Mixing deviations

CLASSES MIXED DEVIATION FROM raoult s law CHANGE IN H BONDING ON MIXING EXAMPLES ... 

The two-parameter van Laar equation cannot represent maxima or minima in the activity coefficients, nor can it represent the mixed deviations from ideality exemplified by the benzene-hexaflnorobenzene system of Fig. 1.4-1. However, it is suparior to the Margules equation for some extremely nonideal systems such as alcohol-hydrocarbon mixtures, for example, the ethanol-n-haptane system of Fig. 1.4-1. For such mixtures the two-parameter Margules equation often incorrectly predicts liquid-liquid phase splitting. Higher order Margules equations can sometimes be u red for these systems, but at the expense of many additional parameters. 

Flow Pattern Ideality. A straightforward interpretation of the observed kinetics can only be made if the flow pattern in the reactor used corresponds to an ideal flow pattern. In particular for plug flow reactors, deviations from the ideal reactor behavior can be encountered. For perfectly mixed reactors such as a batch reactor and a continuous stirred tank reactor, the rotation speed of the stirrer is the key parameter that needs to be set sufficiently high to ensure complete mixing. Deviations from the ideal plug flow pattern can, for example, be caused by a less-dense packing of the catalyst pellets near the reactor wall, by a too high dilution of the catalyst bed with inert pellets or by the importance of effective axial diffusion compared to convection (15). 

A deaning chamber is substantiaiiy iess weii mixed than perfect - at least because the racked parts block fluid flow and cause the flow patterns to be non-uniform. And the chamber shape, while often radially symmetrical, is not longitudinally symmetrical. So, the less than perfectly mixed vessel will retain a fluid component longer than would be expected from the assumption of perfect mixing. Deviation from the well-mixed residence time will be different for every vessel shape and loading of parts, and will be specifically unpredictable (Chapter 2.13.1). 

It should be emphasized that this expression of the entropy of mixing is applicable only to athermic systems or to mixtures exhibiting only weak interactions between molecules—that is, solutions with low enthalpy of mixing. Deviations from ideality could arise in particular in the following situations, which will be... 

Few populations, however, meet the conditions for a true binomial distribution. Real populations normally contain more than two types of particles, with the analyte present at several levels of concentration. Nevertheless, many well-mixed populations, in which the population s composition is homogeneous on the scale at which we sample, approximate binomial sampling statistics. Under these conditions the following relationship between the mass of a randomly collected grab sample, m, and the percent relative standard deviation for sampling, R, is often valid. ... 

In this problem you will collect and analyze data in a simulation of the sampling process. Obtain a pack of M M s or other similar candy. Obtain a sample of five candies, and count the number that are red. Report the result of your analysis as % red. Return the candies to the bag, mix thoroughly, and repeat the analysis for a total of 20 determinations. Calculate the mean and standard deviation for your data. Remove all candies, and determine the true % red for the population. Sampling in this exercise should follow binomial statistics. Calculate the expected mean value and expected standard deviation, and compare to your experimental results. 

Solutions can deviate from ideality because they fail to meet either one or both of these criteria. In reference to polymers in solutions of low molecular weight solvents, it is apparent that nonideality is present because of a failure to meet criterion (2), whether the mixing is athermal or not. 

Figure 6.35 illustrates how anharmonicity mixes the two vibrations Vj and V3 of CO2. If the molecule starts from the point X and proceeds to B it will tend to follow the line of maximum slope shown. In doing so it deviates considerably from the dashed line representing and so involves an admixture of Qi and Qj. 

The degree of mixing is described as variation coefficient standard deviation, X is fraction of additive, andX is average fraction of... 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

The foregoing discussion has dealt with nonideahties in the Hquid phase under conditions where the vapor phase mixes ideally and where pressure-temperature effects do not result in deviations from the ideal gas law. Such conditions are by far the most common in commercial distillation practice. However, it is appropriate here to set forth the completely rigorous thermodynamic expression for the Rvalue ... 

Reac tors that are nominally CSTRs or PFRs may in practice deviate substantially from ideal mixing or nonmixing. This topic is developed at length in Sec. 23, so only a few summary statements are made here. More information about this topic also may be found in Nauman and Buffham (Mixing in Continuous Flow Systems, Wiley, 1983). 

Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with re.sidence time distributions (RTD) obtained with the aid of tracer tests. In other cases a mechanism may be postulated and its parameters checked against test data. The commonest models are combinations of CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely mixed in the vicinity of the impeller and in plug flow near the outlet. 

Equation (2-38) is valid for every region of the surface. In this case only weight loss corrosion is possible and not localized corrosion. Figure 2-5 shows total and partial current densities of a mixed electrode. In free corrosion 7 = 0. The free corrosion potential lies between the equilibrium potentials of the partial reactions and U Q, and corresponds in this case to the rest potential. Deviations from the rest potential are called polarization voltage or polarization. At the rest potential = ly l, which is the corrosion rate in free corrosion. With anodic polarization resulting from positive total current densities, the potential becomes more positive and the corrosion rate greater. This effect is known as anodic enhancement of corrosion. For a quantitative view, it is unfortunately often overlooked that neither the corrosion rate nor its increase corresponds to anodic total current density unless the cathodic partial current is negligibly small. Quantitative forecasts are possible only if the Jq U) curve is known. 

In any mass transfer operation, the compositions of the liquid and vapor phases are assumed to follow the relationship illustrated by the column operating line. This line represents the overall calculated profile down the column however, the composition on each individual square foot of a particular column cross-section may vary from that represented by the operating line. These variations are the result of deviations in the hydraulic flow rates of the vapor and liquid phases, as well as incomplete mixing of the phases across the entire column. 

There is approximately a 22% deviation between the experimental and the distribution mean residenee time. However, the main purpose was to use the information from the RTD eurve to improve the reaetor operation. The results of the RTD provided vital information eoneern-ing the effeets of operating eonditions and struetural designs on solid-mixing patterns in fluidized systems. The perfeet mixing funetion was generated by e , where 6 = t/f. Figure 8-19 shows plots of these funetions against dimensionless residenee time 6. 

Materials information includes toxicity, permissible exposure limits, physical properties, reactivity, corrosivity, thermal and chemical and hazardous effects of inadvertent mixing of different materials.Process information consists of 1) process flow diagrams, 2) process chemistry descriptions, 3) maximum amounts of chemicals, 4) safe ranges for temperatures, pressures, flows oi 5) evaluation of the con.sequences of deviations. 

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