Liquids monotonic

The ratio of the total concentration of alcohols to the total concentration of aldehydes in the liquid monotonically decreased with increasing oxygen concentration in this range, from 7 at low O2 concentrations to 3 at higher O2 concentrations (Fig. 3.33). 

A major contribution to the rational organization of contact angle data was made by Zisman and co-workers. They observed that cos 6 (advancing angle) is usually a monotonic function of 7l for a homologous series of liquids. The proposed function was... 

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

Pindak R, Monoton D E, Davey S C and Goodby J W X-ray observation of a staoked hexatio liquid-orystal B phase Phys.Rev.Leff 46 1135-8... 

In the range of operating temperatures and compositions, the equilibrium relations are monotonic functions of temperature of the MSA. This is typically true. For instance, normally in gas absorption Henry s coefficient monotonically decreases as the temperature of the MSA is lowered while for stripping the gas-liquid distribution coefficient monotonically increases as the temperature of the stripping agent is increased. 

Experimental data on nitrogen obtained from spin-lattice relaxation time (Ti) in [71] also show that tj is monotonically reduced with condensation. Furthermore, when a gas turns into a liquid or when a liquid changes to the solid state, no breaks occur (Fig. 1.17). The change in density within the temperature interval under analysis is also shown in Fig. 1.17 for comparison. It cannot be ruled out that condensation of the medium results in increase in rotational relaxation rate primarily due to decrease in free volume. In the rigid sphere model used in [72] for nitrogen, this phenomenon is taken into account by introducing the factor g(ri) into the angular momentum relaxation rate... 

The calculations show that the liquid pressure monotonically decreases along the heating region. Within the evaporation region a noticeable difference between the vapor and liquid pressures takes place. The latter is connected with the effect of the Laplace force due to the curvature of the interface surface. In the superheated region the vapor pressure decreases downstream. 

The temperature distribution has a characteristic maximum within the liquid domain, which is located in the vicinity of the evaporation front. Such a maximum results from two opposite factors (1) heat transfer from the hot wall to the liquid, and (2) heat removal due to the liquid evaporation at the evaporation front. The pressure drops monotonically in both domains and there is a pressure jump at the evaporation front due to the surface tension and phase change effect on the liquid-vapor interface. 

The temperature distribution along the micro-channel axis is not monotonic. It has a maximum that is located within the liquid domain. An extraordinary form of the temperature profile is a result of the influence of two opposite factors, namely, absorbs heat from the wall and heat transfer from liquid to the front in order to establish the evaporation process. An increase of heat flux on the wall leads to displacement of the point corresponding to maximum temperature towards the inlet cross-section. 

The existence of two stable states (at given values of the operating parameters) is due to the dominant role of the gravity or friction forces at the various meniscus positions. A decrease in the gravity leads to the displacement of the meniscus toward the outlet and to a decrease in the heat losses and an increase in the liquid and vapor velocities. A decrease in the micro-channel diameter leads to a monotonic increase in the liquid and vapor velocities, whereas the dependence of the meniscus position versus d has an extremum. 

Recalling the previous assertion that efficient fractionation requires liquid-liquid phase separation, we conclude that nitrobenzene and amyl acetate should be satisfactory solvents from which to fractionate polyethylene by successively lowering the temperature and that the better solvent xylene should be avoided for this purpose. The character of the phase diagram may, in fact, be used as a criterion of the efficacy of a given solvent for fractionation (see Chap. VIII, p. 344). If the curve representing the precipitation temperature plotted against concentration rises monotonically, crystalline separation is clearly indicated if it passes through a maximum at a low concentration, liquid-liquid separation is virtually assured, and the solvent may be assumed to be a satisfactory one to use for fractionation. 

The improved method guarantees that the EoS will calculate the correct VLE not only at the experimental data but also at any other point that belongs to the same isotherm. The question that arises is what happens at temperatures different than the experimental. As seen in Figure 14.10 the minima of the stability function increase monotonically with respect to temperature. Hence, it is safe to assume that at any temperature between the lowest and the highest one, the EoS predicts the correct behavior of the system. However, below the minimum experimental temperature, it is likely that the EoS will predict erroneous liquid phase separation. 

The above observation provides useful information to the experimenter when investigating systems that exhibit vapor-liquid-liquid equilibrium. In particular, it is desirable to obtain VLE measurements at a temperature near the one where the third phase appears. Then by performing CLS estimation, it is guaranteed that the EoS predicts complete miscibility everywhere in the actual two phase region. It should be noted, however, that in general the minima of the stability function at each temperature might not change monotonically. This is the case with the C02-n-Hexane system where it is risky to interpolate for intermediate temperatures. Hence, VLE data should also be collected at intermediate temperatures too. 

Since members of a homologous series have incremental boiling point differences and if the amount of any homolog in the moving gas phase is related to vapor pressure at the temperature of the experiment, plots of log k vs. carbon number should also be a straight line. (The enthalpy of vaporization increases monotonically with carbon number.) This in fact is observed in gas-liquid equilibrium separation systems. It is the basis of retention index systems pioneered by Kovats for qualitative identification. 

The introduction of this parameter for each aqueous binary pair means that the interaction between the water molecule and the gas molecule in the aqueous liquid phase is much different from that in the nonaqueous phases. For all the aqueous binaries which have been examined in this study, the temperature -dependent interaction parameters take on negative values at ambient temperature and monotonically increase as temperature increases. This indicates that the attraction energy between the water molecular and the other molecules decreases as the temperature increases. 

Nitrogen - Water System. The interaction parameters for the nitrogen - water system have been evaluated using the data of Wiebe and Gaddy (10), Paratella and Sagramora (Vj ), Rigby and Prausnitz (12)and O Sullivan and Smith (13). As with the two previous systems, only one constant interaction parameter was necessary to correlate the vapor phase composition while the interaction parameter for the aqueous liquid phase increased monotonically with temperature. A comparison of the calculated and experimental vapor phase and aqueous liquid phase compositions is given in Table I. 

Recent theoretical studies on the molecular structure of organic/C02 EFL mixtures show that the fraction of the total volume occupied by the van der Waals volumes of the mixture constituents decreases monotonically with addition of CO2 to conditions that correspond to 60% of those of the original liquids. Therefore, as mentioned earlier, significant free volume is present in these mixtures [17]. Large free volumes result in significantly decreased viscosities as compared to those of common liquids. For example, experimental (Figure 9.1) [8] and theoretical studies [17] on methanol/C02 mixtures show an approximate monotonic drop in viscosity with addition of CO2. For example, when 60 mol% CO2 is added to methanol, the viscosity drops by 67%. The low viscosities are expected to be favorable for fast kinetics. 

Therefore, we expect the scattered intensity /(q, t), proportional to ( /q(t)) to be exponential in time, 7(q, t) exp(2fiqr), with the rate Oq = q AT — q with both lower and upper cutoffs in q. If these arguments are valid, flq/ should rise sharply with q, reach a maximum, and then decrease at higher q values. These predictions are fully consistent with the experimental [10] and simulation [57] observations on /(q, t) and Oq. If the mechanism is simply a spinodal decomposition into two liquid phases, then D. /q should show a monotonic linear decrease from a finite positive value at q 0 with a slope independent of quench depth, which is not experimentally observed during... 

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