Mixture theories

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

Gy, RM. (1979) Sampling of Faniculate Mixtures Theory and Bractice, Elsevier, New York. 

In these remarks, one can see a pioneering suggestion of a cluster mixture theory of liquids with short-range (exchange-like) forces, along the lines of Mayer cluster theory (Sidebar 13.5) or quantum cluster equilibrium theory (Section 13.3.4). 

Continuous mixture theory found application in industry and was, as I understand it, incorporated into some of the models the chemical and oil companies were developing. Some of the work on polymerization and coal devolatization also used the notions of continuous mixtures, but there was little development on the formal side until the work of Astarita and Ocone in the latter eighties. Their paper (AIChE J. 34 1299, 1988) introduced the idea of uniform kinetics. This allowed the time scale to be warped and results to be obtained when the underlying reactions were not of the first order. Indeed, it was shown that intrinsic kinetics (i.e. rate laws for A(x)dx) could be found that would mimic any kinetic law for the lump as a whole (AIChE J. 35 529,1989 [248, 249, 259]). 

Gu, W.Y., Lai, W.M, and Mow, V.C. (1998) A mixture theory for charged-hydrated soft tissues containing multi-electrolytes passive transport and swelling behaviors. Journal of Biomechanical Engineering 120, 169-180... 

Abstract A fully coupled model of hygro-thermo-chemo-mechanical phenomena in concrete is presented. A mechanistic approach has been used to obtain the governing equations, by means of the hybrid mixture theory. The final equations are written in terms of the chosen primary and internal variables. The model takes into account coupling between hygral, thermal, chemical phenomena (hydration or dehydration), and material deformations, as well as changes of concrete properties, caused by these processes, e.g. porosity, permeability, stress-strain relation, etc. 

The mathematical model consists of four balance equations. These equations have been obtained in [3] by use of Volume Averaging Theory also called hybrid mixture theory, [11]-[13], The mass balance of the dry air includes both diffusive and advective components of the mass fluxes,... 

Gu, W.Y., W. M. Lai, and V. C. Mow. (1998) A Mixture Theory for Charged-hydrated Soft Tissues Containing Multi-electrolytes Passive Transport and Swelling Behaviors. J. Biomech. Eng. 120, 169-180... 

Frijns, A.J.H. (2000) A Four-Component Mixture Theory Applied to Cartilaginous Tissue Numerical Modelling and Experiments. PhD thesis, Eindhoven University of Technology, Eindhoven... 

Hybrid mixture theory is a hybridization of classical volume averaging of field equations (conservation of mass, momenta, energy) and classical theory of mixtures [8] whose theory of constitution results from the exploitation of the entropy inequality in the sense of Coleman and Noll [9], In [4] the microscale field equations for each species of each phase, modified appropriately to include charges, polarization, and an electric field, are averaged to the macroscale, defined to be the scale where the phases are indistinguishable. Thus at the macroscale the porous media is viewed a mixture, with each thermodynamic property for each constituent of each phase defined at each point in space. 

Bennethum, L.S. (1994) Multiscale, hybrid mixture theory for swelling systems with interfaces, PhD thesis, Purdue University, West Lafayette, 47907. 

Eringen, A.C. (1998) A mixture theory of electromagnetism and superconductivity, International Journal of Engineering Science 36(5,6), 525-543... 

The Theory of Porous Media is the Mixture Theory, restricted by the concept of the Volume Fractions. Hereby, we have a look at a continuum which consists of several constituents. In this investigation we deal with a solid phase a = S), a Liquid phase (a = L) and a Gas phase (a = G). The components of the real structure will be statistically distributed over the control space, so that we gain to a smeared model of the real structure. 

In order to keep also the physical properties for the smeared body, such as the material compressibility or incompressibility of the constituents involved, the mixture theory is restricted by the concept of volume fractions. Therefore, the volume V of the control space is divided into the partial volume fractions n . The sum of the volume fractions has to fill the whole control space. With the concept of volume fractions we obtain the partial density pa for the constituents... 

Binary mixtures, theory, 91-93 Binary mixtures of toluene and... 

McCarty LS, Borgert CJ. 2006. Review of the toxicity of chemical mixtures theory, policy and regulatory practice. Reg Toxicol Pharmacol 45 119-143. 

Adsorption from binary fluid mixtures. Theory 2.28... 

All his life, Temkin contributed to science in many areas, such as diffusion of heavy water into ordinary water, fugacity of gas mixtures, theory of mixtures of molten salts, and mass transfer in chemical engineering. But he left his indelible mark in the fundamentals of catalytic kinetics, on a par with C. J. Christiansen and J. Horiuti. 

In this paper, an earlier theory (12-13) for binary mixtures of backbone LCPs (and/or nonpolymeric molecules) in the nematic (N) LC phase and the isotropic (I) liquid phase has been extended to treat binary mixtures in multiple smectic-A (SA) LC phases, the N LC phase, and the I liquid phase. Either component 1 (Cl) and/or component 2 (C2) in the mixture can be a backbone LCP, a nonpolymeric LC molecule, a polymeric non-LC molecule, or a nonpolymeric non-LC molecule. Cl can also be a side-chain LCP or a combined LCP (including a SS LCP). The new theory of this paper is the mixture analogue of an earlier theory for pure (single-component) systems derived and presented in detail in References 3 and 7-10 (see also References 14-23). When only one component is present, the new mixture theory of this paper reduces to this earlier single-component theory. Therefore, only a short summary of the new mixture theory is presented here. 

Ei ft 0, (In t ) — (In O3) - 0, and E2 — Ej - 0. For the particular Cl side-chain LCPs and Cl combined LCPs (including SS LCPs) studied (3-13) with the earlier single-component analogue of this mixture theory, it has been found that the N LC phase and the I liquid phase for these polymers involve the packing of plate-like sections of backbones and side chains thus, (ln 0- ) 0, (ln f ) 0,... 

Earlier versions (12-13,22) of this new mixture theory have predicted and reproduced experimental trends in various thermodynamic and molecular ordering properties [such as phase transition temperatures, phase stabilities (including of the N LC phase and the I liquid phase), curvatures of lines of coexisting phases, and orientational order P2] in binary mixtures as a function of T, P, system composition, and molecule chemical structures. 

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