Multiphase dispersed systems

This work was supported by Ministry of Science and Environmental Protection of Republic of Serbia as a part of fundamental project Multiphase Dispersed Systems (No. 101822). 

Spasic, A.M. Multiphase Dispersed Systems, ITNMS, Belgrade, 1997, pp. 5. 

According to the classical deterministic approach, the phases that constitute the multiphase dispersed systems are assumed to be a continuum, that is, without discontinuities inside the one entire phase, homogeneous and isotropic. The principles of conservation of momentum, energy, mass, and... 

Chemical Kinetics, Tank and Tubular Reactor Fundamentals, Residence Time Distributions, Multiphase Reaction Systems, Basic Reactor Types, Batch Reactor Dynamics, Semi-batch Reactors, Control and Stability of Nonisotheimal Reactors. Complex Reactions with Feeding Strategies, Liquid Phase Tubular Reactors, Gas Phase Tubular Reactors, Axial Dispersion, Unsteady State Tubular Reactor Models... 

The number of the constituent phases of a disperse system can be higher than two. Many commercial multiphase pharmaceutical products cannot be categorized easily and should be classified as complex disperse systems. Examples include various types of multiple emulsions and suspensions in which solid particles are dispersed within an emulsion base. These complexities influence the physicochemical properties of the system, which, in turn, determine the overall characteristics of the dosage forms with which the formulators are concerned. 

Mixing processes involved in the manufacture of disperse systems, whether suspensions or emulsions, are far more problematic than those employed in the blending of low-viscosity miscible liquids, due to the multiphasic character of the... 

The use of supercritical-fluid-extraction techniques in the fractionation of polysiloxanes has been demonstrated by the data presented. The poly-dispersities of the fractions were comparable with those generally attainable only by anionic-polymerization techniques, with which the incorporation of two functional groups is often difficult to attain. The ability to isolate these well-defined fractions will lead to important fundamental studies on structure-property relationships in multiphase copolymer systems. 

Nigmatulin, R.I. Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int. J. Multiphase Flow 1979, 5, 353. 

The averaged Eulerian-Eulerian multi-fluid model denotes the averaged mass and momentum conservation equations as formulated in an Eulerian frame of reference for both the dispersed and continuous phases describing the time-dependent motion. For multiphase isothermal systems involving laminar flow, the averaged conservation equations for mass and momentum are given by ... 

Several classes of formulations of disperse systems are encountered in the chemical industry, including suspensions, emulsions, suspoemulsions (mixtures of suspensions and emulsions), nanoemulsions, multiple emulsions, microemulsions, latexes, pigment formulations, and ceramics. For the rational preparation of these multiphase systems it is necessary to understand the interaction forces that occur between the particles or droplets. Control of the long-term physical stability of these formulations requires the application of various surfactants and dispersants. It is also necessary to assess and predict the stability of these systems, and this requires the application of various physical techniques. 

A colloidal system represents a multiphase (heterogeneous) system, in which at least one of the phases exists in the form of very small particles typically smaller than 1 pm but still much larger than the molecules. Such particles are related to phenomena like Brownian motion, diffusion, and osmosis. The terms microheterogeneous system and disperse system (dispersion) are more general because they also include bicontinuous systems (in which none of the phases is split into separate particles) and systems containing larger, non-Brownian, particles. The term dispersion is often used as a synonym of colloidal system. 

Most of the methods developed in this book are, by themselves, only applicable to amorphous polymers and amorphous polymeric phases. (An exception with obvious relevance to the properties of multiphase materials is the development of a physically robust predictive model for the shear viscosities of dispersions in Section 13.H.) Their combination with other types of methods to predict the properties of multiphase materials from component properties and multiphase system morphology enables us to expand their applications to include the prediction of selected properties of multiphase polymeric systems where one or more of the phases are amorphous polymers. In other words, the methods developed in this book are used to predict the properties of the amorphous polymeric phases of the multiphase system. These properties are then inserted into equations of composite models and into numerical simulation schemes (along with material parameters of the other types of components, obtained from other sources such as literature tabulations) to predict the properties of the multiphase system. We use existing composite models whenever they are adequate, and develop our own otherwise. 

Some other theoretical methods for investigating rarefied and concentrated disperse systems, based on equations of mechanics of multiphase systems, are described in the books [86,183,205, 312, 313],... 

Dynamic mechanical characteristics, mostly in the form of the temperature response of shear or Young s modulus and mechanical loss, have been used with considerable success for the analysis of multiphase polymer systems. In many cases, however, the results were evaluated rather qualitatively. One purpose of this report is to demonstrate that it is possible to get quantitative information on phase volumes and phase structure by using existing theories of elastic moduli of composite materials. Furthermore, some special anomalies of the dynamic mechanical behavior of two-phase systems having a rubbery phase dispersed within a rigid matrix are discussed these anomalies arise from the energy distribution and from mechanical interactions between the phases. 

The previous sections dealt with physicochemical basis of properties control in dispersed systems such as foams (g/1 system) and emulsions (11/12). Under real conditions, one has to do with multiphase systems, in which the dispersed system is characterised not only by the presence of three phases (1, s, g), but also by a multicomponent composition. From our... 

This new theory of the non-equilibrium thermodynamics of multiphase polymer systems offers a better explanation of the conductivity breakthrough in polymer blends than the percolation theory, and the mesoscopic metal concept explains conductivity on the molecular level better than the exciton model based on semiconductors. It can also be used to explain other complex phenomena, such as the improvement in the impact strength of polymers due to dispersion of rubber particles, the increase in the viscosity of filled systems, or the formation of gels in colloids or microemulsions. It is thus possible to draw valuable conclusions and make forecasts for the industrial application of such systems. 

The new non-equilibrium thermodynamic theory of heterogeneous polymer systems [37] is aimed at giving a basis for an integrated description for the dynamics of dispersion and blending processes, structure formation, phase transition and critical phenomena. Our new concept is derived from these more general non-equilibrium thermodynamics and has been worked out on the basis of experiments mainly with conductive systems, plus some orienting and critical examples with non-con-ductive systems [72d]. The principal ideas of the new general non-equilibrium thermodynamical theory of multiphase polymer systems can be outlined as follows. 

These results, combining the widely known instability (and dissipative structure ) phenomenon of melt fracture with the new non-equilibrium description of multiphase polymer systems, will hopefully stimulate more experimental and theoretical work devoted to these (frozen) dissipative structures. Up to now, it remains open which property of the melt may be responsible for its suddenly occurring capability to disperse fillers (pigments, carbon-black, etc.) or other incompatible polymers above melt fracture conditions. We can only speculate that the creation of microvoids ( = inner surfaces) in particular and a sudden increase of gas solubilisation capability at and above melt fracture allows the polymer melt to wet the surface of the material to become dispersed. This means that a polymer melt might have completely different (supercritical) properties above melt fracture, than we usually observe. 

The predicted drop size for a simple field is proportional to interfacial tension and inversely proportional to shear rate and matrix phase viscosity. Although Newtonian systems are relatively well understood, there are many limitations to this theory for predicting the morphology of a multiphase polymer system. Other difficulties in comparison with such ideal systems may include the complex shear fields applied in processing and the relatively high concentrations of the dispersed phase in most commercial polymer blends. 

In the last two decades, numerous experimental and theoretical studies dealing with reaction-induced phase separation in multiphase polymer systems (mostly porous matrices, toughened plastics, melt processable thermoplastics [143], molecular composites, polymer dispersed liquid crystals, etc.) have been reported. A newcomer in this field should get acquainted with hundreds (possibly thousands) of papers and patents. The intention of this review was to provide a qualitative basis (quantitative occasionally) to rationalize the various factors that must be taken into account to obtain desired morphologies. 

Colloidal systems and dispersions are of great importance in many areas of human activity such as oil recovery, coating, food and beverage industry, cosmetics, medicine, pharmacy, environmental protection etc. They represent multi-component and multiphase (heterogeneous) systems, in which at least one of the phases exists in the form of small (Brownian) or large (non-Brownian) particles (Hetsroni 1982, Russel et al. 1989, Hunter 1993). One possible classification of the colloids is with respect to the type of the continuous phase (dispersions with solid continuous phase like metal alloys, rocks, porous materials, etc. will not be consider). 

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