Surface Tension Model

The Surface Tension model allows the simulation of the surface tension force at a free fluid surface, including open fluid surfaces (as in partial filling) and the surfaces between two fluids (as in co-extrusion).


Theory	Surface Tension on Free Surfaces
Provided by	[physics continuum] > Models > Optional Models
Example Node Path	Continua > Physics > Models > Surface Tension
Requires	Time: Steady or Implicit Unsteady Material: Liquid Flow: Viscous Flow Rheology: Viscoelastic or Generalized Newtonian Optional Models: either Partial Fill or Free Surface
Activates	Interface Inputs	Interfacial Tension. See Interface Settings.
	Material Properties	`Surface Tension`. See Material Properties.

Material Properties

Surface Tension

Specifies the surface tension of the liquid. When the Surface Tension model is selected, the Surface Tension node is introduced under Liquid > [liquid] > Material Properties.

Method	Corresponding Method Node
Constant	Constant Sets the surface tension as a constant in N/m. The default value is zero.
Thermo-Capillary Marangoni Available only when the Viscous Energy and Free Surface models are selected. Not compatible with the Partial Fill model.	Thermo-Capillary Marangoni Surface tension $σ$ depends on temperature as given by Figure 1. EQUATION_DISPLAY $σ = σ_{0} {(1 - \frac{T}{T_{ref}})}^{n}$ (193) where: $σ_{0}$ is the reference surface tension of the material. $T$ is the temperature. $T_{ref}$ is the reference temperature, usually set as the critical temperature $T_{c}$ at which surface tension of the liquid becomes zero. $n$ is an empirical constant.

Method

Corresponding Method Node

Constant

Constant: Sets the surface tension as a constant in N/m. The default value is zero.

Thermo-Capillary Marangoni

Available only when the Viscous Energy and Free Surface models are selected. Not compatible with the Partial Fill model.

Thermo-Capillary Marangoni

Surface tension

σ

depends on temperature as given by

Figure 1. EQUATION_DISPLAY

σ = σ_{0} {(1 - \frac{T}{T_{ref}})}^{n}

(193)

where:

$σ_{0}$ is the reference surface tension of the material.
$T$ is the temperature.
$T_{ref}$ is the reference temperature, usually set as the critical temperature $T_{c}$ at which surface tension of the liquid becomes zero.
$n$ is an empirical constant.

Interface Settings

Interfacial Tension

Specifies the surface tension between two fluids such as in co-extrusion applications. Becomes available under Interfaces > [interface] > Physics Values when there are two different fluids on either side of the interface between two regions. Both fluids must have the Surface Tension and Free Surface models active within each physics continuum, with Free Surface Morpher Specification method set to Displacement at the interface boundary.

Method

Constant

Sets interfacial tension to a constant.

Good Girifalco Fowkes

Determines the surface tension across the interface in terms of the individual surface tensions of the fluids forming the interface. Calculates interfacial tension

σ_{1, 2}

between fluid 1 and fluid 2 as:

Figure 2. EQUATION_DISPLAY

σ_{1, 2} = σ_{1} + σ_{2} - 2 Φ \sqrt{σ_{1} σ_{2}}

(194)

where:

$σ_{1}$ and $σ_{2}$ are the surface tensions on fluids 1 and 2.
$Φ$ is the interfacial tension parameter.

Interfacial Interaction Parameter

ϕ

in Eqn. (194), in the range 0.55 to 1.15. The default is 1.0.