## Solver: twoLiquidMixingFoam Description

twoLiquidMixingFoam is a solver designed for transient simulations of two incompressible, isothermal, and miscible fluids. It handles laminar and turbulent, accommodating both Newtonian and non-Newtonian fluids. `twoLiquidMixingFoam`

solver is designed to handle mixtures consisting of two fluids within the same phase, such as two gases or two liquids.

The solver uses the **PIMPLE** (merged **PISO-SIMPLE**) algorithm for pressure-momentum coupling. This algorithm leverages the strengths of both PISO and SIMPLE methods for pressure-velocity coupling, ensuring robustness in handling transient flows with large time steps. This approach is supplemented by under-relaxation techniques to secure convergence stability. It supports porosity modeling, buoyancy and allows easy integration of passive scalar transport equations, and source terms.

`twoLiquidMixingFoam`

is particularly useful in applications where the dynamics of mixing two liquids are critical, such as in the chemical processing industry, biotechnology (e.g., mixing of different biochemical reactants), environmental engineering (e.g., water treatment processes where different liquid phases are mixed), and in the design of mixing equipment (e.g., impellers in tanks).

## Solver: twoLiquidMixingFoam Features

**Transient****Incompressible****Single-Phase**

- 2 Miscible Fluids
- Mixing

- Laminar and Turbulent (RANS, LES, DES)
- Multicomponent (mixture)
- Newtonian and Non-Newtonian Fluid
- Pressure-Based Solver
- Passive Scalar
- Porosity Modeling
- Buoyancy
- Source Term (explicit/implicit)
- PIMPLE Algorithm
- Solution Limiters:
- Velocity Damping

## Solver: twoLiquidMixingFoam Application

**Chemistry**

- Mixing of Reactants
- Mixing Tanks

**Environmental Flows**

- Water Treatment Process (Mixing of Water and Sludge)

## Solver: twoLiquidMixingFoam Multiphase - Free Surface (VoF) Solvers Comparison

Free Surface (VoF) Solvers In this group, we have included solvers implementing **Volume of Fluid (VoF)** approach to handle multiple immiscible and miscible fluids and interactions between them.

**Free Surface (VoF) - Immiscible**

- interFoam 2 immiscible fluids, DyM
- multiphaseInterFoam multiple immiscible fluids, DyM
- interIsoFoam* 2 immiscible fluids, isoAdvector* method, DyM

- overInterDyMFoam extension of interFoam with Overset, DyM
- compressibleInterFoam compressible version of interFoam with heat transfer
- compressibleInterDyMFoam compressible version of interFoam with heat transfer and DyM

**Free Surface (VoF) - Miscible**

- interMixingFoam 3 fluids (2 miscible and 1 immiscible), DyM
- twoLiquidMixingFoam** 2 miscible fluids

- * isoAdvector - an alternative approach for interface capturing, MULES method used in other VoF solvers
- ** Solver designed to handle mixtures consisting of multiple fluids within the same phase, such as two gases or two liquids

- VoF - Volume of Fluid
- DyM - Dynamic Mesh
- Overset - also known as Chimera Grid (Method)

## Solver: twoLiquidMixingFoam Alternative Solvers

In this section, we propose alternative solvers from different categories, distinct from the current solver. While they may fulfill similar purposes, they diverge significantly in approach and certain features.

- interFoam base version of
`twoLiquidMixingFoam`

, 2 immiscible fluids

## Solver: twoLiquidMixingFoam Results Fields

This solver provides the following results fields:

**Primary Results Fields**- quantities produced by the solver as default outputs**Derivative Results**- quantities that can be computed based on primary results and supplementary models. They are not initially produced by the solver as default outputs.

**Primary Results Fields**

Velocity | \(U\) [\(\frac{m}{s}\)] |

Phase Volume Fraction | \(\alpha\) [\(-\)] |

Hydrostatic Perturbation Pressure | \(p - \rho gh\) [\(Pa\)] |

**Hydrostatic Perturbation Pressure** This value represents the pressure without the hydrostatic component (minus gravitational potential). Read More: Hydrostatic Pressure Effects

**Derivative Results**

Pressure | \(P\) [\(Pa\)] |

Density | \(\rho\) [\(\frac{kg}{m^{3}}\)] |

Vorticity | \(\omega\) [\(\frac{1}{s}\)] |

Courant Number | \(Co\) [\(-\)] |

Peclet Number | \(Pe\) [\(-\)] |

Stream Function | \(\psi\) [\(\frac{m^2}{s}\)] |

Q Criterion | \(Q\) [\(-\)] |

Wall Functions (for RANS/LES turbulence) | \(y^+\) [\(-\)] |

Wall Shear Stress | \(WSS\) [\(Pa\)] |

Turbulent Fields (for RANS/LES turbulence) | \(k\) \(\epsilon\) \(\omega\) \(R\) \(L\) \(I\) \(\nu_t\) \(\alpha_t\) |

Volumetric Stream | \(\phi\) [\(\frac{m^{3}}{s}\)] |

Passive Scalar | \(scalar_i\) [\(-\)] |

Forces and Torque acting on the Boundary | \(F\) [\(N\)] \(M\) [\(-\)] |

Force Coefficients | \(C_l\) [\(-\)] \(C_d\) [\(-\)] \(C_m\) [\(-\)] |

Average, Minimum or Maximum in Volume from any Result Field | \(Avg\) \(Min\) \(Max\) |