Streamline displacement thickness

In addition to the boundary-layer thickness 5, two other thicknesses occur frequently in the boundary-layer literature the displacement thickness S and the momentum thickness 6. To see the meaning of the displaicement thickness, consider the streamlines for the laminar boundary layer on a flat plate, as sketched in Fig. 11.5. 

Here the displacement thickness 6 is the distance that the streamlines are... 

FIG. 12.1 Streamlines (which also represent the electric field) around spherical particles of radius Rs. The dashed lines are displaced from the surface of the spheres by the double-layer thickness k. In (a) kRs is small in (b) kRs is large. 

The characteristic feature of flow FFF is the superimposition of a second stream of liquid perpendicular to the axis of separation. This cross-flow drives the injected sample plug toward a semipermeable membrane that acts as the accumulation wall. The cross-flow liquid permeates across the membrane and exits the channel, whereas the sample is retained inside the channel in the vicinity of the membrane surface. Sample displacement by the cross-flow is countered by diffusion away from the membrane wall. At equilibrium, the net flux is zero and sample clouds of various thicknesses are formed for different sample species. As with other FFF techniques, a larger diffusion coefficient D leads to a thicker equilibrium sample cloud that, on average, occupies a faster streamline of the parabolic flow profile and subsequently elutes at a shorter retention time t,. For well-retained samples analyzed by flow FFF, t, can be related to D and the hydrodynamic diameter d by... 

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