Modeling of the mixing process

The chemical processes occurring within a black smoker are certain to be complex because the hot, reducing hydrothermal fluid mixes quickly with cool, oxidizing seawater, allowing the mixture little chance to approach equilibrium. Despite this obstacle, or perhaps because of it, we bravely attempt to construct a chemical model of the mixing process. Table 22.3 shows chemical analyses of fluid from the NGS hot spring, a black smoker along the East Pacific Rise near 21 °N, as well as ambient seawater from the area. 

The behaviour of elastomers in internal mixers reflects consequently a combination of shear and extensional responses. Any model of the mixing process has to take account of both shear flow and transitory extensional flow, since for the latter the steady state cannot be achieved. Therefore the response of the elastomers in the earlier times of an elongational process gives information about the mixing behaviour. Using a high rate extensometer,... 

Dallas, Tex., 4th-6th April 2000, paper 13 MODELLING OF THE MIXING PROCESS AND ONLINE PREDICTION OF THE RUBBER COMPOUND AND MOULDED PART PROPERTIES WITH INTELLIGENT PROCESS ANALYSIS TECHNOLOGIES Haberstroh E Ryzko P... 

In the design of stirred tank reactors the model of an Ideal stirred tank Is a useful approximation. To understand when It breaks down we can set up more complex models of the mixing process (13) and of the kinetics and estimate the effect of mixing time. The fact that our complex model does not represent a real reactor Is not that Important, since all we want Is an estimate of the Importance of the mixing time. On the other hand, we can not use this complex model to predict the effect of Imperfect mixing In a quantitative way. 

Based on this model the flow rate of ethanol can be estimated by using the specific parameters of the mixing process and kinetic factors (Equation 29.1) ... 

The following model of the corrosion process can be proposed based on the wealth of data provided by the combined application of SPFM, contact AFM, and IRAS At low RFl, the principal corrosion prodnct, hydrated alnminnm snlfate, is solid. It acts as a diffn-sion barrier between the acid and the alnminnm snbstrate and prevents fnrther corrosion. The phase separation observed between the acid and the salt at low RH strongly snggests that the salt inhibits fnrther corrosion once it precipitates. At high RH, on the other hand, alnminnm snlfate forms a liqnid solntion. Snlfnric acid mixes with this solntion and reaches the nnderlying snbstrate, where fnrther reaction can occnr. The flnid snlfate solntion also wets the snrface better and thns spreads the snlfnric acid. The two processes assist each other, and the corrosion proceeds rapidly once the critical RH of 80-90% is reached. 

Consider now a mathematical model for the mixing process that allows the calculation of the distribution function out of the function measured... 

So far, we have seen that deviation from ideal behavior may affect one or more thermodynamic magnitudes (e.g., enthalpy, entropy, volume). In some cases, we are able to associate macroscopic interactions with real (microscopic) interactions of the various ions in the mixture (for instance, coulombic and repulsive interactions in the quasi-chemical approximation). In practice, it may happen that none of the models discussed above is able to explain, with reasonable approximation, the macroscopic behavior of mixtures, as experimentally observed. In such cases (or whenever the numeric value of the energy term for a given substance is more important than actual comprehension of the mixing process), we adopt general (and more flexible) equations for the excess functions. 

These models picture the mixing process as consisting of motion phases and rest phases. In a model proposed by Einstein (E3) and discussed by Jacques and Vermeulen (Jl) and Cairns and Prausnitz (C5), it is assumed that the time represented by a motion phase is much less than that by a rest phase. For the packed bed, the motion phase might be taken as the period when the fluid element is passing through the restriction between particles, and the rest phase as the period when the fluid element is in the void space. If values are assigned to the probabilities of motion or rest, consideration of the geometry of the fluid elements motions will lead to... 

The mixing field is integrated with other models of the key process mechanisms, aiming at giving an entire picture of the process [1]. 

In Table 2 we summarize some of their findings. The table shows the amount of water in the ionic liquid, the amount of ionic liquid in the water, and the width of the interface separating the two phases at the end of the simulation for the different force fields. It is seen that the popular TIP3P model gives quite different results from those of the other force fields and in the simulation of the mixing process there is not even a well defined interface. The other two force fields give similar results. All simulations support that the ionic liquid is essentially water-free, as should be. 

The process model is represented by the heat transfer and the mixing process of the two heated parallel passes (figure 3). The input variables of the process are the thermal duties on the two parallel passes, Q-j-i, = 1, 2, and the associated volume flowrates, m, i =, 2. The mathematical model of the furnace is composed of the model associated to each coil and the model of the mixing node with temperature 7), ... 

Abundance analyses of very metal-poor stars do show that r-process products are present without s-process contamination for [Fe/H] -2 (Burris et al. 2000 Johnson Bolte 2001). In particular, the Ba/Eu ratio approaches the value estimated for the r-process contributions to the solar system abundances. Several very metal-poor stars are known with severe overabundances of the heavy elements (Cowan et al. 1999 Westin et al. 2000 Hill et al. 2002 Cowan et al. 2002). For elements Ba and heavier, the relative abundances in the severely r-process overabundant stars are robustly equal to the solar r-process ratios. This solar-like mix also appears to be present in stars less enriched in the heavy elements. This robustness is a challenge to modellers of the r-process and its site of operation. 

The results of Fig. 13.6 were compared with a 1D axial dispersion model of the same process configuration (i.e., two injector loops, two lines from the loops to the mixing tee, the reactor tubing, and the sample loop tubing with the dimensions cited earlier). The output for the case of a 10 pL min flow rate from each pump, with 10 wt% Tracer 1 injected simultaneously from each injection loop, is shown in Fig. 13.7. The model predicted analytical loop peak concentration (i.e., exceeding 99% of the inlet injector concentration) arrived earlier than the peak concentration resulting from the actual process data. 

The lattice model of Flory-Huggins calculates the entropic changes of the mixing process. The enthalpy effects are considered by the interaction parameter % ... 

To estimate the mixing time from experiments, the kinetics of the second reaction r must be known allowing the calculation of In addition, a model describing the mixing process is indispensable. 

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