Channel thickness

Let H and L be two characteristic lengths associated with the channel height and the lateral dimensions of the flow domain, respectively. To obtain a uniformly valid approximation for the flow equations, in the limit of small channel thickness, the ratio of characteristic height to lateral dimensions is defined as e = (H/L) 0. Coordinate scale factors h, as well as dynamic variables are represented by a power series in e. It is expected that the scale factor h-, in the direction normal to the layer, is 0(e) while hi and /12, are 0(L). It is also anticipated that the leading terms in the expansion of h, are independent of the coordinate x. Similai ly, the physical velocity components, vi and V2, ai e 0(11), whei e U is a characteristic layer wise velocity, while V3, the component perpendicular to the layer, is 0(eU). Therefore we have... 

Typical column dimensions i.d. 7—10 mm Length 25-30 cm Several columns may be coupled in series i.d. 0.1—3 fjLtn Length 100-500 cm Similar to SEC Thin channel Thickness 50-150 /mi Width 1-2 cm Length 30-50 cm... 

Resolution factors Column length ("f) Pore volume ( ) Column length ( ) Column length ( ) Void volume ( ) Column length ( ) Channel thickness ( i )... 

D=mass diffumsion coefficient Z)T=fiiermal diffusion coefficient /=friction coefficient G=(oh (centrifugal acceleration) / =Boltzniann constant meff=particle effective mass r=radius of centrifuge basket s=sedimentation coefficient T = absolute temperature =geometric volume of die channel w=channel thickness y=diermal expansion coefficient p=electrophoretic... 

From Equation 12.19, it can be seen that the maximum efficiency is achieved when retention is high (e.g., X is low, see Equation 12.10) and the channel thickness is made as thin as possible. 

Cross-flow FFF or, as it was known in the past, FIFFF draws its name from the field type used to transport sample components across the channel thickness to the accumulation wall [3,8]. The... 

The ThFFF separation system is made up of a flat ribbon-like channel obtained by placing a trimming-spacer between two flat bars kept at different temperatures (at the upper wall) and (at the lower wall), with AT = Tg- The thickness of the spacer defines the channel thickness w. In the channel cross section, the thermal diffusion process pushes the analyte toward the so-called accumulation wall, usually the cold wall (thermophobic substances) the combination of the flow profile and the thermal diffusion produces the fractionation. 

The classical FEE retention equation (see Equation 12.11) does not apply to ThEEE since relevant physicochemical parameters—affecting both flow profile and analyte concentration distribution in the channel cross section—are temperature dependent and thus not constant in the channel cross-sectional area. Inside the channel, the flow of solvent carrier follows a distorted, parabolic flow profile because of the changing values of the carrier properties along the channel thickness (density, viscosity, and thermal conductivity). Under these conditions, the concentration profile differs from the exponential profile since the velocity profile is strongly distorted with respect to the parabolic profile. By taking into account these effects, the ThEEE retention equation (see Equation 12.11) becomes ... 

Feed Channel (Thickness Exaggerated -Actually <1/32 Inch Thickness Allowing Smooth Cylindrical Over-Wrap Sidewall)... 

Cross-flow FFF (F1FFF) utilizes a second fluid flow to transport sample components across the channel thickness to the accumulation wall, and the position of individual species in the laminar carrier profile corresponds to their ordinary (Fick s) diffusion coefficient. As the particle size increases, the diffusion coefficient (decreases until it becomes a relatively insignificant transport process. For micron-size particles, the extent of protrusion into the channel becomes the decisive factor in determining the order of elution. 

This can be easily checked by assuming that the flow inside this section of the screw can be modeled using a simple shear flow, and that most of the conduction occurs through the channel thickness direction. For such a case, the energy equation in that direction, say the -direction, reduces to... 

We note first that immediately following the injection of a sample at the head of the channel, the flow of carrier is stopped briefly to allow time for the sample particles to accumulate near the appropriate wall. As the particles concentrate near the wall, the growing concentration gradient leads to a diffusive flux which counteracts the influx of particles. Because channel thickness is small (approximately 0.25 mm), these two mass transport processes quickly balance one another, leading to an equilibrium distribution near the accumulation wall. This distribution assumes the exponential form... 

By refining column design, the Instrumental band broadening H, has been reduced to a level insignificant in comparison with the other terms of Equation 7. The nonequilibrium term, linear in carrier velocity , also depends on channel thickness w and inversely on particle diffusion coefficient D. The dependence of coefficient x on X is well known, although the function is complex (14). Its limiting form is described by... 

Figure 2. Fractionation of four samples of Dow polystyrene latex beads by sedimentation FFF. The nominal particle sizes are given in the figure. Flowrate = 12 ml/hr, channel thickness w = 0.0127 cm, void volume V° = 2.0 ml, and field strength G = 193.7 gravities. Reproduced with permission from Ref. 20. Copyright 1980 John Wiley.

Figures 4 and 5 show plots of the apparent number and weight averages determined by SFFF plotted against the corresponding data from DCP measurements. For perfect agreement, the data would lie along a line with slope of one with an intercept of zero. The deviation of these plots from linearity at larger particle sizes is probably due to a steric effect which occurs in SFFF when the particle diameter becomes a significant fraction of the channel thickness (2). The particle size limit above which the SFFF channel used in this work is expected to exhibit this effect is...

A highly effective means of reducing natural convection is to reduce channel thickness w. Not only does u(y) at any relative position y/w depend on the square of w, but the reduction of tv in some situations will lead to the more rapid dissipation of heat, thus reducing AT as well. 

We see that A is a dimensionless form of , representing the ratio of to channel thickness w. 

Thus retention parameter A can be considered as a ratio of two energies dissipative energy 5 7 and the energy F w expended in driving components across channel thickness w. We have shown before (see Section 8.2) that energy ratios of this kind are crucial to separation. 

When transversely oriented focusing forces of the type used in isoelectric focusing or isopycnic sedimentation are used to confine different components to different thin bands or laminae in an FFF channel, we have a variant of FFF called hyperlayer FFF. Suppose component A is focused at y = 15.2 /xm and B at y = 127 /xm (0.005 in). You may assume that the thin bands form a 6-function distribution in coordinate y and that channel thickness w = 254 /xm. What is the R value for each of the two components ... 

Detection is one of the most difficult problems in micro chemical processes. Because sample volume becomes extremely small in such systems, an ultrasensitive detection method is indispensable. For example, limited sample channel thickness causes very small signal-to-background ratio in absorption spectroscopy, thus only very concentrated samples can be analyzed. 

For samples with a broad size distribution in the micron range, it is important to avoid the transition region between the normal and the steric mode during the measurement. This can be achieved by proper adjustment of the channel thickness, channel flow and the strength of the applied field [69]. The transition region in Fig. 6 can be experimentally determined by plotting the retention ratio vs. the particle size, as illustrated in Fig. 7 for the example of flow-FFF. 

It has already been stated that a simple way to enhance the resolution of an FFF measurement is to reduce the channel thickness. This however can lead to other problems as the effects of surface irregularities are enhanced, due to the increase of the surface-to-volume ratio of the channel, and lead to increasing, unpredictable solute-wall interactions, etc. Furthermore, non-uniformities in the channel planarity will also be a problem with very small channel thicknesses, especially in Fl-FFF where the accumulation wall is a membrane. Another possibility for the reduction of H is to reduce the flow velocity of the carrier liquid which, in turn, leads to longer retention times and slower separation. However, in Fl-FFF, one has the possibility to increase the flow rate with cost to resolution but simultaneously increase also the cross-flow rate. Nevertheless, this enhances sample absorption onto the membrane. The third possibility for the reduction of H is to increase the solute diffusion. This can be done by decreasing the solvent viscosity by increasing the temperature. 

Fl-FFF is the most universally applicable FFF technique as the separation only relies on differences in the diffusion coefficients. Thus, it nicely complements S-FFF or Th-FFF with respect to size distribution analysis [225]. Fl-FFF is capable of separating almost all particles (up to 50 pm [226] or even much larger) and colloids and polymers down to -2 nm [17] or 103 g/mol [227]. The lower limit is determined by the pore size of the membrane material. The need for such membrane covering the accumulation wall is the principle disadvantage of Fl-FFF due to possible interactions with the solute and the danger of a membrane-induced non-uniformity in the channel thickness, especially since thinner channels are highly favored for faster separations. However, the advantages of Fl-FFF usually more than balance the potential pitfalls and sources of error. Consequently, Fl-FFF is the FFF technique which has been developed the most in recent years in instrumentation [48] and has found the most widespread distribution. 

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