Bulk displacement

Table A.2 Ratio of surface and bulk displacements, and Debye temperatures of several metals f 1],...

Of the two classes of displacement, only the relative displacement is selective. While the two may, and often are, used in combination, bulk displacement cannot be used alone because of its nonselectivity. All separa-... 

The equations above describe relative displacement which, as noted before, is displacement through (not with) the medium. Recall that bulk displacement (or transport with the medium), mainly in the form of flow, can occur also. The latter generates an additional flux density of... 

Quantity W is simply the sum of all direct displacement velocities—those caused by bulk displacement at velocity v plus those caused by chemical potential gradients which impel solute at velocity /. 

As noted earlier, flow is a form of bulk displacement in which components entrained in a flowing medium are carried along nonselectively with the medium. Flow displacement thus stands in contrast to the other major transport mechanism—relative displacement—which is selective. 

Natural convection is the flow induced by the unequal pull of gravity on fluid elements of different densities. For example, if we inject a globule (or layer) of dense aqueous solution marked with a dye into a beaker of water, the dense globule will be observed to sink under the influence of gravity, as illustrated in Figure 4.8. That sinking motion is actually a form of bulk displacement or flow, specifically natural convective flow. 

Elastic adhesives deform when exposed to such internal stress and are less affected by shrinkage. Fillers also reduce the rate of shrinkage by bulk displacement of the resin in the adhesive formulation. This results in an increase in the inherent bond strength of the adhesive. Fillers may improve operational bond strength by 50 to 100 percent although all of this improvement is not due to reduced shrinkage (see Sec. 9.3.11). ... 

Fillers improve the thermal properties of the cured epoxy formulation by bulk displacement of organic components. This reduces long-term shrinkage and thermally induced weight loss. However, the glass transition temperature is not significantly affected and in some cases may be lowered. 

Stresses caused by items 1 and 2 above are magnified by the mismatch in thermal expansion coefficients between the adhesive and the substrate. Incorporating fillers into the adhesive formulation can often reduce these stresses. Fillers also reduce the thermal shrinkage during aging by bulk displacement of the polymeric resin. 

In most separation processes, bulk displacements also take place simultaneously. Generally, bulk displacements move molecules of all components at the same speed and in the same direction. On the other hand, the spontaneous microscopic species-specific movement in response to forces acting on a particular species (mentioned in the preceding paragraph) is identified as relative displacement (Giddings, 1978). These two types of displacements may occur simultaneously or consecutively (Sweed, 1971). 

Bulk displacement may be caused by fluid flow or direct mechanical conveying of a complete phase or fraction from one location or vessel to another. Consider, for example, the mechanical decantation of the upper phase from vessel A to vessel B. In vessel B, additional separation takes place because of the redistribution of components of the upper phase in vessel A between itself and the lower phase in vessel B (Figure 3.1.1). But all the components in the upper phase of vessel A are displaced to the new vessel B at the same rate and in a nonselective fashion. Such a procedure is followed in laboratory decantations as well as in industrial decanters. 

Bulk displacement by fluid flow is much more common. When a multicomponent mixture moves in a vessel or in a region of a vessel at a certain bulk velocity, the fluid motion carries all the components, in general, at the same velocity. In the case of a flat velocity profile with convective transport being dominant over diffusive transport, the fluid flows like a "plug (Froment and Bischoff, 1979), and every species has the same displacement and velocity. If no forces are present to impart different displacement rates to different components, all components will he non-selectively carried hy hulk fluid motion and there would not he any separation. ... 

There can be separation processes in which bulk displacement could vary from location to location due to gradients in bulk velocity. Additional complexities and sometimes separation can be achieved by a time dependence in the bulk displacements. The effects of spatial and temporal dependence of bulk displacement will be treated in later chapters. 

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