Batch flux

Since the iq ward velocity of any ecific concentration is constant then  

The value of U2 is found as the slope of the settling curve at a point vshere the layer having the concentration C2 comes to the pu suifrice ie. U2 is the slope of a tangoit to the settling curve at H2, t2- The mtercept of the tang t on the /f axis is thus H2 + C2/2 which is given the symbolLTi and hence  

The height Hi represents the hei t that the pu would occupy if all solids were present at the concentration C2. 

All the data to produce a batch flux curve, i.e. G-C, which is inqjortant design information for continuous thickener design procedures, can be obtained in the following 

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Flux Decline Plugging, Fouling, Polarization Membranes operated in NFF mode tend to show a steady flux decline while those operated in TFF mode tend to show a more stable flux after a short initial decline. Irreversible flux decline can occur by membrane compression or retentate channel spacers blinding off the membrane. Flux decline by fouling mechanisms (molecular adsorption, precipitation on the membrane surface, entrapment within the membrane structure) are amenable to chemical cleaning between batches. Flux decline amenable to mechanical disturbance (such as TFF operation) includes the formation of a secondary structure on the membrane surface such as a static cake or a fluid region of high component concentration called a polarization layer. 

Because the batch flux data are obtained in a closed system with no outflow, the net solids flux is zero in the batch system and Eq. (14-40) reduces to FL = —(pV%/ 1 — cp). Note that FL and Vs are of opposite sign, because the displaced liquid moves upward as the solids settle. The relative velocity between the solids and liquid is Vr = Vs — VL which, from Eq. (14-20), is Vr = Fs/(1 — relative velocity that controls the dynamics in the thickener. If the underflow draw-off rate from the thickener is gu, the additional solids flux in the thickener due to superimposition of this underflow is qu = Qu/A = Vu. Thus, the total solids flux at any point in the thickener (qs) is equal to the settling flux relative to the suspension (i.e., the batch flux qsb) at that point, plus the bulk flux due... 

Figure 14-7 Typical batch flux curve with operating lines (...) underloaded ...

You must determine the maximum feed rate that a thickener can handle to concentrate a waste suspension from 5% solids by volume to 40% solids by volume. The thickener has a diameter of 40 ft. A batch flux test in the laboratory for the settled height versus time was analyzed to give the data below for the solids flux versus solids volume fraction. Determine ... 

An interesting situation arises if it is desired to avoid the upward propagation of kinematic waves by moving the sediment downward at a rate such that the upward-propagating concentration differences are stationary relative to the container walls. The downward motion of the sediment is obtained by its continuous withdrawal uniformly over the settler cross section. The process is termed continuous thickening. The continuous sedimentation process is thus composed of the batch gravitational flux and solid convective flux pu. This is illustrated in Fig. 5.4.7, where the total solids flux curve is the sum of the batch flux and the convective flux the shape of the curve of Fig. 5.4.5 illustrates the batch flux (Petty 1975). 

From the single-batch settling test data given in the previous exan le construct a batch flux curve. Determine the required area for continuous thickening from 3 to 15% by (a) the Yoshioka Construction and (b) by the Coe-Clevenger procedure. 

Figure 33 Determination of interface and layer velocities from a batch flux plot...

For the batch flux plot shown in Figure 3W3.1, the sediment has a solids concentration of... 

Using this information we can plot the concentration profile in the test vessel 50 min after the start of the test. A sketch of the profile is shown in Figure 3W3.3. The shape of the concentration profile within the variable concentration zone may be determined by the following method. Recalling that the slope of the batch flux plot (Figure 3W3.1) at a value of suspension concentration C is the velocity of a layer of suspension of that concentration, we find the slope at two or more values of concentration and then determine the positions of these layers after 50 min ... 

Lines of slope F/A, L/A and —V/A drawn on the flux plot represent the fluxes in the feed, underflow and overflow, respectively (Figure 3W4.2). The total flux plot for the section below the feed point is found by adding the batch flux plot to the underflow flux line. The total flux plot for the section above the feed point is found by adding the batch... 

Use the batch flux plot in Figure 3E9.1 to answer the following questions. (Note that the sediment concentration is 0.44 volume fraction.)... 

Table 3E12.1 Batch flux test data ...

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