Two-fluid flows of a mixture of a gas and solid particles with “films” and “filaments” appearing in flows past impermeable surfaces

Abstract

The two-fluid model with dispersed phase, representing a solid medium with zero intrinsic pressure, is used to study the appearance of “films” and “filaments” in the flow of a mixture of a gas and solid particles past impermeable surfaces. The films, endowed with surface properties (mass, etc.) and the filaments with analogous linear properties, first introduced in /1/ in the hydrodynamics of media without pressure with prohibited overtaking, appear in two-fluid models as a result of the intersection of dispersed-phase trajectories caused, for example, by inhomogeneities in the initial distributions /2–6/. In /7/ films were used to describe thin boundary layers of the solid phase forming at the walls and moving along them, and the possibility of the film separating (parting) from the wall is noted(∗∗). The equations and conditions governing the formation, motion and separation of the films and filaments from surfaces are derived below, and various models of the detachment of films and their subsequent evolution are presented. It is shown how a detached (free) film collects particles, separating the regions containing a mixture from those of pure gas, and acting as if it were a filter. In the models with absorbent walls, where the particles terminate their existence, the same regions are separated by the tangential discontinuities of the particulate continuum through which pure gas flows. Cases are noted of the flows in nozzles where a film, after detaching itself, either becomes reattached to the wall or forms a filament on the axis. It is shows that particles may form zones of finite volume in flows past blunt bodies. The possibility of a film forming in a rarefaction flow, when a two-phase mixture flows supersonically past a sharp bend, is demonstrated.