Modeling, fluid systems

Table 3.9 shows many various rheological models used to categorize and model fluid systems. It is written in terms of the three-dimensional form (where terms are discussed in Macosko (1994)) and the simple two-dimensional shear-flow relationship (where terms have been defined here). 

F. Mighri, M.A. Huneault, Drop deformation and breakup mechanisms in viscoelastic model fluid systems and polymer blends. Canad. J. Chem. Eng. 80, 1028-1035 (2002)... 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonideahties occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and soHd orHquid solutes (rl,i4—r7,r9,i49,r50). 

A number of theoretical models have been proposed to describe the phase behavior of polymer—supercritical fluid systems, eg, the SAET and LEHB equations of state, and mean-field lattice gas models (67—69). Many examples of polymer—supercritical fluid systems are discussed ia the Hterature (1,3). 

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

Phase transitions in adsorbed layers often take place at low temperatures where quantum effects are important. A method suitable for the study of phase transitions in such systems is PIMC (see Sec. IV D). Next we study the gas-liquid transition of a model fluid with internal quantum states. The model [193,293-300] is intended to mimic an adsorbate in the limit of strong binding and small corrugation. No attempt is made to model any real adsorbate realistically. Despite the crudeness of the model, it has been shown by various previous investigations [193,297-300] that it captures the essential features also observed in real adsorbates. For example, the quite complex phase diagram of the model is in qualitative agreement with that of real substances. The Hamiltonian is given by... 

Freezing transitions have been examined in recent years by density functional methods [306-313]. Here we review the results [298] of a modification of the Ramakrishnan-Yussouff theory to the model fluid with Hamiltonian (Eq. (25)) a related study of phase transitions in a system of hard discs in two dimensions with Ising internal states which couple anti-ferromagnetically to their neighbors is shown in Ref. 304. First, a combined... 

A successful method to obtain dynamical information from computer simulations of quantum systems has recently been proposed by Gubernatis and coworkers [167-169]. It uses concepts from probability theory and Bayesian logic to solve the analytic continuation problem in order to obtain real-time dynamical information from imaginary-time computer simulation data. The method has become known under the name maximum entropy (MaxEnt), and has a wide range of applications in other fields apart from physics. Here we review some of the main ideas of this method and an application [175] to the model fluid described in the previous section. 

Numerical results for the some model polydisperse systems have been reported in Refs. 81-83. It has been shown that the effect of increasing polydispersity on the number-number distribution function is that the structure decreases with increasing polydispersity. This pattern is common for the behavior of two- and three-dimensional polydisperse fluids [81] and also for three-dimensional quenched-annealed systems [83]. 

However, we also need to discuss how the attractive interactions between species can be included in the theory of partly quenched systems. These interactions comprise an intrinsic feature of realistic models for partially quenched fluid systems. In particular, the model for adsorption of methane in xerosilica gel of Kaminsky and Monson [41] is characterized by very strong attraction between matrix obstacles and fluid species. Besides, the fluid particles attract each other via the Lennard-Lones potential. Both types of attraction (the fluid-matrix and fluid-fluid) must be included to gain profound insight into the phase transitions in partly quenched media. The approach of Ford and Glandt to obtain the chemical potential utilizing... 

We present and discuss results for MD modeling of fluid systems. We restrict our discussion to systems which are in a macroscopically steady state, thus eliminating the added complexity of any temporal behavior. We start with a simple fluid system where the hydrodynamic equations are exactly solvable. We conclude with fluid systems for which the hydrodynamic equations are nonlinear. Solutions for these equations can be obtained only through numerical methods. 

The analysis of tubular contactors for heat transfer with phase changes in fluid-fluid systems was shown to be heavily dependent on a proper understanding of two-phase hydrodynamics. It was shown that three basic flow patterns exist within a tube, each with a different heat-transfer mechanism. The formulation of the proper mass and energy models pinpointed three key... 

Conway, M.W. Almond, S.W. Briscoe, J.E. Harris, L.E. "Chemical Model for the Rheological Behavior of Crosslinked Fluid Systems," SPE Paper 9334, 1980 SPE Annual Technical Conference and Exhibition, Dallas, September 21-24. 

Figure 55. Physical model for multiscale modelling of particle-fluid system.

To model fluid mixing, we will use the fresh water as a reactant, titrating it into a system containing the saline water and formation minerals. To do so, we pick up the fluid from the previous step to use as a reactant ... 

The CD model was first proposed by Curl (1963) to describe coalescence and breakage of a dispersed two-fluid system. In each mixing event, two fluid particles with distinct compositions first coalesce and then disperse with identical compositions.75 Written in terms of the two compositions (f>A and [Pg.292]

The general notion of a boundary later is found in many aspects of modeling physical systems. Recognizing boundary-layer behavior can very often lead to important simplifications in the analysis and modeling of such systems. Certainly the analysis and study of fluid mechanics is greatly facilitated by the exploitation of boundary-layer approximations. 

The phase behaviour of binary polymer - supercritical fluid systems can be modelled with an equation of state model. In general, non-cubic equations of state are used, mainly from the PHCT and SAFT families. Lattice-fluid equations of state are also commonly used for the... 

If flow is cocurrent the lower sign is used if countercurrent the upper sign is used. Since the mass flowrate of the cooling fluid is based upon the cross-sectional area of the reactor tube the ratio G Ip Gq SpC(= H is a measure of the capacities of the two streams to exchange heat. In terms of the limitations imposed by the onedimensional model, the system is fully described by equations 3.9S and 3.96 together with the mass balance equation ... 

The unrestricted form of the primitive model (UPM) becomes important for more complex fluid systems. Stell argued that symmetry breaking in the UPM may play an important role in determining critical behavior [17]. In spite of this potential utility, the UPM is rarely explored. In MC simulations of the cluster structure in the UPM, Camp and Patey [259] compared results for asymmetrical charges Xq = z+/z = 1,2,4 at the diameter ratio Xa = vapor phase contains, above all, neutral clusters such as trimers for Xq — 2 and tetrahedral pentamers for Xq = 4, as well as higher clusters. At Xq = 4 asymmetry effects not covered by simple theories seem to play a role. 

Mixtures of equisized charged spheres were also treated by the MSA. Such a system is then uniquely characterized by the ratio of the critical temperatures of the pure components. Harvey [235] found that a continuous critical curve from the dipolar solvent to the molten salt is maintained until the critical temperature of the ionic component exceeds that of the dipolar component by a factor of about 3.6. This ratio is much higher than theoretically predicted for nonionic model fluids. We recall that for NaCl the critical line is still continuous at a critical temperature ratio of about 5. Thus, the MSA of the charged-hard-sphere-dipolar-hard-sphere system captures, at least in part, some unusual features of real salt-water systems with regard to their critical curves. 

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