Liquid modeling

Wood W W 1968 Monte Carlo studies of simple liquid models Physics of Simple Liquids ed H N V Temperley, J S Rowlinson and G S Rushbrooke (Amsterdam North Holland) chapter 5, pp 115-230... 

Some results reported by Zandbergen and Beenakker are shown in Fig. 26. Considering the severe simplifying assumptions made, the calculated phase boundary is in gratifying agreement with that found experimentally. Because of symmetry with respect to mole fraction in the three-liquid model, the calculated T-y curve shown is necessarily a parabola whose maximum is at... 

The solidus, the liquidus, the oxygen-potential model for the solid Pu/0 system, and the oxygen-potential model for the liquid Pu/0 system each depend upon the temperature and composition. Because the oxygen-potential model has a greater effect on the vapor pressure and composition at high temperature than do the solidus and liquidus, we have fixed the functional forms and the parameter values for the oxygen-potential model. We choose the IAEA solidus (32) and determine the liquidus that is consistent with it and with the two parts of the oxygen-potential model. The calculated liquidus, which is based on the liquid model parameters, is very close to the IAEA liquidus (33). 

Scheme 7.2 Preparation of /V-methylimidazolium-based ionic liquids - model reaction of case study 2.

Usually, mass transfer in gas-liquid models is based on a film model (see Fig. 5.4-13). The rate of transfer of A from the gas bubble to the liquid, i.e. absorption of A in the liquid phase, equals ... 

For comparison purposes, some model compounds and model polymers were reacted with the gases. Liquid models were used as dilute solutions in hexane or hexadecane model polymers were used as solid films. n-Peroctanoic acid was synthesised from n-octanoic... 

As for normal liquids, modeling of droplet processes of melts provides tremendous opportunities to improve the understanding of the fundamental phenomena and underlying physics in the processes. It also provides basic guidelines for optimization and on-line control of the processes. This section is devoted to a comprehensive review of process models, computational methods, and numerical modeling results of the droplet processes of melts. The emphasis of this section will be placed on the droplet processes in spray atomization for metal powder production, and spray forming for near-net shape materials synthesis and manufacturing. Details of these processes have been described in Ref. 3. 

The second RPT criterion relates to the temperature of the hot liquid. That is, this temperature must exceed a threshold value before an RPT is possible. From one theory of RPTs, the superheated-liquid model (described later), this criterion arises naturally, and the threshold hot-liquid temperature is then equal to the homogeneous nucleation temperature of the colder liquid T. This temperature is a characteristic value for any pure liquid or liquid mixture and can be measured in independent experiments or estimated from theory. From alternate RPT theories, the threshold temperature may be equated, approximately, to the hot fluid temperature at the onset of stable film boiling. 

The superheated-liquid model introduced earlier to explain LNG-water RPTs was not considered applicable for smelt-water explosions since the very large temperature difference between the smelt and water would, it... 

Thus, it would appear that overpressures experienced in the air from LNG RPTs for spills less than about 30 are not particularly large unless one is very close to the spill site. Overpressures in the water are much larger, as shown in Table X from transducer measurements about 0.7 m from the surface. In fact, in one instance, the overpressure in the water exceeded the critical pressure of the LNG this would not have been expected from the superheated liquid model. 

In this article, we suggest that a modified superheated-liquid model could explain many facts, but the basic premise of the model has never been established in clearly delineated experiments. The simple superheated-liquid model, developed for LNG and water explosions (see Section III), assumes the cold liquid is prevented from boiling on the hot liquid surface and may heat to its limit-of-superheat temperature. At this temperature, homogeneous nucleation results with significant local vaporization in a few microseconds. Such a mechanism has been rejected for molten metal-water interactions since the temperatures of most molten metals studied are above the critical point of water. In such cases, it would be expected that a steam film would encapsulate the water to... 

To prove or disprove such a modified superheated-liquid model, experiments are necessary to delineate the rates and products of reaction between molten metals and water in a high-temperature environment with and without substrates which could participate in the reaction. 

The model is certainly complex, but perhaps no more so than previous ionic liquid models described in Sections 5.5.1 and 5.5.2. The initial experience (Selleby 1996) suggests that the number of terms needed to describe a ternary system such as Fe-Mn-S is quite similar for both ionic two-sublattice liquid and associate models (see next section). The modelling of ionic liquids is, in the main, complex and the advantages of the various techniques can only become apparent as they become more commonly used. 

First, all of what we believe to be the reliable phase diagram and thermodynamic data are considered simultaneously. If a particular set of data is not considered in fixing the values of the adjustable parameters of the liquid model, it is still required that the final values for these adjustable parameters lead to a good fit to this data as well as all the rest. 

The constraints imposed upon the interaction coefficients in the A-C binary are given here. Those for the B-C binary can be obtained by analogy. The constraints generally serve to reduce the number of independent coefficients and at the same time insure that the liquid model will match selected experimental values exactly regardless of how well the liquidus points and other data can be fit. 

---