[1] The modeling of two-phase flows has a tremendous variety of engineering and scientific applications: pollution dispersion in the atmosphere, fluidization in combustion processes, aerosol deposition in spray medication, along with many others.
The starting point for a mathematical description of almost any type of fluid flow is the classical set of Navier–Stokes equations.
To describe particle-laden flows, we must modify these equations to account for the effect of the particles on the carrier, or vice versa, or both - a suitable choice of such added complications depend on a variety of the parameters, for instance, how dense the particles are, how concentrated they are, or whether or not they are chemically reactive.
In most real world cases, the particles are very small and occur in low concentrations, hence the dynamics are governed primarily by the continuous phase.
The dispersed phase is typically (though not always) treated in a Lagrangian framework, that is, the dynamics are understood from the viewpoint of fixed particles as they move through space.
In reality, there are a variety of other forces which act on the particle motion (such as gravity, Basset history and added mass) – as described through for instance the Basset–Boussinesq–Oseen equation.
Particles (particularly those with Stokes number close to 1) are known to accumulate in regions of high shear and low vorticity (such as turbulent boundary layers), and the mechanisms behind this phenomenon are not well understood.
These features are particularly difficult to capture using RANS or LES-based models since too much time-varying information is lost.
Due to these difficulties, existing turbulence models tend to be ad hoc, that is, the range of applicability of a given model is usually suited toward a highly specific set of parameters (such as geometry, dispersed phase mass loading and particle reaction time), and are also restricted to low Reynolds numbers (whereas the Reynolds number of flows of engineering interest tend to be very high).
At intermediate St, particles are affected by both the fluid motion and its inertia, which gives rise to several interesting behaviors.
[3][4] They showed that a neutrally buoyant particle in a laminar pipe flow comes to an equilibrium position between the wall and the axis.
Feng et al. have studied this through detailed direct numerical simulations and have elaborated on the physical mechanism of this migration.
Recently it was found that even for non-neutrally buoyant particles similar preferential migration occurs .
Experimental and particle-resolved DNS studies have explained the mechanism of this migration in terms of the Saffman lift and the turbophoretic force .
[7][8] These preferential migration are of significant importance to several applications where wall-bounded particle-laden flows are encountered and is an active area of research.