### 1.4.7. Transport Properties

#### 1.4.7.1. Dynamic Viscosity

Dynamic viscosity (), also called absolute viscosity, is a measure of the resistance of a fluid to shearing forces, and appears in the momentum equations.

##### 1.4.7.1.1. Value

You can specify a dynamic viscosity directly using either a constant value or a CEL expression.

##### 1.4.7.1.2. Rigid Non Interacting Sphere and Interacting Sphere Models

This model is based on elementary kinetic theory [82] and is valid for gases using user supplied equations of state or either of the built in equation of state models (Ideal Gas, Real Gas):

| (1–29)

where is dynamic viscosity in P, is the molecular weight in g/mol and is temperature in Kelvin and is the collision diameter, in Angstroms, and is calculated using [83]:

| (1–30)

where is the critical molar volume in cm3/mol. The Rigid Non Interacting Sphere model assumes that the collision function, , is unity, while the Interacting sphere model assumes that molecular collisions contribute to the viscosity and uses non-unity :

| (1–31)

where

and where is the critical temperature. This model was published by Chung et al. [83] [158].

##### 1.4.7.1.3. Non-Newtonian Model

For Generalized Newtonian fluids, you can specify a shear-strain-rate-dependent viscosity model. Several models are available. For details, see Non-Newtonian Flow.

##### 1.4.7.1.4. Ideal Mixture

For fixed and variable composition mixtures, the `Ideal Mixture` option is used by default when you do not set a dynamic viscosity. This option causes the viscosity of the mixture to be computed by a mass-fraction-weighted average.

##### 1.4.7.1.5. Sutherland’s Formula

This approximation for viscosity is valid for dilute gases and was obtained from the kinetic theory by Sutherland [81]. In this case viscosity varies only with temperature as:

| (1–32)

where is the reference molecular viscosity, is the Sutherland constant and is a characteristic of the gas, is usually 273.0 K, and n is the temperature exponent, usually set to 1.5 for most gases.

#### 1.4.7.2. Thermal Conductivity

Thermal conductivity, , is the property of a fluid that characterizes its ability to transfer heat by conduction.

Thermal conductivity of gases tends to increase with increasing temperature, although it is relatively insensitive to changes in pressure, except at very high or very low pressures.

Thermal conductivity of liquids generally decreases with increasing temperature (notable exceptions are water and glycerine).

Typical values are in the range 0.005-0.5 W/mK for gases and 0.08-0.6 W/mK for liquids.

For Fixed and Variable Composition Mixture, the Thermal conductivity is determined by a mass fraction weighted arithmetic average. You can set Thermal conductivity for the mixture in the Materials details view instead, if you want.

##### 1.4.7.2.1. Sutherland’s Formula

Sutherland’s formula for thermal conductivity is identical to that for dynamic viscosity. The only change being the reference value is now a reference thermal conductivity. This formula is still based on kinetic theory so still applies only to dilute gases.

##### 1.4.7.2.2. Modified Euken Model

The modified Euken thermal conductivity model is available whenever you have selected Real Gas, NASA Format or Zero Pressure polynomial for specific heat capacity. You must use one of those two specific heat capacity options because the Euken model requires the zero pressure polynomial coefficients. This model is also based on the kinetic theory of gases and is valid for gases over a fairly large range of temperatures below the critical point. The Modified Euken Model is described in Poling, Prausnitz & O’Connell [84] and is given by:

| (1–33)

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