Flow separation is the ejection of fluid particles from a small neighborhood of a solid boundary. Such a breakaway from the boundary is often due to the detachment of a boundary layer, but it also occurs in highly viscous flows where the boundary layer description is inapplicable. Accordingly, we will treat separation here as a purely kinematic phenomenon: the formation of a material spike from a flow boundary.Such material spikes form along attracting LCSs, as we have already seen inthe previous chapter. We consider LCSs acting as separation or attachment profiles here separately because their contact points with the boundary and their local shapes near the boundary can be located from a purely Eulerian analysis along the boundary. Since the attachment points of material separation profiles cannot move under no-slip boundary conditions, such profiles necessarily create fixed separation. In contrast, material spikes emanating from off-boundary points generally result in moving separation in unsteady flows. We will discuss how both fixed and moving separation can be described via material barriers to transport.

In this chapter, we will be concerned with barriers to the transport of inertial (i.e., small but finite-size) particles in a carrier fluid. As a general rule, the more the density of inertial particles diverts from the carrier fluid density, the more they tend to depart from fluid trajectories. Specifically, while small enough neutrally buoyant particles often remain close to fluid motion, the same is not true for heavy particles (aerosols) and light particles (bubbles). Practical flow problems involving inertial particles tend to be temporally aperiodic and hence the machinery of LCSs discussed in earlier chaptersis also highly relevant for inertial particles. By inertial LCSs (or iLCSs, for short), we mean coherent structures composed of distinguished inertial particles that govern inertial transport patterns. In contrast, LCSs (composed of distinguished fluid particles) govern fluid transport patterns. The purpose of this chapter is to examine how iLCSs differ from LCSs of the carrier fluid.