# Two Fluid: Immiscible¶

Immiscible fluid models, as the name suggests, are simulations involving a two immiscible fluids with Newtonian or non-Newtonian rheology. Common applications include two-phase gas flow simulations, colloid suspensions, and oil-water systems, Users must specify, for each fluid, the density and the constitutive relationship between fluid stress and fluid strain. The two immiscible fluids do not need to have the same constitutive relationships. Users must also specify a surface tension between the two fluids. As discussed in particleFields, additional phases (such as discrete bubbles and discrete solid particle) can be added to the system and one- or two-way coupled to the fluid. Secondary miscible fluids with arbitrary densities and viscosities, as discussed in Miscible Fluids, can also be added to the base fluids. Thermal fields and scalar fields can also be superimposed on the single phase fluid, as discussed in Basic Concepts and Scalar Fields.

For each fluid, users can chose from one of four constitutive relationships:

Newtonian

Power law (with or without a yield stress)

Carreau

Custom expression

Briefly speaking, relationships (1)-(3) are familiar Newtonian and non-Newtonian rheology models. Relationship (4) represent custom expressions that may be more complex functions of strain, stress, age, species concentration, miscible fluid volume fraction, custom variables, particle concentration, and temperature. Additional details for each of these relationships are provided in Fluid Rheology

Unlike the single phase fluid, which is assumed to fill the entire interior zone of the lattice, users must specify which portions of the interior zone are initially filled with each fluid. The “Background Fluid” describes the primary fluid in the tank. This background is typically defined as fluid1, but can be redefined by the user. The initial distribution of the secondary fluid (which is typically fluid2) can be specified using any combination of parametric geometry and/or user-imported geometry. By default, the secondary fluid condition is a parametric “Fluid Height Box”. This cuboid geometry is anchored to the main lattice domain, but the height of the box aligned with the “UP-direction” can be adjusted. The background initial condition is assumed to be Fluid 1, while the Fluid Height Box is assumed to be Fluid 2. Ad discussed in initialFluid, an arbitrary number of initial condition regions can be added to the model.