Logarithmic mean concentration difference

In a bioreactor, one is interested in the transfer per unit of volume of reactor, called Kia or the volumetric mass-transfer coefficient, a is the interfacial surface area per unit of volume of liquid. In a perfectly mixed tank, C has identical values at any point and C depends on the conditions in the gas phase at the outlet of the reactor. Several authors [60] consider that a better estimate of the driving force is given by the logarithmic mean concentration difference between the entry and the exit of gas. 

O. Shell side of microporous hollow fiber module for solvent extraction Na, = V[dha-)/L]N%N°s M Nsh- D Nlt = K = overall mass-transfer coefficient (3 = 5.8 for hydrophobic membrane. (3 = 6.1 for hydrophilic membrane. [E] Use with logarithmic mean concentration difference. dh = hydraulic diameter 4 x cross-sectional area of flow wetted perimeter (p = packing fraction of shell side. L = module length. Based on area of contact according to inside or outside diameter of tubes depending on location of interface between aqueous and organic phases. Can also be applied to gas-liquid systems with liquid on shell side. [118]... 

The mass transfer rate (or the evaporation rate) in this case can be determined by defining the logarithmic mean concentration difference in an analogous manner to the logarithmic mean temperature difference. 

Different equations can be derived for various flow geometries which describe the removal efficiency of a solute from a solution [19,20]. The average concentration of feed and dialysate can be adequately described by the logarithmic mean concentration and for a counter-current flow the average concentration difference is given by... 

A Cta concentration difference Logarithmic mean value of C kmol/m3 NL-3... 

Now let us discuss the sensitivity of the taste sensor. The sensor had detection errors ( in the unit of logarithmic concentration) 0.73% for saltiness, 0.65% for sourness and 3.4% for bitterness in the mixed aqueous solution [27]. Humans usually cannot distinguish two tastes with a concentration difference below 20% [4], Here, 20% means the error of 7.9% (=log 1.2). Therefore, ability of detection of the sensor is superior to that of... 

Since part of the gas mixture (e.g. air) is absorbed as it bubbles through the liquid column, the composition of the gas mixture changes. Furthermore, the pressure in the liquid is higher at the gas inlet than in the head space above it. This difference in partial pressure is taken into account by the mean logarithmic concentration difference, Acm ... 

Introducing the logarithmic mean of the driving concentration difference calculated from eq. (E 1.11), the liquid phase balance of Cl2 is as follows... 

ACr)In logarithmic mean driving concentration difference for ketone transfer (mol m 3)... 

ACjj) In logarithmic mean driving concentration difference for hydrogen transfer (mol m"3) gas superficial velocity (m s l) liquid superficial velocity (m s l)... 

Order respect to N-Br-amino acid concentration. With the aim of establishing the reaction order with respect to the N-bromoalanine concentration, we have obtained the values of the initial rates for different N-bromoamino acid concentrations with a fixed OH" concentration of 0.23M. The logarithmic plot shows to be a straight line (Fig. 3) with a slope of 1.07 0.03. This means that the decomposition reaction of N-Br-alanine is first order with respect to the N-bromoalanine concentration. From the plot of initial rate against initial N-bromoalanine concentration (Table 1) we can obtain for the pseudofirst order rate constant for N-bromoalanine decomposition a value of 0.0160 0.(XX)4 s-f... 

According to Stevens law the logarithm of the perceived intensity is linearly related to the logarithm of the odour intensity. In the figure this relationship is given for two substances, one with a slope of 1.00 and one with a slope of. 67. As can be seen from the figure, this means that an odour concentration of 100 odour units/m3 is related to very different perceived odour intensities for the two substances. This means that odour concentrations computed in odour units/m3 should not be used as an indication of perceived odour intensity, but can only be used in relative measurements where the effects of measures taken to reduce odour pollution are compared, or in studies where dispersion models are used to find the distance to the source at which threshold is reached. 

The three models are compared in the figure below (note the double logarithmic scale). As predicted by Eq. 3 of Box 21.5, if the mean input concentration, CNTAin, is much smaller than C - 4.0xl0 1°M, then C(fXAoo CNTAin that is, NTA behaves like a conservative compound. In contrast, for CNTAin C, C (A 3 increases as the square root of the input. Note that for the three models an interpolation from the measured input rate (13 mol d 1) to other input rates predict very different CNTAoo values. 

Note that the pH scale is logarithmic, not arithmetic. To say that two solutions differ in pH by 1 pH unit means that one solution has ten times the H+ concentration of the other, but it does not tell us the absolute magnitude of the difference. Figure 2-15 gives the pH of some common aqueous fluids. A cola drink (pH 3.0) or red wine (pH 3.7) has an H+ concentration approximately 10,000 times that of blood (pH 7.4). 

Figure 2b is a compilation of all the data obtained on cruises showing mean values and ranges of DMS concentration plotted on a logarithmic scale. The mean values for winter and summer are 0.1 and 9.4 nmol DMS (S) l1 respectively, a seasonal difference of two orders of magnitude. As yet, the data set for DMSP is not as comprehensive as for DMS, out as the former is the precursor of the latter, a similar seasonal pattern might be expected. For... 

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