Volume turnover

Constant-volume batch diafiltration is the most efficient process mode. Sequential batch diafiltration is a series of dilution-concentration steps. Continuous diafiltration practiced in one or more stages of a cascade system has the same volume turnover relationship for overall recoveries as sequential batch diafiltration. The residence time however is dramatically reduced. If recovery of permeable solids is of primary importance, the permeate from the last stage may be used as diafiltration fluid for the previous stage. This countercurrent diafiltration arrangement results in higher permeate solids at the expense of increased membrane area. 

The casein retentate, when used as cheese milk, can almost be fully depleted of all whey proteins through a sufficient number of diafiltration volume turnovers. In contrast to conventional cheese technology, it is then possible to UHT treat the cheese milk in order to destruct spore formers. The whey proteins can be used as a WPG or WPI product or treated further in order to fractionate the whey proteins in their main components. Alternatively the whey proteins can particulated to form WPP see Section 19.5.1. Both approaches are options to build a platform for novel product matrices with specific properties such as gelling, foaming or emulsification. 

Since continuous diafiltration involves the processing of a fixed volume (V0), it is convenient to speak of the number of volume turnovers, Vt/V0 required to... 

When the permeable species is partially rejected by the membrane (as in fractionation), a higher wash volume turnover will be required to achieve the same degree of clearance. Figure 3.96 may be used to predict solute clearance for a specified membrane retention (R). 

Levick JR, et al. Synovial fluid determinants of volume turnover and material concentration. In Kuettner K, editor. Articular cartilage and osteoarthritis. New Ymk Raven Press 1992. p. 529-41. 

For blending of low viscosity Hquids to practical homogeneity, turnover of three tank volumes is normally adequate. For viscous Hquids or for a higher degree of Hquid homogeneity, a greater number of turnovers is needed. 

P = volume of cryst hzer/circulation rate (turnover). mV(mVs) = s... 

The time required to pass through the high shear zone will be proportional to the volume of the vessel divided by the flow from the turbine. This will be porportional to 1/ND. With a turbine in turbulent flow, turnover is relatively rapid and all the fluid will pass through the impeller region in a relatively short period of time. The flow regime in an anchor or helically agitated vessel can be inferred from the flow studies by Smith and Peters (], 13j. These indicated... 

Average turnover time (defined as storage volume divided by annual inflow or outflow volume, assuming steady state) is a measure of... 

The enormous volume of the oceans results in an average turnover time of more than 2600 years, compared to less than 10 days for atmospheric water. Although the reservoir is much smaller than the oceans, the cryosphere has the longest turnover time due to the small input flux. Average turnover times for all seven reservoirs, calculated from the data in Fig. 6-3, are shown in Table 6-3. 

Many hydrologic reservoirs can be further subdivided into smaller reservoirs, each with a characteristic turnover time. For example, water resides in the Pacific Ocean longer than in the Atlantic, and the oceans surface waters cycle much more quickly than the deep ocean. Similarly, groundwater near the surface is much more active than deep reservoirs, which may cycle over thousands or millions of years, and water frozen in the soil as permafrost. Typical range in turnover times for hydrospheric reservoirs on a hillslope scale (10-10 m) are shown in Table 6-4 (estimates from Falkenmark and Chapman, 1989). Depths are estimated as typical volume averaged over the watershed area. 

Before deriving the rate equations, we first need to think about the dimensions of the rates. As heterogeneous catalysis involves reactants and products in the three-dimensional space of gases or liquids, but with intermediates on a two-dimensional surface we cannot simply use concentrations as in the case of uncatalyzed reactions. Our choice throughout this book will be to express the macroscopic rate of a catalytic reaction in moles per unit of time. In addition, we will use the microscopic concept of turnover frequency, defined as the number of molecules converted per active site and per unit of time. The macroscopic rate can be seen as a characteristic activity per weight or per volume unit of catalyst in all its complexity with regard to shape, composition, etc., whereas the turnover frequency is a measure of the intrinsic activity of a catalytic site. 

Having established that waste is an inevitable product of any real process, one consequence of increased efficiency, and the associated reduced cost, can be greater demand and turnover. The benefits of technological improvements will be offset (and possibly completely eliminated) by greater product volume. Other strategies of addressing the problem of waste thus need to be developed. We can now address the first question posed above. 

Newport In terms of physical limits, we tend to think of DNA, but on the other hand there is RNA degradation and protein turnover. This is how an egg is made. Even though it is only a tetraploid organism, RNA degradation is slowed down significantly, so less DNA is needed. The other physical limitation is the surface area volume relationship. How many receptors or growth factors can be inserted into a membrane ... 

Run Electrocatalyst E (V versus N.H.E.) Total volumec of CO produced (ml) Turnover frequency (h-1) overall turnover of Ni Average current efficiency6 (%) Volume of H2 produced/ml H2 CO in gas produced... 

Figure 3.53 shows the volume of CO produced, and the turnover number of the rhenium catalyst, as a function of the charge passed. Over 14 hours of electrolysis the Re catalyst underwent 300 catalytic cycles without loss of activity and showed no degradation, as seen by isolation and characterisation... 

Figure 3.53 Volume or CO produced and turnover number with respect to catalyst as a function of coulombs consumed in the eleclroreduclion of C02 to CO by Rc(bipyHCO),CI. From...

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