Zone spreading flow rate

The above phenomena have been incorporated into a theoretical approach which explicitly associates zone spreading with flow velocity and the rates of various equilibration processes. This is the generalized nonequilibrium theory developed by the author [5]. While the theoretical details are too lengthy to develop here, some semi-quantitative reasoning can be used to understand the nature of nonequilibrium-induced zone spreading and the parameters that control it. 

In FFF, however, the fractogram is recorded in dependence of time so that a correction via extrapolation to infinite time in order to eliminate diffusion effects is not possible. A different strategy may be used for the correction of zone spreading which suffers from a number of assumptions and restrictions. A number of authors, reviewed by Janca [459], have dealt with the methods of correction for zone spreading which was found to be particularly extensive at high flow rates or low retentions. The results are summarized below. 

T3q3ical patterns of rivulet spreading on a vertical copper surface which was observed in [22] are shown in Fig. 13 for different overheating of the wall relative to saturation temperature AT=Tw-Ts. The Reynolds number was defined as Re=(Q/dv), where Q is the volumetric flow rate, and d is the width of the open cross-section of the nozzle. One can see that the higher the wall superheat, the narrower the spreading zone. At overheating of 0.39K the rivulet starts to contract on hot wall. The... 

The non-equilibrium effect is decreased by decreasing the solvent flow velocity V. So low solvent flow rates are used in high resolution work, but not so low that the diffusion term becomes large. The best compromise is V =k2DI[R —R). In practice the values of the variables are such that flow rates of a few ml/hr cm (sometimes written cm hr ) cross sectional area of the resin bed will give low zone spreading with excellent resolution. In many applications where speed is more important than resolution, higher flow rates are used. 

The second term,. represents the zone spreading that each sample component exhibits due to diffusion along the column axis. Diffusion coefficients in aqueous solution are generally low, so the contribution of this term is relatively small unless the retention time is quite long due to a very slow flow rate or a high retention factor. 

Resistance to mass transfer, is by far the major contributor to sample zone spreading within the column. This term is minimized by a column packing that attains equilibrium of the analyte between the mobile and stationary phases as quickly as possible. A moderate linear flow rate, u, should be employed because cr mt increases with flow rate. 

Sorption effects by the gel matrix may alter the values of and for certain solutes, and the use of against log plots to select a gel, takes into account neither those effects nor zone spreading in the column, and variations in flow-rate (which could arise, for example, from differences in viscosity of sample and eluant). Taken together these may have an important effect on the separation, and hence on the choice of the best gel for a particular purpose. The behaviour of small molecules on tightly cross-linked gels is profoundly influenced by adsorption, ion exclusion, ion exchange and various other processes which dominate the size differences between solutes. 

Figure 21-6 Solute requires a finite time to equilibrate between the mobile and stationary phases. If equilibration is slow, solute in the stationary phase lags behind that in the mobile phase, thereby causing the band to spread. The slower the flow rate, the less the zone broadening by this mechanism.

Axial diffusion may cause substantial zone broadening for late-eluting sample ions or when a very slow eluent flow rate is employed. The magnitude of zone spreading by axial diffusion is a function of the time spent in the column and the diffusion coefRcient of the particular ion. 

In Refs. an analytical solution of the two-dimensional problem of flame spread over a horizontal surface is described. Formulas for the determination of the location of the chemical reaction, fuel flow to the latter, and temperature in the reaction zone have been derived. From these formulas it follows that the distance between the material surface and the chemical reaction zone is greater farther away from the flame front. Also the influx of fuel and oxidant to the reaction zone is smaller and the temperature is higher, and attains in the limit a level corresponding to adiabatic combustion. Thus, the temperature in the flame front may be substantially below the adiabatic temperature of combustion because of heat transfer to the combustible material. A criterion determining the effect of the gas-phase reaction rate on the com-... 

---