Defining the Liquid and the Particle Phases of the Suspension

The particle phase comprises Polymethylmethacrylate (PMMA) spherical particles with a density of 1182 kg-m⁻³. The liquid phase is a Newtonian tetrabromoethane/oil mixture with the same density as the particles and a dynamic viscosity of 4.95 Pa-s.

The Morris and Boulay model [976] is used to specify the viscosity of the mixture. This model goes beyond considering purely shear viscosity and takes into account normal stress contributions that causes shear induced migration of particles in shear flow. For more information, see Morris and Boulay Model.

To define the phases:

Create the liquid phase.

You specify the density and dynamic viscosity of the liquid phase.

In the Suspension continuum, right-click the Models > Multiphase > Phases node and create a new phase.
Rename the Phase 1 node to Oil.

For the Oil phase, select the following models:


Group Box	Model
Enabled Models	Laminar (Pre-selected) Flow (Pre-selected)
Material	Liquid Continuous Liquid Rheology (Selected automatically)
Equation of State	Constant Density

Click Close.

Edit the Phases > Oil > Models > Liquid > H2O > Material Properties node and set the following properties:


Node	Property	Setting
Density > Constant	Value	1182 kg/m^3
Dynamic Viscosity > Constant	Value	4.95 Pa-s

Create the particle phase.

You specify the density of the particle phase. The default particle diameter of 0.001 m is appropriate for this simulation.

Create a second phase and rename it to Particles.

For the Particles phase, select the following models:


Group Box	Model
Enabled Models	Laminar (Pre-selected) Flow (Pre-selected)
Material	Particle Solid Particle Rheology (Selected automatically)
Equation of State	Constant Density (Selected automatically)

Click Close.
Select the Phases > Particles > Models > Particle > Al > Material Properties > Density > Constant node and set Value to 1182 kg/m^3.

When the particle phase approaches maximum packing, the normal stress tends to repel the particles, which can impede further particle migration. If you increase the maximum packing fraction

ϕ_{m}

to between 0.68 and 0.72, the simulation can produce a better result. This increase in

ϕ_{m}

is not necessarily unphysical: experimental studies have shown that as the particles in a suspension experience a strong shear flow, they can align into rows that exhibit a hexagonal close packing [977] that increases

ϕ_{m}

in the rheology [973].

Edit the Phases > Particles > Models > Solid Particle Rheology node and set Maximum Solid Fraction to 0.68.

Select the Models > Multiphase > Mixture > Material Properties node and set the following properties:


Node	Property	Setting
Normal Relative Viscosity	Method	Morris and Boulay Model
Relative Viscosity	Method	Morris and Boulay Model

Both the relative (shear) and normal relative viscosities are limited to a maximum viscosity of 10000.

If the suspension approaches maximum packing and starts to jam, the viscosity tends towards infinity. The Maximum Viscosity is a numerical limit that helps to keep the simulation stable.

The default values for the contact contribution are $K_{s}$ = 0.1 for the shear contact contribution (relative viscosity, see Eqn. (5253)) and $K_{n}$ = 0.75 for the normal contact contribution (normal relative viscosity, see Eqn. (5254)).

Save the simulation.