Theory

The theory of separation by SPLITT cell was formulated by J. C. Giddings in terms of experimentally controllable flow rates in the inlet and outlet sub-streams and it has been developed and implemented through the years; SPLITT fractionation theory can now be found in numerous publications. The separation is performed inside a thin channel, where the behaviour of a sample particle depends on the balance between the external force field and frictional forces (as for field flow fractionation techniques (FFF)), combined with the action of the fluxes operative within the cell.

In Figure 1 the sample, suspended in a suitable carrier fluid, is introduced through the top inlet a' at a predetermined volumetric flow rate V(a'). At the same time, pure carrier fluid enters through the bottom inlet b' at a flow rate V(b'); where the two inlet streams join to form a single stream we have the ISP. When the fluid stream reaches the end of the channel, it is mechanically divided into two fractions by the outlet splitter.

The differential displacement of the particles occurs towards wall B, based on the driving force exerted on each type of particle by the applied field and the frictional resistance offered by the carrier fluid to particle motion. Thus different types of particle occupy different laminae while the flow through the channel displaces them axially towards the outlet end.

The total volumetric flow rate V in the channel can be written both in terms of inlet flow rates or outlet flow rates

and since the walls A and B are parallel and their dimensions much larger than w (thickness) and b (width), the velocity profile is essentially two-dimensional (see Figure 2). The mean fluid velocity v can be computed as V/bw, and the velocity parabolic profile across the cell thickness is described by the equation:

where vmax is the maximum fluid velocity found at the midplane (x = w/2) of the cell.

By looking at the flow stream components (see Figure 1) it is possible to find a relation which takes into account the fluid flow proceeding in the transport layer V(i):

Figure 2 Upper view of the 'Splitter' used in the gravitational SPLITT cell.

V(t) can be obtained by combining eqns [1] and [3]

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