CFD Online Discussion Forums - Direct numerical simulation of species transport equation with phase change

Hello all.

I am interesting to simulate a concentration(species) field for a phase change problem. My computational field is comprised an immisible two-phase flow.

Typically, Eulerian-based ( such as VOF) or hybrid methods such as Front Tracking is applied for the simulation of such flows.

There is an interface between two phases (phase (1) and phase(2)) called $\Gamma \$ in my computational domain as presented at the attached image.

The phase (1) is a liquid phase consisted of S1-species (a liquid species) and S2-species(solid particles dissolved in species of S1 into the liquid phase (1)) .The phase (2) is the gas phase consisted of S1-species (gas species state) and S3-species in the gas state.

In the interface( $\Gamma \$ ) , a mass transfer rate ( $\dot{m}\$ ) is assigned to determine species (1) (S1) mass transfer from phase(1) to phase (2).

A species (concentration) transport equation is required for assessment of S1-species concentration (mass fraction of S1-species) field in both phases.
Typically, This equation is presented as follows for pure phase domains:

$\frac{\partial Y_{s1(g)}}{\partial t}+\nabla .\left(Y_{s1\left(g\right)}{\mathbf u}\right)=\nabla .(D_{s1\left(g\right)}\nabla Y_{s1\left(g\right)})\$ for gas phase (1)
$\frac{\partial Y_{s1(l)}}{\partial t}+\nabla .\left(Y_{s1\left(l\right)}{\mathbf u}\right)=\nabla .(D_{s1\left(l\right)}\nabla Y_{s1\left(l\right)})\$ for liquid phase (2)

That, (g) and (l) refer to phase(1) and phase(2), respectively. Also, Y and D denote concentration value and mass diffusivity , respectively.

However, for the interface( $\Gamma \$ ) study, it is essential to have a comprehensive species (concentration) equation even upon the interface( $\Gamma \$ ) .

How can CFD user assign and obtain a good interface( $\Gamma \$ ) condition for species transfer equation?
Is there a known and "general" direct numerical method for the evaluating of species transfer equation in the interface similar with that at the momentum and temperature equations?

What's the general interface( $\Gamma \$ ) condition for S1-concentration (S1-species) transport equation?

The "general" term denotes the importance of S1-species concentration whether being dense or diluted .

The aim is to govern a comprehensive S1-species transfer equation with a logical and suitable interface condition concerning each value of concentration (S1-species dense or S1 species-diluted) .

Thanks in advance for any help.

P.Maroul