Models for liquids

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... 

A5 The Gay-Beme model for liquid crystal systems and some typical arrangements. 

Figure 10.3 The model for liquid phase sintering of high-melting solids with liquid metals as a sintering aid...

Fig. 5 shows data from a simulation of TIP4P water that is confined on both sides by a rhombohedral mercury crystal with (111) surface structure. Bosio et al. [135] deduce from their X-ray studies that a solid o-mercury lattice with a larger lattice constant in the z direction may be used as a good structural model for liquid mercury. Thus, the mercury phase was modeled as a rigid crystal in order to simplify the simulations. The surface of such a crystal shows rather low corrugation. 

In summary the results of our 2H NMR investigation illustrate the spacer model for liquid crystalline polymers, indicating, however, that the decoupling of the mesogenic groups from the main chain, while effective, is not complete. 

Any convenient model for liquid phase activity coefficients can be used. In the absence of any data, the ideal solution model can permit adequate design. 

The Lattice-Gas and Other Simple Models for Liquid-Liquid Interfaces... 

Yu HB, Hansson T, van Gunsteren WF (2003) Development of a simple, self-consistent polarizable model for liquid water. J Chem Phys 118(1) 221—234... 

Halley JW, Rustad JR, Rahman A (1993) A polarizable, dissociating molecular-dynamics model for liquid water. J Chem Phys 98(5) 4110-4119... 

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

M. W. Mahoney and W. L. Jorgensen, A five-site model for liquid water and the... 

Recent solid state NMR studies of liquid crystalline materials are surveyed. The review deals first with some background information in order to facilitate discussions on various NMR (13C, ll, 21 , I9F etc.) works to be followed. This includes the following spin Hamiltonians, spin relaxation theory, and a survey of recent solid state NMR methods (mainly 13C) for liquid crystals on the one hand, while on the other hand molecular ordering of mesogens and motional models for liquid crystals. NMR studies done since 1997 on both solutes and solvent molecules are discussed. For the latter, thermotropic and lyotropic liquid crystals are included with an emphasis on newly discovered liquid crystalline materials. For the solute studies, both small molecules and weakly ordered biomolecules are briefly surveyed. 

Figure 6,9 Melting relations in Mg2Si04-Fe2Si04 system. Experimental data confirm validity of Richardson s (1956) ideal model for liquid. Reprinted from B. J. Wood and D. G. Fraser, Elementary Thermodynamics for Geologists, 1976, by permission of Oxford University Press.

To overcome this problem an extension of the sublattice model was proposed by Hillert et al. (1985) which is now known as the ionic two-sublattice model for liquids. As in the previous case it uses constituent fractions as composition variables, but it also considers that vacancies, with a charge corresponding to the charge of the cations, can be introduced on the anion sublattice so that the composition can move away from the ideal stoichiometry and approach an element with an electropositive character. The necessary neutral species of an electronegative element are added to the anion sublattice in order to allow the composition to approach a pure element. The sublattice formula for the model can then be written as... 

In the same way, Larachi et al. [48] evaluated with an important trickle-flow-regime database (4,000 experiments) different phenomenological models for liquid holdup and two-phase pressure drop in TBR. Table 5.2-5 summarizes the respective scatters (mean relative error and deviation) between the experimental values of pressure drop, AP/Z, and liquid holdup, fit, and their predictions by the different models. 

Figure 14.8. Model for liquid-liquid extraction. Subscript i refers to a component i = 1, 2,..., c. In the commonest case, F1 is the only feed stream and FN is the solvent, or Fk may be a reflux stream. Withdrawal streams Uk can be provided at any stage they are not incorporated in the material balances written here.

Muller and Klein [27] have compared the predictive capabilities of model 11.5.3 with selected, linear Csw versus Kow regression models such as model 11.4.9. Known models of the latter type have usually been derived from mixed Kow data (i.e., Kov/ is either estimated, experimental, or an average of several values, depending on what information is available for a compound). Muller and Klein derived a model for liquid compounds with unambiguous input ... 

Recent work has supported early observations (e.g. Aggarwal 1976 Hashimoto et al. 1983) of a liquid micellar phase between the BCC micelle phase and the disordered phase. A representative TEM image from a spherical micellar liquid phase is shown in Fig. 2.18. Kinning and Thomas (1984) analysed SANS data obtained by Berney et al. (1982) on PS-PB diblocks and PS/PS-PB blends where the minority (PB) component formed spherical micelles with only liquid-like ordering. The Percus-Yevick model for liquids of hard spheres was used to obtain the interparticle contribution to the scattered intensity (Kinning and Thomas 1984). The ordering of an asymmetric PS-PI diblock was observed by Harkless... 

Another empirical model for liquid pressure—volume behavior is the generalized equation for the molar volumes of saturated liquids given by the... 

Metha B, Chuang KT, Nandakumar K. Model for liquid-phase flow on sieve trays. Trans IChemE 1998 76 843-848. 

A detailed model for a gas-liquid column with external recirculation loop has been published by Orejas [11]. The model takes into account the axial dispersion and mass transfer from bubbles. An important conclusion is that the mass-transfer rate is fast compared with the chemical reaction. As a result, a pseudohomoge-neous model for liquid-phase reaction may be applied for design purposes. 

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