Flux plot thickeners

Azam, F. 1998. Microbial control of oceanic carbon flux The plot thickens. Science 280 694-696. 

Azam F (1998) Microbial control of oceanic carbon flux the plot thickens. Science 280 694-696 Azam F, Long RA (2001) Oceanography - sea snow microcosms. Nature 414 495-498 Barlow RG (1982) Phytoplankton ecology in the Southern Benguela Current. 3. Dynamics of a bloom. J Exp Mar Biol Ecol 63 239-248... 

Azam, F. (1998). Microbial control of oceanic carbon flux The plot thickens. Science 280, 694. Azam, F., Fenchel, T., Field, J. G., Gray, J. S., Meyer-Reil, L. A., and Thingstad, F. (1983). The ecological role of water-column microbes in the sea. Mar. Ecol. Prog. Ser. 10, 257—263. 

These material balances link the total continuous flux plots for the upflow and downflow sections in the thickener. 

Figure 3.15 shows flux plots for a critically loaded thickener. The line of slope F/A represents the relationship between feed concentration and feed flux for a volumetric feed rate, F. The material balance equations [Equations (3.43) and (3.44)] determine that this line intersects the curve for the total flux in the downflow section when the total flux in the upflow section is zero. Under critical loading conditions the feed concentration is just equal to the critical value giving rise to a feed flux equal to the total continuous flux that the downflow section can deliver at that concentration. Thus the combined effect of bulk flow and settling in the downflow section provides a flux equal to that of the feed. Under these conditions, since all particles fed to the thickener can be dealt with by the downflow section, the upflow flux is zero. The material balance then dictates that the concentration in the downflow section, Cb, is equal to Cp and the underflow concentration, Cp is FCp/L. The material balance may be performed graphically and is shown in Figure 3.15. From the feed flux line, the feed flux at a feed concentration, Cp is Ups = FCf/A. At this flux the concentration in the downflow section is Cb = Cp. The downflow flux is exactly equal to the feed flux and so the flux in the upflow section is zero. In the underflow, where there is no sedimentation, the underflow flux, LCl/A, is equal to the downflow flux. At this flux the underflow concentration, Cl is determined from the underflow line.

Figure 3.16 Total flux plot for an underloaded thickener...

Figure 3.19 Alternative total flux plot shape overloaded thickener...

In an overloaded thickener, the concentration in the bottom section of the thickener is equal to (when the total flux plot does not go through a minimum) ... 

The batch and continuous flux plots suppUed in Kgure 3E11.1 are for a thickener of area 200 handling a feed rate of 0.04 m /s and an underflow rate of 0.025 m /s. 

The solid symbols in Fig. 4 plot resistance factor vs. flux for the second (46-md) core section (solid triangles) and for the third (17.5-md) core section (solid squares) for the degraded HPAM. As mentioned earlier, the open symbols in Fig. 4 plot resistance factors for undegraded (fresh) polymer solutions from 55-, 269-, and 5120-md cores. The onset of shear-thickening behavior occurred at approximately the same x-axis value for aU five cases. At low flux values, resistance factors for four of the five curves leveled out (i.e., approached Newtonian behavior) at a valne consistent with the viscosity of the polymer solntion (10 cp). For the exception, fresh polymer injected into a 55-md core (open circles), resistance factors increased from 10 to 26 as flux decreased from 1.1 to 0.035 ft/D (i.e., the correlating parameter on the x axis decreased from... 

Fig. 8 plots resistance factor vs. flux during injection of many polymer solutions into a 5120-md porous polyethylene core. For polymer concentrations even as low as 25 ppm (one-eighth the value of C ), shear thickening was evident. In contrast, viscosity vs. shear rate showed Newtonian behavior, with a value very close to 1 cp. As described in the literature (Durst et al. 1982), the elongational flow field associated with porous media can accentuate viscoelastic behavior that is not apparent from a pure shear field. This observation provides our first reason to doubt that the transition from Newtonian behavior to shear-thinning behavior in a viscometer correlates directly with the onset of shear thickening in porous media. 

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