Filtration curves

Equation 18 defmes a parabolic relationship between filtrate volume and time. The expression is valid for any type of cake (i.e., compressible and incompressible). From a plot of V + C versus (t+Tq), the filtration process may be represented by a parabola with its apex at the origin as illustrated in Figure 5. Moving the axes to distances C and Tq provides the characteristic filtration curve for the system in terms of volume versus time. Because the parabola s apex is not located at the origin of this new system, it is clear why the filtration rate at the beginning of the process will have a finite value, which corresponds to actual practice. 

Fig. 4. — (a) Gel-Filtration (G. F.) and (b) Electrophoretic (E. P.) Patterns of a Typical, Pig-mucosal Heparin. [Shoulders on the gel-filtration curve (Sephadex G-75, column 180 X 1 cm, 10% Na acetate + 10% EtOH) and bands in the electrophoretograms (cellulose acetate, low amperage, 0.1 Af barium acetate) indicate heparin species differing from each other as regards both mean mol. wt. and degree of sulfation (d.s.). The dashed curve is the electrophoretogram of the fraction of lowest mol. wt. (separated by gel-filtration), accounting for 10% of the total heparin.44]... 

A sample of 2 ml of the stressed suspension is applied to the filtrometer and the initial flow rate is determined. The filtration curve is plotted automatically. 

When CMP was first emerging as an important process, microporous membranes were tested in a tangential flow filtration (TFF) mode. In typical CMP slurries, TFF was found to be unacceptable due to the high solids content. Also, there was insufficient control of the retentate build-up on the membrane face, called concentration polarization. TFF works best with applications that have lower solids and a greater spread between retained and passed species. The excessive polarization we observed with high solids silica slurries prevented useful fractionation. TFF may be useful for the newer slurries with low solids content. Three critical questions to any filter design in slurry applications are (i) how sharp can the filtration curve be to enable clean fractionation, (ii) how is retained material handled to control filter life, and (iii) how does media selection affect the above two points. 

The above conditions aUow 90% recovery of the input ceUs, and differences in filterability of cells among different lines appear both in filtration time and filtration kinetics. AU the filtration curves exhibit steep slopes in the beginning and then decrease, so that 50%... 

Data from precoat tests, however, generally produce filtrate curves with much steeper slopes. The precoat bed has a greater resistance than most filter fabrics, and the particles which are separated on a continuous precoat usually form a cake which has a relatively low resistance when compared to that of the precoat bed. Once the thickness of the deposited solids becomes significant, their resistance increases. Thus, at very short form times, the slope of the filtrate curve may be close to 1.0, but as form time increases, the slope of the curve will decrease and will approach -tO.5 (Fig. 18-113). 

The functional form of the static filtration curve (Figure 33) may be readily derived if it is assumed that the flow of the filtrate through the filter cake is governed by Darcy s law (126). The flow rate of the filtrate dVfe/df is given by Darcy s equation... 

The anticipated filtration curve for microemboli-laden blood is described as follows The rate of obstruction of the filter pores by rigid particles would be... 

Control blood (freshly drawn and not exposed to the biomaterial discs) should exhibit a constant flow rate, while blood from the parallel-disc exposure should produce an exponential filtration curve (Equation 4) from which the effective concentration of microemboli can be determined from a semilog plot of flow rate vs. time. 

There are some solicls, however, which form a less permeable cake, even in very thin layers. With these solids, the resistance of the deposited cake will be very high when compared to that of the precoat bed, and the slope of the filtrate curve will be -1-0.5 for all values of form time. 

This optimisation calculation can be solved graphical by plotting the filtrate volume time data with the origin di laced on the time axis to the point required for cake discharge. A tangent from zero to the filtrate curve thoi identifies the optimum point, as shown below in Figure 11.31. 

Laboratory Exercise Filtration Curves Using a Filter Press... 

Figure 14.3 Commercial pressure filtration apparatus and data acquisition unit to assess the full filtration curve following the VDI Richtlinie 2762. The media holder allows the testing of a large variety of filter media.

The filtration curve can be assessed by using a filtration apparatus as, for example, described in the VDI Richtlinie 2762. The filtered volume is determined as a function of time, allowing the calculation of both the resistance of the filter cake and the filtration media using Equation 14.3. The apparatus allows the testing of a variety of filter media (Figure 14.3). 

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