### 5.8.4. Coalescence Models

CFX-Solver supports two coalescence models.

#### 5.8.4.1. Prince and Blanch Model

The model of Prince and Blanch [62] assumes that the coalescence of two bubbles occurs in three steps. First, the bubbles collide trapping a small amount of liquid between them. This liquid film then drains until the liquid film separating the bubbles reaches a critical thickness. The film then ruptures and the bubbles join together.

The coalescence kernel is therefore modeled by a collision rate of two bubbles and a collision efficiency relating to the time required for coalescence:

| (5–166)

The collision efficiency is modeled by comparing the time required for coalescence with the actual contact time during the collision :

| (5–167)

| (5–168)

| (5–169)

where is the initial film thickness, is the critical film thickness when rupture occurs, and is the equivalent radius:

| (5–170)

The turbulent contributions to collision frequency are modeled as:

| (5–171)

where the cross-sectional area of the colliding particles is defined by:

| (5–172)

the turbulent velocity is given by:

| (5–173)

and is a calibration factor. The buoyancy contribution to collision frequency is modeled as:

| (5–174)

where:

| (5–175)

and is a calibration factor.

The shear contribution to collision frequency is currently neglected.

#### 5.8.4.2. User-Defined Models

A custom model for the coalescence rate kernel may also be provided. The model may be a CEL expression or User Routine involving the diameter and/or mass represented by groups and as well as any fluid variable. Note that the model must give symmetric coalescence rates ().

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