### 5.11.1. Additional Variable Interphase Transfer Models

It is possible for an Additional Variable to be coupled to a different Additional Variable across a phase interface between fluids and .

The total source to per unit volume due to interaction with other phases is given by:

| (5–204)

where:

| (5–205)

The simplest models for interphase transfer between and take the driving force to be proportional to the difference in bulk Additional Variable values across the phase interface:

| (5–206)

| (5–207)

The first of these is used if the Additional Variable is defined per unit mass. The latter is used if the Additional Variable is defined per unit volume.

The coefficients are defined by analogy with heat transfer. For details, see Inhomogeneous Interphase Heat Transfer Models.

Transfer of an Additional Variable across a phase boundary is described by an additional variable transfer coefficient . It is the amount of crossing a unit area per unit time per unit difference in across the phase boundary. Thus:

| (5–208)

| (5–209)

So, you have:

| (5–210)

It is often convenient to express the Additional Variable transfer coefficient in terms of a dimensionless Sherwood number , analogous to the Nusselt number in heat transfer.

| (5–211)

The diffusivity scale is the kinematic diffusivity for a volumetric variable, and the dynamic diffusivity for a specific variable.

#### 5.11.1.1. Particle Model Correlations

In the particle model, the diffusivity scale is that of the continuous phase, and the length scale is the mean diameter of the dispersed phase:

| (5–212)

For laminar forced convection around a spherical particle, theoretical analysis shows that . For a particle in a moving incompressible Newtonian fluid, the Sherwood number is a function of the particle Reynolds number and the Additional Variable Prandtl number .

Details on the models available in CFX for Additional Variable transfer are available. For details, see Particle Model Correlations in the CFX-Solver Modeling Guide. Some additional details for the Interface Flux model are provided below.

- Interface Flux

  You specify directly the interfacial flux from Additional Variable in fluid 1 to Additional Variable in fluid 2 of a specified fluid pair. This is the rate of Additional Variable transfer per unit time per unit interfacial area from phase 1 to phase 2. Hence, the amount of Additional Variable transferred to fluid 2 from fluid 1 per unit volume is given by:

  | (5–213)

  may be given as a constant or an expression.

  Typically, will be a function of the fluid 1 and fluid 2 Additional Variable fields, and possibly other variables. In this case, you may accelerate convergence of the coupled solver by also specifying optional fluid 1 and fluid 2 Additional Variable flux coefficients.

  | (5–214)

  The solver takes the absolute value of these flux coefficients to ensure that they are positive. This is required for numerical stability. The partial derivatives need not be computed exactly; it is sufficient for the specified coefficients to simply approximate the partial derivatives. Specification of Additional Variable flux coefficients affects only the convergence rate to the solution of the coupled transfer equations; it does not affect the accuracy of the converged solution.

  For example, the simple model using a transfer coefficient multiplied by bulk specific Additional Variable differences may be recovered using:

  | (5–215)

#### 5.11.1.2. Mixture Model Correlations

If you are using the mixture model, the Sherwood number is defined in terms of a mixture diffusivity scale and the mixture length scale:

| (5–216)

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