Particle flow is generally understood as an independent application or discipline in the field of flow simulation. Strictly speaking, however, this is not the case, because particle flow also belongs to the two-phase and multiphase flows. It is usually modelled according to the Euler-Lagrange method.
With the Euler-Lagrange method, disperse flows with slip, which means different velocities between phases, and inhomogeneous particle, bubble or drop distribution can be observed. The method is not suitable for multiphase flows of immiscible liquids or with a not insignificant volume fraction of the second phase, approx. from 10%. However, the mass fraction of the disperse phase may be larger than that of the continuous phase.
As with single-phase flow, the continuous phase is described mathematically using the Euler method. This formulation for the fluid mechanical and thermodynamic state variables is based on a fixed control volume. The Lagrange method for describing the disperse phase is based on a control volume that moves with the flow field. The particles are accompanied through the flow field, so to speak. Mathematically, this corresponds to a vector description.
The phases can exchange impulse, moment and energy. Depending on the strength of the interaction, the coupling must be considered uni- or bidirectional. In the latter case, the particles also influence the flow of the continuous phase.