Concentration profiles in a turbulent suspension when gravity is not affecting deposition

An idealized representation of the dispersed flow in a fully-developed annular pattern is considered for the case of zero gravitational effects. The walls of a two-dimensional channel are represented as presenting arrays of infinitesimal particle sources. The behavior of a single source is described by modeling the fluid turbulence seen by the particles with a modified Langevin equation. By carrying out the calculations over a wide range of dimensionless time constants the deposition process could be followed, as the controlling mechanism changed from Brownian diffusion, to turbulent diffusion, to free-flight, to unidirectional non-turbulent trajectories. The calculation of local mean particle accelerations allowed a direct evaluation of the turbophoretic velocity. A consideration of the concentration profiles indicates that a Boussinesq representation of turbulent mixing is not valid in an Eulerian analysis.