# Miscible Fluids¶

## General¶

This functionality is used to model interactions between miscible fluids with user defined density and rheology. Examples of miscible fluids include glycerin/water, brine/salt water, and most biomass/water combination. Common applications of these models include fluid dilution, miscible fluid blending, and simulations of cleaning/washing.

## Adding miscible fluids¶

The initial and boundary conditions of the miscible fluid are specified by the user. By default, the base fluid is assumed to occupy the entire tank. Children geometry, with user defined miscible volume fractions, can be added to the model to define initial conditions. To lattice precision, the total initial volume of the miscible fluid will be equal to the product of the specified volume fraction and the child geometry volume. If a more precise miscible fluid volume is to be specified, users may enter an exact to be defined within the child geometry. The volume fraction within the child geometry will then be set at runtime to realize the exact, user-defined initial miscible fluid volume.

The miscible fluid volume fraction at each inlet can be specified to be a function of time and position across the inlet. Both the average volume fraction across the fluid and total miscible fluid volume are reported as standard output.

Users must specify the density of each fluid and a constitutive relationship between fluid stress, fluid strain, and the volume fraction of the secondary miscible fluid. This relationship may also be a function of other fluid variables, including strain, energy dissipation rate, species concentration, time, temperature, age, etc. At each simulation time step, the solver uses this user-provided constitutive relationship to calculate the local viscosity at each point within the lattice domain.

## Miscible fluid rheology¶

We now present multiple examples for defining miscible fluid constitutive relationships.
Consider a base fluid with a kinematic viscosity of 1e-6 m^2/s and secondary miscible fluid with a kinematic viscosity of 1e-4 m^2/s. Let the name of the miscible fluid be `miscible_a`

Assume the mixture viscosity is calculated using a weighted average concentration. An appropriate constitutive relationship to specify would be:

```
nu=(1-miscible_a)*1e-6+miscible_a*1e-4;
```

Note that `miscible_a`

represents the local volume fraction, which ranges from 0 to 1.

Next, consider two miscible power law fluids with a base fluid kinematic viscosity of 1e-3*s^0.9 m^2/s and miscible fluid viscosity of 1e-4*s^0.8 m^2/s. Note that the rheology of each fluid is a function of strain, s, and assume the mixture viscosity is calculated using a weighted average concentration.

An appropriate constitutive relationship to specify would be:

```
if(s>1){
nu=(1-miscible_a)*(1e-3*powf(s,0.9))+(1-miscible_a)*(1e-4,powf(s,0.8));
}else{
nu=(1-miscible_a)*(1e-3)+(1-miscible_a)*(1e-4);
}
```

Note that the `if`

logic is used here to avoid a vanishing viscosity at zero shear rates.

Important

The quality of the simulation prediction will be directly correlated to the quality of the user-specified constitutive relationship

## Miscible fluid density¶

That effective fluid density is take to be the volume-fraction averaged density. This relationship does not need to be specified by the user.