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:
 | (5–207) |
where:
 | (5–208) |
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:
 | (5–209) |
 | (5–210) |
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:
 | (5–211) |
 | (5–212) |
So, you have:
 | (5–213) |
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.
 | (5–214) |
The diffusivity scale 
is the kinematic diffusivity 
for a volumetric
variable, and the dynamic diffusivity 
for a specific variable.
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:
 | (5–215) |
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:
(5–216)
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. 
(5–217)
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:
(5–218)
