to define the number of phases. You can do this using the **No. of Phases** input. Additionally, for those solvers, you will have to define surface tension between every pair of the phases.

### Diameter Models

![img 5959f059ec86e](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959f059ec86e.png)

For multiphase solvers that use the Euler formulation, you will have to additionally define a **Diameter Model** for the dispersed phase. The diameter model defines the granularity of the dispersed phase.

Available Diameter Models:

- **Constant**
- **Isothermal**

#### Constant Diameter Model

![img 5959f069b7915](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959f069b7915.png)

In this model, the diameter of the dispersed phase is fixed.

**Inputs:**

- **\(d [-]\)** - diameter

#### Isothermal Diameter Model

![img 5959f074bf3de](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959f074bf3de.png)

In this model, the dispersed phase diameter can change due to isothermal expansion.

**Inputs:**

- **\(d_0 [m]\)** - reference diameter for the isothermal expansion
- **\(p_0[Pa]\)** - reference pressure for the isothermal expansion

## Material Database

![img 5959f0e341a5a](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959f0e341a5a.png)

Instead of specifying each of the material properties by hand, you can load them from the material database. When you click the **Material Database** button, the **Material Selection** dialog will be displayed.

### Material Selection

![img 5959f0eecc7ae](https://help.sim-flow.com/documentation/panels/images/transport-properties/img_5959f0eecc7ae.png)

In the **Material Selection** dialog, you can apply material properties of one of the available materials.

To apply material properties:

1 Select a checkbox next to the material name.
2 Click **Apply** to load properties from the selected material.