Multiphase Flow Modeling in OpenFOAM: Mixture, Drift–Flux, and Euler

Multiphase Flow Modelling: From Simple Mixture Models to Full Two-Fluid Descriptions

Multiphase flows are everywhere—bubbles rising in water, sediment transport in rivers, sprays in combustion engines, boiling and condensation in heat exchangers. What makes them challenging is not just that multiple phases coexist, but that these phases may move at different speeds, interact strongly at interfaces, and exchange momentum, mass, and energy.

In computational fluid dynamics (CFD), we therefore rely on different modelling methodologies, each making different assumptions about how much of this physics we explicitly resolve. In OpenFOAM, these methodologies form a clear and practical hierarchy:

Mixture (single-momentum) models
Drift–flux models
Euler–Euler (two-fluid) models

Understanding this hierarchy is crucial—not only to choose the right solver, but also to avoid over-complicating a problem (or worse, using a model that cannot represent the physics you care about).

Let’s walk through these approaches step by step.

1) Mixture (Single-Momentum) Model

The mixture model is the simplest way to represent a multiphase flow. The core assumption is very strong:

All phases move with the same velocity field.

Mathematically,

\mathbf{U}_1 = \mathbf{U}_2 = \cdots = \mathbf{U}.

Instead of solving separate momentum equations for each phase, we solve one momentum equation for the mixture:

\frac{\partial (\rho \mathbf{U})}{\partial t} + \nabla \cdot (\rho \mathbf{U} \otimes \mathbf{U}) = -\nabla p + \nabla \cdot \boldsymbol{\tau} + \rho \mathbf{g}

with the mixture density defined as

\rho = \sum_k \alpha_k \rho_k

Here, the volume fractions $\alpha_k$ evolve through transport equations, but relative motion between phases is neglected.

When does this make sense?

When phases are well mixed
When density contrast is small
When slip velocity is negligible

Key takeaways

One velocity field
No interfacial momentum exchange
Very low computational cost
Limited physical fidelity

This is often where beginners start, but it is rarely where realistic multiphase simulations end.

2) Drift–Flux Model

The drift–flux model is a smart middle ground. It acknowledges an important reality:

Phases may move relative to each other—but we don’t want to solve multiple momentum equations.

Here, each phase velocity is written as:

\mathbf{U}_k = \mathbf{U} + \mathbf{U}_k^{\mathrm{drift}}

where:

$\mathbf{U}$ is the mixture velocity
$\mathbf{U}_k^{\mathrm{drift}}$ is a modeled slip velocity, obtained from correlations or mechanistic models

The momentum equation is still solved for the mixture, but now includes additional stress terms arising from slip:

\frac{\partial (\rho \mathbf{U})}{\partial t} + \nabla \cdot (\rho \mathbf{U} \otimes \mathbf{U}) = -\nabla p + \nabla \cdot \boldsymbol{\tau} + \rho \mathbf{g} + \nabla \cdot \boldsymbol{\tau}_{\mathrm{drift}}

Why is this useful?

Captures buoyancy-driven segregation
Accounts for particle settling
Much cheaper than two-fluid models

Key takeaways

One momentum equation
Slip velocity is modeled, not solved
Good balance of cost and realism
Accuracy depends heavily on chosen correlations

Drift–flux models are especially popular in industrial multiphase pipe flows and reactor modelling.

3) Euler–Euler (Two-Fluid) Model

The Euler–Euler approach is the most physically detailed model in this hierarchy.

Here, each phase has its own momentum equation:

\rho_k \left( \frac{\partial \mathbf{U}_k}{\partial t} + \mathbf{U}_k \cdot \nabla \mathbf{U}_k \right) = -\nabla p_k + \nabla \cdot \boldsymbol{\tau}_k + \mathbf{M}_k

where $\mathbf{M}_k$ represents interfacial momentum exchange, including:

Drag
Lift
Virtual mass
Turbulent dispersion

This model explicitly resolves strong slip, phase coupling, and complex flow regimes such as bubbly flows, fluidized beds, and dense particle suspensions.

Key takeaways

Separate velocity fields
Explicit interfacial force models
High physical fidelity
High computational and modelling cost

This is the go-to approach when interfacial physics truly matters.

A Natural Hierarchy of Modelling Fidelity

These models are not competitors—they form a logical progression:

\text{Mixture} \;<\; \text{Drift–Flux} \;<\; \text{Euler–Euler}

As you move right:

Accuracy increases
Modelling effort increases
Computational cost increases

The best model is not the most complex one—it’s the simplest model that captures the physics you need.

Learn All of This—Step by Step—in a Beginner-Friendly OpenFOAM Course

To help learners navigate this hierarchy without feeling overwhelmed, We have designed a step-by-step course on multiphase CFD using OpenFOAM, starting from the absolute basics and building toward more advanced models.

What the course covers

Fundamentals of multiphase flow, phase change, and multi-species modelling

Clear explanation of when and why to use solvers such as:

interFoam
interIsoFoam
compressibleInterFoam
twoPhaseEulerFoam
multiphaseEulerFoam

Simple, computationally light 2D test cases, including:

Water column collapse
Rising air bubble in water
VOF vs isoAdvector interface tracking
Euler–Euler bubbly flow
Basic multiphase mixing

Strong focus on hands-on learning

You will learn how to:

Define multiple phases and species
Set thermophysical properties
Initialize phase distributions correctly
Choose appropriate interfacial models (drag, phase interaction)
Work confidently with:
- controlDict
- fvSchemes
- fvSolution
- setFields

By the End of the Course

The course directly addresses common beginner issues:

Incorrect phase initialization
Stability problems
Discretization errors
Solver crashes and divergence

Every lecture comes with ready-to-run OpenFOAM case files, plus PDF notes summarizing theory, modelling assumptions, and solver guidelines—ideal for long-term reference.

Enrol Now