# Test Case for Constant Attachment Model

## Description

0D test case for attachment modelling[^1] using a constant user-defined value
for species mass transfer. Phases of water, aggregates (of bubbles and attached
particles species), and free particles are initialized in the domain. Initially,
the mass fraction of the (attached) particle species is set to a value of $0$,
corresponding to unloaded bubbles. Then due to attachment, the mass of the
(free) particle phase moves to the (attached) particle species in the aggregate
phase. Eventually, the mass transfer rate goes to zero when the maximum bubble
surface loading is reached.

## Technical Information

- 0D.
- The mass transfer rate is $10$ kg m$^{-3}$ s$^{-1}$.
- The maximum bubble surface loading is $0.5$.
- $d_B = 3$ mm and $d_P = 0.1$ mm.
- Multicomponent phases are used for the aggregates (of bubble and particle
species) and the particles (of particle species only).

## Post processing

The volume fractions of the three phases are observed over time. Due to
attachment, the volume fraction of the free particle phase decreases, while
that of the aggregate phase increases. The volume fraction of water remains
constant.

## Keywords

0D, multiphase, three-phase, multicomponent, gas, solid, liquid, isothermal,
incompressible, attachment, flotation, phase transfer

## Literature

[^1]: Bhutani, G., & Brito-Parada, P. R. (2020). A framework for polydisperse
      pulp phase modelling in flotation. Separation and Purification Technology,
      236, 116252.
