Microstructured energy balance

Because densification occurs via the shrinkage of thermodynamically unstable pores, densification and microstructure development can be assessed on the basis of the dihedral angle, 0, formed as a result of the surface energy balance between the two solid-vapour and one solid-solid interface at the pore-grain boimdary intersection... 

Each chapter starts with a description of the main polymers produced by the particular method, the key microstructural features, the applications and the sought properties. Then the polymerization kinetics and its effect on the configuration of industrial reactors is discussed. Afterwards the mass and energy balances for the reactors are developed. The examples focus on the main polymers produced by the particular class of polymerization, but the general concepts, principles and methodology are emphasized. 

Mass and Energy Balance in Multi-injection Microstructured Reactors... 

Theories of Viscous Sintering describes the concept of energy balance by which Frenkel first analyzed sintering, and it reviews the microstructural models that have been developed. Effects of a distribution of pore sizes and of gas trapped in the pores are considered. 

We propose the balance principles for an immiscible mixture of continua with microstructure in presence of phenomena of chemical reactions, adsorption and diffusion by generalizing previous multiphase mixture [9] and use a new formulation for the balance of rotational momentum. New terms are also included in the energy equations corresponding to work done by respective terms in the micromomentum balances. 

In real suspensions and sols several interaction forces (or interaction free energies) play a role. Some are attractive and some are repulsive. The total interaction free energy is determined by the sum of all these contributions. The microstructure of the dispersion depends on the sum of the contributions. Because this sum is the total of large positive (repulsive) and large negative (attractive) contributions, the final result is a delicate balance. Prediction of the overall force between the particles requires that the separate contributions are accurately known which is often rather difficult in practice. Nevertheless, it is... 

Thus the third principle simply asserts that, in its motion as a whole, a body does not know whether it is a mixture or not but in this paper the skeleton of the medium consists of a continuum with microstructure, as defined by Capriz (1989), and therefore it must satisfy balance equations there proposed. The first and the second principles affirm that the whole is no more than the sum of its parts and that the mixture s constituents, imagined as splitted in geometry, must be considered united in physics by suitable forces or energies, respectively. We should also notice how, unlike balance equations, constitutive proposals for dependent fields are usually affected by microstructural independent variables in addition to gross ones. 

In Eq. (8), D is the rate of deformation and T D is the stress power. In addition to the standard formulation of the balance of internal energy, some terms depending on k are present, which represent the energetic contributions associated with the microstructural parameter k. Note that it is not necessary to specify the physical meaning of the microstructural quantities k, S, and pk in terms of the underlying microstructure even if this is desirable in view of the interpretation. 

Note that according to Eqs. (15) and (16) the free Helmholtz energy serves as a potential for the stresses T and for the microstructural flux S. According to the assumption of elastic material behavior, results of this type have to be expected. The additional balance equation for k [Eq. (17)] possesses the same structure as the balance of equihbrated forces obtained in Refs. [14, 20, 33] and appHed, e.g., in Ref [36]. Following the MuUer-Liu approach, Svendsen [39] also derived a generalization of Eq. (17) for a model with scalar-valued stractural parameters. 

When two or more components are present in a thin film, there is the potential for phase separation and therefore a wide range of microstructural variation. In addition, for solution-processed materials, the solvent acts as a further component that is controllably removed during fabrication. Therefore, in the case of small-mole-cule/polymer systems, there can be several factors that determine the overall phase behavior first, the thermodynamics of mixing between components and the balance of entropic and enthalpic contributions to the free energy of mixing, AG ixi second, the interaction between solution and substrate or atmosphere interfaces and finally, the kinetics of solvent evaporation and changes to the solution that this induces, such as viscosity variation or phase separation within the solution. It should be noted that these processes are often far from thermodynamic equilibrium leading to a film microstructure that can sometimes be difficult to predict. 

For the inventory analysis of the industrial-scale production of m-anisaldehyde, two simpliflcations were made. First, the work-up procedure was disregarded because it is the same for both alternatives. Second, the results obtained for the laboratory-scale synthesis had demonstrated that the contribution of the supply of the peripheral equipment is irrelevant for the environmental impact of the overall systems. For this reason, only the fabrication of the reaction devices was included in the balance on the industrial scale and lifetimes of 10 years for the batch vessel and of 1 year for the microstructured devices were assumed. Thus, the system boundary spans from the production of the starting materials and solvents over the supply of energy and inert gas, the fabrication of the reaction devices, the realization of the model reaction including rinsing and transports, to the disposal of waste. 

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