Pinch effect

This author has previously suggested that the mechanism of flux enhancement might be due to the "tubular pinch effect" ( ). The lower density (0.94 g/cc) MMA beads show less tendency to... 

Fig. 9.4.10 Apparatus for the gas flow-arc plasma method. The apparatus is composed of two components. The upper part is a glass Dewar, which accumulates small particles in a cryogenic matrix on the trim cooled with liquid nitrogen (LN). Sorv, inlet of organic vapor Syr, syringe for transferring produced colloids under anaerobic conditions RP, rotary pump S, target sample. Lower part is for plasma discharge. A BN furnace has gas inlets (G) and is specially designed for Ar gas to flow in screwed stream hence the plasma is emitted in a jet flame due to a plasma pinch effect. The black parts are copper electrodes cooled by water. In order to maintain a constant spacing between the surface of sample and tbe upper electrode, the sample position can move vertically so that the current through the sample to the upper electrode is precisely controlled and constant. This is very important to produce powders with a narrow size distribution.

Huber et al. (loc. cit.) and Yuan and Spiegel [Chem. Ing. Tech. 54, 774 (1982)] added lateral mixing to the model. Lateral deflection of liquid by the packing particles tends to homogenize the liquid, thus counteracting the channeling and pinching effect. 

FIGURE 4.12 Schematic drawings of CE chips with added microelectrodes to achieve the pinching effect (a) the conventional cross type CE microchip, (b) two Au electrodes of equal lengths were added (x = y = 0.5 mm) [562]. Reprinted with permission from the Royal Society of Chemistry. 

The pinching effect. Local changes in L/V ratio, causing local composition pinches (Sec. 9.2.2). 

Lateral mixing effect. Packing particles deflect both liquid and vapor laterally. This promotes mixing of vapor and liquid and counteracts the pinching effect (Sec. 9.2.3). 

There are some special cases in FFF related to the two extreme limits of the cross-field driving forces. In the first case, the cross-field force is zero, and no transverse solute migration is caused by outer fields. However, because of the shear forces, transverse movements may occur even under conditions of laminar flow. This phenomenon is called the tubular pinch effect . In this case, these shear forces lead to axial separation of various solutes. Small [63] made use of this phenomenon and named it hydrodynamic chromatography (HC). If thin capillaries are used for flow transport, this technique is also called capillary hydrodynamic fractionation (CHDF). A simple interpretation of the ability to separate is that the centers of the solute particles cannot approach the channel walls closer than their lateral dimensions. This means that just by their size larger particles are located in streamlines of higher flow velocities than smaller ones and are eluted first (opposite to the solution sequence in the classical FFF mode). For details on hydrodynamic chromatography,see [64-66]. 

Osmotic Pinch Effect Feed is pumped into the membrane train, and as it flows through the membrane array, sensible pressure is lost due to friction effects. Simultaneously, as water permeates, leaving salts behind, osmotic pressure increases. There is no known practical alternative to having the lowest pressure and the highest salt concentration occur simultaneously at the exit of the train, the point where AP - AH is minimized. This point is known as the osmotic pinch, and it is the point backward from which hydraulic design takes place. A corollary factor is that the permeate produced at the pinch is of the lowest quality anywhere in the array. Commonly, this permeate is below the required quality, so the usual practice is to design around average-permeate quality, not incremental quality. A 1 MPa overpressure at the pinch is preferred, but the minimum brine pressure tolerable is 1.1 times n. 

This behavior has been explained by the so-called tubular pinch effect, which enhances movement of particles away from the boundary layer thus reducing concentration polarization effect (see Sec. 3.3). 

These observations lead to the conclusion that the back-diffusive transport of colloidal particles away from the membrane surface into the bulk stream is substantially augmented over that predicted by the Leveque or Dittus-Boelter relationships. It is known that colloidal particles flowing down a tube tend to migrate across the velocity gradient toward the region of maximum velocity this is called the "tubular pinch effect". 

Tubular Pinch Effect. The lateral movement of particles across the streamlines in laminar flow was first observed and recorded in 1836 by Poiseville. He noted that the region immediately adjacent to the walls of blood capillaries tends to be free of blood cells. 

Figure 3.49 Particle migration to center line of flowing channel (tubular pinch effect). Brandt and Bugliarello (1966).

The tubular pinch effect can explain much of the anamolous UF data for colloidal suspensions. With UF, the water flux through the porous wall will still carry particles to the wall, but the "lift" of particles away from the wall (due to the tubular pinch effect) will certainly augment the back diffusive mass transfer described by the Leveque and Dittus-Boelter relationships. 

The data of Figure 3.44 show similar flux values for whole blood and plasma. Presumably, the tubular pinch effect tends to depolarize the membrane surface of red cells yielding a flux similar to that obtained with plasma alone. In some cases, the flux with the red cells present is higher than that with plasma alone. The migration of the larger red cells away from the membrane surface tends to drag the plasma proteins along. 

Equations 25 and 26 also predict that the radial migration velocity (V) will increase as the tube radius (R) decreases. Thin channels are more effective in depolarizing the membrane surface via the tubular pinch effect. This may explain the larger discrepancies between experimental and theoretical flux values in 15 mil channels (see Figure 3.46) than in 30 mil channels (see Figure 3.47). 

Green and Belfort39 have combined the equations for particle migration due to the tubular pinch effect with the normal back-diffusive transport to calculate... 

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