Critical mixing

Particular attention should be paid to nonstandard production technologies including nonstandard methods of sterilization, sterile filtration and aseptic processing, lyophilization, microencapsulation, and certain critical mixing and coating operations. With such processes pilot-scale manufacture may not be predictive of industrial scale manufacture, and data on three full-scale production batches may be required in the application. 

These fluctuations, which are referred to as order-parsmeter fluctuations in studies of critical phenomena (3). comprise the driving forces for transport in the system. For liquid mixtures near a critical mixing point, the order parameter is concentration, and for pure gases near the vapor-liquid critical point, the order parameter is density. For gas mixtures such as supercritical solutions near the critical line, the order parameter is again density, which is a function of composition and temperature compared to a pure gas where density is a function of only temperature at constant pressure. 

The dec8y rate of the order-parameter fluctuations is proportional to the thermal diffusivity in case of pure gases near the vapor-liquid critical point and is proportional to the binary diffusion coefficient in case of liquid mixtures near the critical mixing point (6). Recently, we reported (7) single-exponential decay rate of the order-parameter fluctuations in dilute sugercritical solutions of liquid hydrocarbons in CO for T - T 10 C. This implied that the time scales associated with thermal diffusion and mass diffusion are similar in these systems. 

Aliphatic amines Convenience Room temperature cure, fast elevated-temperature cure Low viscosity Low formulation cost Moderate chemical resistance Critical mix ratios Strong skin irritant High vapor pressure Short working life, exothermic Poor bond strength above 80°C Rigid, poor peel and impact properties Adhesives and sealants Casting and encapsulation Coatings... 

Anhydride Good heat and chemical resistance Long elevated-temperature cure Critical mix ratio Rigid Composites Electrical encapsulation Adhesives... 

While studying polymer distribution between the emulsion phases it was found that in the systems mentioned above obtained both by copolymerization of styrene with polybutadiene rubber and mixing styrene solutions of polymers when the composition is far enough from the critical mixing point, thermodynamic equilibrium is reached.At this thermodynamic equilibrium the ratio of polymer concentration (Cp) in rubber (index ) as well as in polystyrene (index ) phases is practically constant (table II),... 

The agitator pow er draw is related to the critical mixing parameters by ... 

Effect of Pressure on Critical Mixing Temperature in the System Cyclohexane + Aniline... 

The phenomenon of critical mixing occurs not only in liquid solutions but also in solid solutions mixed crystals). The conditions of stability for a solid solution are identical with those discussed above for liquid solutions. In particular, a system is always stable with respect to phase separation if it is ideal (c/. chap. XV, 14), and it can only become unstable if the activity coefficients depart sufficiently from unity. ... 

The conclusions of the above discussion of critical mixing may be summarized in the following way ... 

The critical mixing factors in a stirred tank at e impeller speed and type, as well as their influence on local turbulence and overall circulation. Since all aspects of these factors cannot be maintained constant on scale-up either locally or globally, the extent to which changes in the crystallizing environment will affect nucleation is extremely difficult to predict. To the mixing issue must be added the uncertainties caused by soluble and insoluble impurities that may be present in sufficiently different concentrations from batch to batch to cause variation in induction time, nucleation rate, and particle size. 

Phenalkamine properties are positioned roughly between those of the polyamines and polyamides. They combine the best properties of each of these familiar types of curing agents. The phenal kamines have an intermediate viscosity, the chemical and hydrolytic resistance of the polyamines, and the low toxicity of the polyamides. They have the fast cure and ability to cure at reduced temperatures of the polyamines while exhibiting better compatibility than either the polyamines or the polyamides. The phenalkamines also provide flexibility comparable to the polyamides with similar easy-to-use, relatively non-critical mix ratios. 

Field or laboratory observations of miscibility gaps, spinodal gaps, critical mixing points or distribution coefficients can be used to estimate solid-solution excess-free-energies, when experimental measurements of thermodynamic equilibrium or stoichiometric saturation states are not available. As an example, a database of excess-free-energy parameters is presented for the calcite, aragonite, barite, anhydrite, melanterite and epsomite mineral groups, based on their reported compositions in natural environments. 

Critical mixing points can also be used to calculate the non-ideality of a solid-solution series. The critical temperature T of a SSAS system refers to the lowest possible temperature at which a complete solid-solution series may form (in. In a regular solid-solution series, a miscibility gap will occur only if an is greater than 2 and the following relation may be derived between ao, T and T the current temperature of the solid-solution system (2) ... 

Most heat capacity measurements have been made on binary mixtures rather than on the one-component liquids. This is doubtless due to the relative ease of finding convenient critical mixing temperatures. Some examples of binary mixture work are given in References 2, 3, 28, 29, 54,57, 110,115, 116, 122, and 131, and for measurements on one component see References 80 and 113. 

Both the dielectric constant and dielectric loss show peaks at the critical mixing temperatmre of a binary mixture, This evidence indicates anomalies in orientational correlations and relaxation in the critical region, but how the orientational correlations are related to composition correlations (which more generally characterize the critical region) is imknown. 

Mixing induces turbulence and a decrease in the boundary layer thickness at the ice-liquid interface. The thinner the boundary layer, the shorter the time interval necessary for solute diffusion from the interface into the bulk liquid. The extent of incorporation in the ice depends in part on the relative velocity of solute diffusivity and the advancing ice front formation. Therefore, once a critical mixing rate is reached, further turbulence increase has no appreciable effect (Figures 2 and 3). 

Equation (9-128) relates the difference in composition of the two liquid phases to the temperature T. Equation (9-128) is usually solved graphically by plotting w = tanh Z and w = lRTIa)Z and noting the points of intersection of the two curves. These curves are plotted in Fig. 9-13. If (IRTIoc) > 1, the two curves intersect only at the point m = 0 i.e., the two phases always have the same composition and, therefore, are miscible. Because of our symmetry assumption, X2 = Xi in this case. For (IRTIa) < 1, Eq. (9-128) also has a nonzero solution and the system is heterogeneous. Thus, a nonideal liquid solution will have a critical mixing temperature if a is positive. At the critical temperature, IX/2RT, = 1 and T, = o /2R. 

A theoretical justification for using the blending time as a scaleup criterion is that is usually proportional to t and is the critical mixing time if most of the extra byproduct formation occurs in or near the feed plume. If the ratio dg/D is kept the same, with d = aD, and the average rate of energy dissipation is e = then Eq. (6.7) becomes... 

This holds as long as the batch is larger than the critical mixing quantity. See e.g. Hall and Nioholls (1980) or Cafaro and Cerda (2004). 

Fluorocarbon—hydrocarbon near critical mixing temperature Liquid metal-liquid metal Hydrogen-bonded organic liquid—water Non-polar saturated organic—water Aromatic hydrocarbon/water... 

Aliphatic amines Rapid cure Critical mix ratios... 

From Eq. (4) we note that the nonequilibrium enhancement strongly depends on the value of the Soret coefficient. Since the information on the Soret coefficient ST available in the literature is limited, it was decided to measure ST of polystyrene-toluene solutions in our laboratory as well [22]. For this purpose an optical beam-deflection method was used. This method was first applied by Giglio and Vendramini [24] to polymer solutions and binary liquid mixtures near a critical mixing point. The method was subsequently improved by Kolodner et al. [25] and by Zhang et al. [14] for measuring mass diffusion and thermal diffusion in liquid... 

The variables in Eq. (6.46) are either defined there or are the same as in Eq. (6.39). The two equations of state offer similar predictions regarding EVT behavior, thermal expansion, and compressibility. The modification suggests higher free-volume content, primarily due to the greater number of external degrees of freedom. However, the modified relation provides better prediction of the polymer-solvent miscibility and P dependence of the critical mixing temperature. 

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