Surface Tension Force Model Reference

Surface tension plays a fundamental role in many natural and industrial phenomena. Examples can be found in the studies of capillarity, low-gravity fluid flow, hydrodynamic stability, surfactant behavior, cavitation, and droplet dynamics in clouds and in fuel sprays used in internal combustion engines [580].

Table 1. Surface Tension Force Model Reference
Theory	See Surface Tension.
Provided By	[phase interaction] > Models > Optional Models
Example Node Path	[phase interaction] > Models > Surface Tension Force
Requires	Physics continuum selections: Material: Multiphase (Automatically activates: Multiphase Interaction Multiphase Model: Volume Of Fluid (VOF) (Automatically activates: Segregated Flow, Gradients.) A phase interaction is required. In order to comply with the usual convention on contact angle values, the primary phase should be the liquid phase. Phase interaction selections: Optional Models: Surface Tension Force
Properties	Key properties are: Marangoni Convection, Contact Angle Hysteresis, Semi-implicit Surface Tension. See Surface Tension Force Properties.
Activates	Materials	Surface Tension See Materials and Methods.
	Boundary Inputs	Contact Angle See Boundary Settings.
	Field Functions	See Field Functions.

Surface Tension Force Properties

Marangoni Convection

Marangoni convection develops along a free surface when a concentration or temperature gradient exists across that interface. These gradients cause the surface tension coefficient to vary across the free surface.

These effects can be neglected if the spatial variation of surface tension coefficients is small. If constant surface tension coefficients are set for the phase interaction, activating this property has no effect.

When activated, this property includes the effect of spatial variations in the surface tension coefficient. The tangential surface tension force Eqn. (2611) is accounted for.

Contact Angle Hysteresis

When activated, this property allows you to specify different values for the advancing and receding contact angles. This feature lets you model droplets that are in a pinned state. For example, water droplets on an inclined surface under the shearing action of airflow, such that the surface tension, gravity and shear forces are in balance, so there is no net droplet motion.

You specify the advancing and receding contact angles as a phase interaction property for the respective boundaries. The Quasi-Dynamic and Kistler methods are available. The difference between these methods is how the advancing and receding contact angles vary for non-zero contact line velocities or capillary numbers.

See Boundary Settings.

Semi-implicit Surface Tension

When activated, an additional stabilization term is added to the momentum equations. See Eqn. (2613) in Stabilization Term for Semi-implicit Surface Tension.

This setting is applicable in cases where surface tension is a dominant physical mechanism.

Materials and Methods

Applies to the phase interaction.

Surface Tension: Specifies the surface tension coefficient ( $σ$ in Eqn. (2605)) for the phase interaction. This coefficient is used to calculate the surface tension force between each of the defined phases in the phase interaction. It is entered as a scalar profile.

Boundary Settings

For wall boundaries, under Phase Conditions > Surface Tension > Physics Values:

Contact Angle

When Contact Angle Hysteresis is not activated (the default setting), the following methods are available:

Method	Corresponding Value Nodes
Blended Kistler Uses the Kistler method to define a dynamic contact angle. The dynamic contact angle is blended with the equilibrium contact angle over a specified range for the equilibrium capillary number. See Blended Kistler Correlation.	Blended Kistler Sets the following properties: Equilibrium Contact Angle This value is $θ_{e}$ in Eqn. (2618). Equilibrium Capillary Number The range for the equilibrium capillary number. This range is used when performing the weighted averaging of the dynamic contact angle. This value is ${C a}_{e q}$ in Eqn. (2619). Advancing/Receding Sets the following properties: Advancing Contact Angle This value is $θ_{s}$ in Eqn. (2616) when the capillary number is positive. Receding Contact Angle This value is $θ_{s}$ in Eqn. (2616) when the capillary number is negative.
Constant Field Function Table User Code	Uses the selected method to define the contact angle. You can use the Capillary Number field function in the definition of a user field function to specify your own user-defined dynamic contact angle correlation.

Method

Corresponding Value Nodes

Blended Kistler

Uses the Kistler method to define a dynamic contact angle. The dynamic contact angle is blended with the equilibrium contact angle over a specified range for the equilibrium capillary number.

See Blended Kistler Correlation.

Blended Kistler

Sets the following properties:

Equilibrium Contact Angle: This value is $θ_{e}$ in Eqn. (2618).
Equilibrium Capillary Number: The range for the equilibrium capillary number. This range is used when performing the weighted averaging of the dynamic contact angle. This value is ${C a}_{e q}$ in Eqn. (2619).

Advancing/Receding

Sets the following properties:

Advancing Contact Angle: This value is $θ_{s}$ in Eqn. (2616) when the capillary number is positive.
Receding Contact Angle: This value is $θ_{s}$ in Eqn. (2616) when the capillary number is negative.

Constant

Field Function

Table

User Code

Uses the selected method to define the contact angle.

You can use the Capillary Number field function in the definition of a user field function to specify your own user-defined dynamic contact angle correlation.

When Contact Angle Hysteresis is activated, the following methods are available:

Method	Corresponding Value Nodes
Kistler Uses the Kistler method to define a dynamic contact angle. The advancing and receding contact angles depend on the capillary number: the advancing contact angle increases for increasing advancing contact line velocity, the receding contact angle decreases for increasing receding contact line velocity. See Kistler Correlation.	Kistler No properties. Advancing/Receding Same as described above.
Quasi-Dynamic Similar to the Kistler method (above), except that a constant contact angle is used for the advancing and receding edges. The advancing and receding contact angles do not depend on the capillary number. If the computed contact angle is above the advancing angle or below the receding angle, the specified advancing angle or receding angle is used.	Quasi-Dynamic No properties. Advancing/Receding Same as described above.

Field Functions

The following field functions are made available to the simulation when the Surface Tension Force model is activated in a phase interaction.

Capillary Number of [phase interaction]: This scalar field function is defined at wall boundaries and can be used in the definition of a user field function to specify your own user-defined dynamic contact angle correlation.
Computed Contact Angle of [phase interaction]: The contact angle of the phase pair at a wall boundary. This angle is computed based on the angle that the free surface makes with the wall. The free surface itself is given by the volume fraction field.
Contact Angle of [phase interaction]: The surface tension contact angle. This scalar field function is defined at wall boundaries.

SurfaceTension Force of [phase interaction]: The surface tension vector in force per unit volume. This field function is defined at fluid pair interface.