Mixing incomplete

As a means of determining relative reactivities, the competition method using nitronium tetrafluoroborate in sulpholan has been criticised as giving results which arise from incomplete mixing of the reagents before reaction is complete. The difficulty of using the competition method when the rate of reaction is similar to, or greater than,... 

Filtration of viscose is not a straightforward chemical engineering process. The solution of cellulose xanthate contains some easy-to-deal-with undissolved pulp fibers, but also some gel-like material which is retarded rather than removed by the filters. The viscose is unstable and tends to form more gel as it ages. Its flow characteristics make the material close to the walls of any vessel or pipe move more slowly, get older, and gel more than the mainstream viscose. So while filtration can hold back gels arising from incomplete mixing, new gels can form in the pipework after the filters. 

DMPPO and polystyrene form compatible blends. The two components are miscible in all proportions (59). Reported dynamic—mechanical results that indicate the presence of two phases in some blends apparendy are caused by incomplete mixing (60). Transition behavior of thoroughly mixed blends indicates that the polymers are truly compatible on a segmental level (61). CompatibiUty may be attributed to a %— % interaction between the aromatic rings of the two polymers sufficient to produce a negative heat of mixing. However, the forces are very small, ie, = ca40 J/mol (9.6 cal/g), and any... 

The Colburn equation is based on complete mixing on the plate. For incomplete mixing, e.g., liquid approaching plug flow on the plate, Rahman and Lockett [I. Chem. E. Symp. Sei No. 61, 111 (1981)] and Lockett et al. [Chem. Eng. ScL, 38, 661 (1983)] have provided corrections for Eq. 14-44. Figure 14-26 and Eq. 14-94 may be used to evaluate the effects of entrainment on efficiency. 

Ejfects of Gas and Liquid Mixing As noted previously, it is necessary in most instances to convert point efficiency E g to Murphree plate efficiency E, ,. This is true because of incomplete mixing only in small laboratoiy or pilot-plant columns, under special conditions, is the assumption E g = E, , likely to be valid. For a crossflow plate with no hquid mixing there is plug flow of hquid. For this condition of liquid flow, Lewis [Ind. Eng. Chem., 28, 399 (1936)] analyzed effects of gas mixing on efficiency. He considered three cases ... 

The theoiy enables a reasonable estimate of sample quantity needed to attain specified accuracy of a composition variable. The result is an ideal quantity—not realized in practice. Actual quantities for practical estimation are larger by an appropriate multiple to account for the reality that material is incompletely mixed when stored in stockpiles or carried on conveyors. Sample quantity to accommodate incompletely mixed sohds can be specified through evaluating variance by autocorrelation of data derived with a series of stockpile samples, or from multiple sample extractions taken from a moving stream (Gy, Pitard). 

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. 

ThemodelweconstructedinFigureScanbethoughtofasametaphorforoneunitwith incomplete mixing. Rather imagine that in this poorly mixed unit some of the fluid goes... 

The contaminant removal and temperature effectiveness in the mixing strategy are equal to 1. In practical installations incomplete mixing in the room and unfavorable temperature gradient and location of the exhaust openings in relation to air supply may, however, cause short-circuiting of the supply air into the exhaust openings and the efficiency may remain below 1. 

TABLE 12.9 Required Mixing Lengths (L/D) to Keep the Error due to Incomplete Mixing Smaller Than 5% or 10% ... 

Danckwerts, P.V., 1958. The effect of incomplete mixing on homogeneous reactions. Chemical Engineering Science, 8, 93-99. 

The variation of time for which fluid elements remain with the tank is expressed as a residence time distribution and this can be calculated from a simple material balance if mixing is complete. For incomplete mixing, the calculation presents difficulties. 

Fig. 16.3 Propagated outbreaks of infection showing the incidence of new cases ( ), diseased individuals ( ), and recovered immune (A). The dotted line indicates the incidence pattern for an incompletely mixed population group.

One possible cause of Th isotope heterogeneity between minerals could be that they crystallized in a heterogeneous magma formed by incomplete mixing of two (or more)... 

Typical flow rates in FTA vary between 0.5 and 5.0 ml/min per channel, although higher values have also been used. Most of the published work on CL with HA is based on equal flow rates for every stream entering the manifold. Nevertheless, if different rates must be used, deterioration of repeatability and reproducibility might appear due to incomplete mixing and anomalous hydrodynamic characteristics. These problems can be avoided if the general rule that the ratio of the fastest to the slowest flow rate should not exceed the value of 3 or 4 is followed. 

The explosion efficiency is one of the major problems in the equivalency method. The explosion efficiency is used to adjust the estimate for a number of factors, including incomplete mixing with air of the combustible material and incomplete conversion of the thermal energy to mechanical energy. The explosion efficiency is empirical, with most flammable cloud estimates varying between 1 % and 10%, as reported by a number of sources. Others have reported 5%, 10%, and 15% for flammable clouds of propane, diethyl ether, and acetylene, respectively. Explosion efficiencies can also be defined for solid materials, such as ammonium nitrate. 

Fig.9. Schematic representation of the difference between complete mixing and incomplete mixing.

The effect of incomplete mixing on homogeneous reactions. Chemical... 

In industrial reactors, the full equilibration of the chain length distribution is prevented by incomplete mixing, as well as by the residence time distribution, thus resulting in considerable deviations from the equilibrium polydispersity index. These deviations are generally higher for continuous plants than for batch plants and increase with increasing plant capacity as demonstrated in Figure 2.2. 

The relationship of agitation problems (failure, incomplete mixing, shear energy input) with thermal runaway reactions and ways of avoiding these, are discussed. 

It was postulated that the aqueous pores are available to all molecular species, both ionic and non-ionic, while the lipoidal pathway is accessible only to un-ionised species. In addition, Ho and co-workers introduced the concept of the aqueous boundary layer (ABL) [9, 10], The ABL is considered a stagnant water layer adjacent to the apical membrane surface that is created by incomplete mixing of luminal contents near the intestinal cell surface. The influence of drug structure on permeability in these domains will be different for example ABL permeability (Paq) is inversely related to solute size, whereas membrane permeability (Pm) is dependent on both size and charge. Using this model, the apparent permeability coefficient (Papp) through the biomembrane may therefore be expressed as a function of the resistance of the ABL and... 

Hinton RW, Davis AM, Scatena-Wachel DE (1987) Large negative Ti anomalies in refractory inclusions from the Murchison carbonaceous chondrite evidence for incomplete mixing of neutron-rich supernova ejecta into the solar system. Astrophys J 313 420-428... 

Lugmair GW, Marti K, Scheinin NB (1978) Incomplete mixing of products from r-, p-, and s-process nucleosynthesis Sm-Nd systematics in Allende inclusion EK141. Lunar Planet Sci IX 672-673 Lugmair GW, Shimamura T, Lewis RS, Anders E (1983) Samarium-146 in the early solar system evidence from neodymium in the Allende Meteorite. Science 222 1015-1018 Lugmair GW, Shukolyukov A (1998) Early solar system timescales according to Mn- Cr systematics. Geochim Cosmochim Acta 62 2863-2886... 

The data show a wide range the values in Columns B and C are relatively high, while those in Column E are relatively low. The authors suggested that these variations may reflect irregularities in the spray application of the pesticide. A second, more local, variability was attributed to incomplete mixing of the soil after the spray application. The result is a large value for the overall standard deviation, 166 mg per square meter. 

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