Real plate number

The Murphree efficiency EmV is only equal to the point efficiency Emv if the liquid on the plate is perfectly mixed. On a real plate this will not be so, and to estimate the plate efficiency from the point efficiency some means of estimating the degree of mixing is needed. The dimensionless Peclet number characterises the degree of mixing in a system. For a plate the Peclet number is given by ... 

It should be noted that Eqs. (1.7) and (1.8) are valid only if the migration velocity of a sample zone is constant during the elution, which means that the plate number can be determined only from isocratic chromatograms obtained at a constant composition of the mobile phase, temperature and flow rate. Plate number values evaluated from a gradient-elution chromatogram are subject to gross errors and have no real meaning. 

Numerical calculations are easily made to compare in a real case the four different distributions derived as solutions of Eq. 6.24 with as many different boimdary conditions. Then we observe that the peak profiles obtained are very close, unless the plate number is small, much smaller than the values encountered in practical applications. These differences can be completely neglected in practice. 

Tray efficiency is required to convert the number of theoretical stages identified as necessary to a number of real plates for installation in a tower. Many... 

The above-mentioned equation for n in fact is only valid for isocratic separations and if the peaks are symmetric the peak capacity is larger with gradient separations. Tailing decreases the peak capacity of a column. In real separations the theoretical plate number is not constant over the full k range. However, it is even more important to realize that a hypothetical parameter is discussed here. It is necessary to deal with peaks that are statistically distributed over the accessible time range. The theory of probabilities allows us to proceed from ideal to near-real separations. Unfortunately, the results are discouraging. 

Number of theoretical [(equilibrium) stages Number of orifices or perforations per plate Number of drops Power for one real stage Total flow rate Weight (or mass flow rate) of raffinate... 

What is obtained in this way is the number of theoretical plates, which means that the liquid is assumed to be completely mixed and that the gas and liquid are in equilibrium. Departure from these conditions are accounted for by means of the Murphree efficiency. When the operating and equilibrium lines are straight, the overall tray efficiency, E, which is the ratio of the number of ideal to real plates, can be computed analytically from... 

A theoretical model for the calculation of the number of theoretical plates using the Newton-Raphson method is presented by Kaibel et al. (31). However, it does not incorporate a constraint on T so that temperature becomes an independent variable. Such an assumption is obviously highly questionable. Nevertheless, this difficulty can be overcome by incorporating such a constraint into the equations. The problem of different plate efficiencies for concentration and reaction equilibrium is, however, considerably more difficult to handle. It would appear that the best approach will be to abandon completely the concept of theoretical plates and efficiencies and develop instead a plate-to-plate calculation method based on real plates. Here the extension of the differential equations for packed columns into difference equations and their subsequent modification to apply to each individual plate offers the best chance of success. 

The value assumed for yAn + Is correct when these two estimates of q coincide. This enables constmction of the pseudoequilibrium curve, which is then used with the operating curve to step off the number of real plates needed to accomplish the desired change in D-phase composition from y, 2 to y i. 

Since a large number of theoretical plates are desired, h should be as small as possible. Naturally, there are no real plates in a column. The concept of a theoretical plate is a variable, the value of which depends on the particle size, the flow velocity, the mobile phase (viscosity) and, especially, on the quality of the packing, h can be calculated using the following equation ... 

A 1.7.5 For packed columns, draw curves of HETP in mm, AF in kPa and kPa/m, and number of theoretical plates as a function of boilup rate expressed in mL/h and absolute rate in (mL/h) X cm. For real plate columns, the efficiency should be plotted as percent of a theoretical plate per real plate and AP should be plotted both in kPa/real plate and in absolute units of kPa/theoretical plate using the same units for boilup rate as above for pack columns. The efficiency of the column corresponds to the value of N determined from the curve at 75 % of its maximum boilup rate. 

Al.7.9 For real plate columns, divide 14 and 18 by plate efficiency to obtain the number of actual plates (rounded to the nearest integer) for an acceptable column. 

E.coli recA y.luxCDABE strain were grown for 16-18 hours at 37°C in LB-broth in the presence of 20 pg/ ml of ampicillin. Immediately before the experiment the culture was diluted 1 20 by fresh culture medium and incubated until early log-phase. The grown biomass was mixed with AR solutions in final concentrations of ICfs, ICH n ICfs M, with used for their dilution with distilled water (control) and incubated for 60 minutes. The luminescence intensity of UV-irradiated E.coli recA lux and intact specimens were registered by plate bioluminometer LM OIT (Immimotech, Czech Rep.) in a real time. The number of viable cells was determined from the colony-forming units (CFU) on a surface of a LB-agar after the subsequent incubation within 24 hours at 37 °C. A quantitative estimation of an induction of the SOS-system calculated on formula... 

In some methods, the Murphree plate efficiencies can be incorporated into the procedure for calculating the number of stages and the number of real stages determined directly. 

The use of a plate efficiency correction enables the simulation of columns with a real number of plates to be simulated. This may be important in the study of real columns, when incorporating an allowance for plate hydrodynamic behaviour. 

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