Pre-Integrated S-Gamma Phase Interaction Models Reference

Table 1. Pre-Integrated S-Gamma Phase Interaction Models Reference
Model Names	S-Gamma Breakup
	S-Gamma Coalescence
Theory	See S-Gamma Breakup and Coalescence.
Provided By	[phase interaction] > Models > Optional Models
Example Node Path	[phase interaction] > Models > S-Gamma Coalescence
Requires	These models are available only for a Continuous-Dispersed phase interaction. The dispersed phase must have the Pre-Integrated S-Gamma model activated. See S-Gamma Model Reference.
Properties	Key properties are: Breakup Factor See S-Gamma Breakup Model Properties. Coalescence Factor See S-Gamma Coalescence Model Properties.
Activates	Model Controls (child nodes)	For S-Gamma Breakup: Viscous Breakup See Viscous Breakup Properties. Inertial Breakup See Inertial Breakup Properties. For S-Gamma Coalescence: Viscous Coalescence See Viscous Coalescence Properties. Inertial Coalescence See Inertial Coalescence Properties.
	Field Functions	See S-Gamma Breakup Field Functions and S-Gamma Coalescence Field Functions.

S-Gamma Breakup Model Properties

Breakup Factor: A multiplier for breakup terms.

Viscous Breakup Properties

Lets you control the specific characteristics of the viscous breakup process.

Viscous Breakup Timescale

Sets how the breakup timescale is calculated.

Method	Corresponding Method Nodes
Standard	None. Uses the default timescale from Eqn. (2204).
User Defined	User-Defined Viscous Breakup Timescale This node has the following property: Diameter Exponent Sets the exponent $a$ for the particle diameter in the timescale expression (Eqn. (2200)). The default setting is 1.0. This node has the following child node: Viscous Breakup Timescale Sets the multiplier $τ′$ in the timescale expression (Eqn. (2200)).

Method

Corresponding Method Nodes

Standard

None.

Uses the default timescale from Eqn. (2204).

User Defined

User-Defined Viscous Breakup Timescale

This node has the following property:

Diameter Exponent: Sets the exponent $a$ for the particle diameter in the timescale expression (Eqn. (2200)). The default setting is 1.0.

This node has the following child node:

Viscous Breakup Timescale: Sets the multiplier $τ′$ in the timescale expression (Eqn. (2200)).

Viscous Breakup Fragments

Sets the number of fragments that form during breakup.

Method	Corresponding Method Nodes
Standard	None. Uses the default fragmentation number in Eqn. (2203).
User Defined	User-Defined Viscous Breakup Fragments This node has the following property: Diameter Exponent Sets the exponent $b$ for the particle diameter in the fragment number expression (Eqn. (2199)). The default setting is 3.0. This node has the following child node: Viscous Breakup Fragments Sets the multiplier $N'$ for the number of fragments in Eqn. (2199).

Method

Corresponding Method Nodes

Standard

None.

Uses the default fragmentation number in Eqn. (2203).

User Defined

User-Defined Viscous Breakup Fragments

This node has the following property:

Diameter Exponent: Sets the exponent $b$ for the particle diameter in the fragment number expression (Eqn. (2199)). The default setting is 3.0.

This node has the following child node:

Viscous Breakup Fragments: Sets the multiplier $N'$ for the number of fragments in Eqn. (2199).

Viscous Critical Diameter

Sets how the critical diameter is calculated.

Method	Corresponding Method Nodes
Standard	None. Uses the default critical diameter from Eqn. (2202).
User Defined	User-Defined Viscous Critical Diameter This node has the following child node: Viscous Breakup Dcrit Sets the viscous critical diameter, $d_{c r}$ in Eqn. (2202).

Method

Corresponding Method Nodes

Standard

None.

Uses the default critical diameter from Eqn. (2202).

User Defined

User-Defined Viscous Critical Diameter

This node has the following child node:

Viscous Breakup Dcrit: Sets the viscous critical diameter, $d_{c r}$ in Eqn. (2202).

Inertial Breakup Properties

Lets you control the specific characteristics of the inertial breakup process.

For setting user-defined values for the breakup timescale and fragments, use the function of the form $N (d) = N' d^{b}$ . You set $N'$ as a constant or field function and set $b$ as a constant in the Diameter Exponent property (see Eqn. (2199)).

Concentration Correction Factor

This value is

C_{α}

in Eqn. (2205). This value is used in the calculation of the critical droplet diameter, since the presence of nearby droplets dampens the disruptive power of the inertial forces.

Inertial Breakup Timescale Coefficient

Time coefficient

k_{b r}

in Eqn. (2206).

Inertial Breakup Timescale

Sets how the breakup timescale is calculated.

Method	Corresponding Method Nodes
Standard	None. Uses the default timescale from Eqn. (2206).
User Defined	User-Defined Inertial Breakup Timescale This node has the following property: Diameter Exponent Sets the exponent $b$ for the particle diameter in the timescale expression (Eqn. (2200)). The default setting is 1.5. This node has the following child node: Inertial Breakup Timescale Sets the multiplier $τ′$ in the timescale expression (Eqn. (2200)).

Method

Corresponding Method Nodes

Standard

None.

Uses the default timescale from Eqn. (2206).

User Defined

User-Defined Inertial Breakup Timescale

This node has the following property:

Diameter Exponent: Sets the exponent $b$ for the particle diameter in the timescale expression (Eqn. (2200)). The default setting is 1.5.

This node has the following child node:

Inertial Breakup Timescale: Sets the multiplier $τ′$ in the timescale expression (Eqn. (2200)).

Inertial Breakup Fragments

Sets how the breakup fragmentation is calculated.

Method	Corresponding Method Nodes
Standard	None. Uses the default fragmentation number in Eqn. (2203).
User Defined	User-Defined Inertial Breakup Fragments This node has the following property: Diameter Exponent Sets the exponent $b$ for the particle diameter in the fragment number expression (Eqn. (2199)). The default setting is 0.0. This node also has the following child node: Inertial Breakup Fragments Sets the multiplier $N'$ for the number of fragments in Eqn. (2199).

Method

Corresponding Method Nodes

Standard

None.

Uses the default fragmentation number in Eqn. (2203).

User Defined

User-Defined Inertial Breakup Fragments

This node has the following property:

Diameter Exponent: Sets the exponent $b$ for the particle diameter in the fragment number expression (Eqn. (2199)). The default setting is 0.0.

This node also has the following child node:

Inertial Breakup Fragments: Sets the multiplier $N'$ for the number of fragments in Eqn. (2199).

Inertial Critical Diameter

Sets how the critical diameter is calculated.

Method	Corresponding Method Nodes
Standard	None. Uses the default critical diameter from Eqn. (2205).
User Defined	User-Defined Inertial Critical Diameter This node has the following child node: Inertial Breakup Dcrit Sets the inertial critical diameter, $d_{c r}$ in Eqn. (2205). You can specify a constant or field function.

Method

Corresponding Method Nodes

Standard

None.

Uses the default critical diameter from Eqn. (2205).

User Defined

User-Defined Inertial Critical Diameter

This node has the following child node:

Inertial Breakup Dcrit

Sets the inertial critical diameter, $d_{c r}$ in Eqn. (2205).

You can specify a constant or field function.

S-Gamma Coalescence Model Properties

The constant and field function methods for coalescence imply that particles of all sizes have an equal probability of coalescence. The other methods are size-selective.

Coalescence Factor: The calibration coefficient, $F_{c l}$ in Eqn. (2211).
Hamaker Constant: The value $A_{H}$ in Eqn. (2220), which is used in the calculation of critical film thickness.

Viscous Coalescence Properties

Lets you control the specific characteristics of the viscous coalescence process.

Viscous Collision Rate

Sets how the collision rate is calculated.

Method	Corresponding Method Nodes
Standard	None. Calculates the collision rate using Eqn. (2214).
User Defined	User-Defined Viscous Coalescence Collision Rate This node has the following child node: Viscous Coalescence Collision Rate Sets the value for $K_{c o l l}$ in Eqn. (2214).

Method

Corresponding Method Nodes

Standard

None.

Calculates the collision rate using Eqn. (2214).

User Defined

User-Defined Viscous Coalescence Collision Rate

This node has the following child node:

Viscous Coalescence Collision Rate: Sets the value for $K_{c o l l}$ in Eqn. (2214).

Viscous Coalescence Probability

Sets the mode of calculating the probability of a collision resulting in coalescence. The choice of this mode can affect the particle size, since increased mobility enhances coalescence, possibly leading to predictions of excessively large particle sizes (typically for bubbles or drops).

Fully Immobile Interface
Coalescence is blocked by contaminants in the fluid (Eqn. (2216)).
Partially Mobile (Short Collision Time)
Coalescence is partially blocked by contaminants in the fluid (Eqn. (2217)).
Partially Mobile (Quasi-Steady Flow in Film)
Coalescence takes place faster due to less blockage (Eqn. (2218)).
Fully Mobile Interface
Coalescence takes place as quickly as possible – no material is blocking it (Eqn. (2219)).
User Defined
Activates the User-Defined Viscous Coalescence Probability method node, where you specify a value for the coalescence probability, $P_{c l}$ in Eqn. (2215).

Inertial Coalescence Properties

Lets you control the specific characteristics of the inertial coalescence process.

Probability Factor

This value is

k_{c l, 2}

in Eqn. (2222), and is used in the calculations for inertial collision probability.

Inertial Collision Rate

Sets how the collision rate is calculated.

Method	Corresponding Method Nodes
Standard	None. Uses the default collision rate calculation from Eqn. (2221).
User Defined	User-Defined Inertial Coalescence Collision Rate This node has the following child node: Inertial Coalescence Collision Rate Sets the value for the inertial coalescence collision rate, $K_{c o l l, i}$ in Eqn. (2221).

Method

Corresponding Method Nodes

Standard

None.

Uses the default collision rate calculation from Eqn. (2221).

User Defined

User-Defined Inertial Coalescence Collision Rate

This node has the following child node:

Inertial Coalescence Collision Rate: Sets the value for the inertial coalescence collision rate, $K_{c o l l, i}$ in Eqn. (2221).

Inertial Coalescence Probability

Sets the method of calculating the probability of a collision resulting in coalescence.

Method	Corresponding Method Nodes
Standard	None. Uses the default coalescence probability calculation from Eqn. (2222).
User Defined	User-Defined Inertial Coalescence Probability This node has the following child node: Inertial Coalescence Probability Sets the value for the inertial coalescence probability, $P (d_{e q})$ in Eqn. (2222).

Method

Corresponding Method Nodes

Standard

None.

Uses the default coalescence probability calculation from Eqn. (2222).

User Defined

User-Defined Inertial Coalescence Probability

This node has the following child node:

Inertial Coalescence Probability: Sets the value for the inertial coalescence probability, $P (d_{e q})$ in Eqn. (2222).

S-Gamma Breakup Field Functions

The following field function is made available to the simulation when the S-Gamma Breakup model is used:

Inertial Breakup Dcrit of [phase interaction]: The critical diameter $d_{c r}$ in Eqn. (2205).

The following field functions are made available to the simulation when the S-Gamma Breakup model is used and the Interaction Source Storage Retained property is activated in the S-Gamma solver:

S0 Inertial Breakup Source of [phase interaction]: The inertial contribution to $s_{b r}$ in the $S_{0}$ transport equation (Eqn. (2185)).
S2 Inertial Breakup Source of [phase interaction]: The inertial contribution to $s_{a, b r}$ in the $S_{2}$ transport equation (Eqn. (2194)).
S0 Viscous Breakup Source of [phase interaction]: The viscous contribution to $s_{b r}$ in the $S_{0}$ transport equation (Eqn. (2185)).
S2 Viscous Breakup Source of [phase interaction]: The viscous contribution to $s_{a, b r}$ in the $S_{2}$ transport equation (Eqn. (2194)).

S-Gamma Coalescence Field Functions

The following field functions are made available to the simulation when the S-Gamma Coalescence model is used:

Inertial Coalescence Collision Rate of [phase interaction]: The inertial collision rate $K_{c o l l, i}$ in Eqn. (2221).
Inertial Coalescence Probability of [phase interaction]: The inertial probability $P (d_{e q})$ in Eqn. (2222).
Viscous Coalescence Collision Rate of [phase interaction]: The viscous collision rate $K_{c o l l, v}$ in Eqn. (2214).
Viscous Coalescence Probability of [phase interaction]: The viscous probability $P_{v} (d_{e q})$ in Eqn. (2215).

The following field functions are made available to the simulation when the S-Gamma Coalescence model is used and the Interaction Source Storage Retained property is activated in the S-Gamma solver:

S0 Inertial Coalescence Source of [phase interaction]: The inertial contribution to $s_{c l}$ in the $S_{0}$ transport equation (Eqn. (2185)).
S2 Inertial Coalescence Source of [phase interaction]: The inertial contribution to $s_{a, c l}$ in the $S_{2}$ transport equation (Eqn. (2194)).
S0 Viscous Coalescence Source of [phase interaction]: The viscous contribution to $s_{c l}$ in the $S_{0}$ transport equation (Eqn. (2185)).
S2 Viscous Coalescence Source of [phase interaction]: The viscous contribution to $s_{a, c l}$ in the $S_{2}$ transport equation (Eqn. (2194)).