Polyhedral dispersant

The composite materials have been used to form selective membranes for the separation of liquid mixtures [181]. The membranes should consist of a polymer which is soluble in the liquid components) to be separated, as the dispersed phase-derived polymer, and a continuous phase-derived polymer which is insoluble in all components of the liquid mixture. Thus, membranes consisting of polystyrene in polyacrylamide will separate toluene from cyclohexane, and those comprising polyacrylamide in crosslinked polystyrene can be used for water removal from ethanol. Due to the very thin films of polymer which separate the polyhedral dispersed phase cells, the permeation rates, which are measured by pervaporation, are relatively high. 

Krotov, V. V., The hydrodynamic stability of polyhedral disperse systems and their kinetics under the conditions of spontaneous breakdown. 1. Aspects of the hydrodynamic stability, Colloid Journal, Vol. 48, No. 4, 1986. 

Krotov, V. V., The structure, syneresis, and kinetics of destruction of polyhedral disperse systems. In Problems of Thermodynamics of Heterogeneous Systems and the Theory of Surface Phenomena. Vol. 6, pp. 110-191 Izd. Leningrad. Univ., Leningrad, 1982 [in Russian]. 

Krotov,. V.,The theory ofsyneresis of foams and concentrated emulsions. 1. Local multiplicity of polyhedral disperse systems, Colloid Journal, Vol. 42, No. 6, 1980. 

As was mentioned in the introduction, HIPEs contain an internal phase volume fraction greater than 0.74. Since this is the maximum volume which can be occupied by uniform, undeformed spherical particles, the dispersed phase droplets must either be non-uniform, i.e. polydisperse, or deformed into non-spheri-cal, polyhedral cells. 

The shape of the dispersed phase droplets was investigated experimentally by Lissant and coworker by scanning electron microscopy (SEM) on cured HIPEs of water in a styrene-based resin [5], At high internal phase volumes, droplets were indeed polyhedral, and appeared to be relatively monodisperse in size. 

The non-aqueous HIPEs showed similar properties to their water-containing counterparts. Examination by optical microscopy revealed a polyhedral, poly-disperse microstructure. Rheological experiments indicated typical shear rate vs. shear stress behaviour for a pseudo-plastic material, with a yield stress in evidence. The yield value was seen to increase sharply with increasing dispersed phase volume fraction, above about 96%. Finally, addition of water to the continuous phase was studied. This caused a decrease in the rate of decay of the emulsion yield stress over a period of time, and an increase in stability. The added water increased the strength of the interfacial film, providing a more efficient barrier to coalescence. 

Crosslinked polyacrylamide latexes encapsulating microparticles of silica and alumina have also been prepared by this method [179], Three steps are involved a) formation of a stable colloidal dispersion of the inorganic particles in an aqueous solution containing acrylamide, crosslinker, dispersant, and initiator b) HIPE preparation with this aqueous solution as the dispersed phase and c) polymerisation. The latex particles are polyhedral in shape, shown clearly by excellent scanning electron micrographs, and have sizes of between 1 and 5 pm. 

Sodium / -naphthalenesulfonate was chosen as the surface-active electrolyte because its structure is simple and rigid. It does not form micelles, so there is no question as to the species adsorbed on the surface. It is a strong electrolyte and is expected to be essentially completely ionized at saturation coverage. SNS stabilized dispersions flocculate over periods of minutes to months depending on the concentration of SNS. Sterling FTG has a non-polar, non-ionic, hydrophobic surface. The ultimate particles have large, flat, polyhedral surfaces. The particle size distribution of the dry carbon is narrower than that of most colloidal carbons (2). 

A foam is a coarse dispersion of gas in liquid, and two extreme structural situations can be recognised. The first type (dilute foams) consist of nearly spherical bubbles separated by rather thick films of somewhat viscous liquid. The other type (concentrated foams) are mostly gas phase, and consist of polyhedral gas cells separated by thin liquid films (which may develop from more dilute foams as a result of... 

A foam is a colloidal dispersion in which a gas is dispersed in a continuous liquid phase. The dispersed phase is sometimes referred to as the internal (disperse) phase, and the continuous phase as the external phase. Despite the fact that the bubbles in persistent foams are polyhedral and not spherical, it is nevertheless conventional to refer to the diameters of gas bubbles in foams as if they were spherical. In practical occurrences of foams, the bubble sizes usually exceed the classical size limit given above, as may the thin liquid film thicknesses. In fact, foam bubbles usually have diameters greater than 10 pm and may be larger than 1000 pm. Foam stability is not necessarily a function of drop size, although there may be an optimum size for an individual foam type. It is common but almost always inappropriate to characterize a foam in terms of a given bubble size since there is inevitably a size distribution. This is usually represented by a histogram of sizes, or, if there are sufficient data, a distribution function. 

A dispersion of gas bubbles in a liquid, in which at least one dimension falls within the colloidal size range. Thus a foam typically contains either very small bubble sizes or, more commonly, quite large gas bubbles separated by thin liquid films. The thin liquid films are called lamellae (or laminae ). Sometimes distinctions are drawn as follows. Concentrated foams, in which liquid films are thinner than the bubble sizes and the gas bubbles are polyhedral, are termed polyederschaum . Low-concentration foams, in which the liquid films have thicknesses on the same scale or larger than the bubble sizes and the bubbles are approximately spherical, are termed gas emulsions , gas dispersions , or kugelschaum . See also Evanescent Foam, Froth, Aerated Emulsion. 

Wet foams in which the liquid lamellae have thicknesses on the same scale or larger than the bubble sizes. Typically in these cases the gas bubbles have spherical rather than polyhedral shape. Other synonyms include gas dispersion and kugelschaum . If the bubbles are very small and have a significant lifetime, the term microfoam is sometimes used. In petroleum production the term is used to specify crude oil that contains a small volume fraction of dispersed gas. See also Foam. 

A foam consists of a high volume fraction of gas dispersed in a liquid where the liquid forms a continuous phase. Wet foams with a high water content, e.g. immediately after the formation, can have more or less spherical bubbles. As a consequence of a drainage process of the foam lamellae, the wet foam loses water with time. Due to the resulting high volume fraction of gas, the bubbles are no longer spherical but they are deformed into a polyhedral shape. The polyhedra are separated from each other by thin liquid films. The intersection lines of the lamella are termed plateau borders (see Figure 3.28). 

The most important parameters characterising a polyhedral foam are expansion ratio, dispersity and foam stability. The expansion ratio n is the ratio between the foam volume V and the volume of the liquid content Vl in it... 

In [64] the possible stable configurations of films in polyhedral foams is discussed from the thermodynamic point of view that any disperse system tends to minimum surface energy. Almgren and Taylor [64] modelled the shape of the films and the angles between them with wire devices and studied several film configurations. They established that only film configurations which obey Plateau laws are stable with respect to minor deformations. 

Dispersity of gas emulsions and polyhedral foams is a very important parameter which determines many of their properties and processes occurring in them (diffusion transfer, drainage, etc.) and, therefore, their technological characteristics and areas of application. The kinetics of changes in dispersity indicates the rate of foam inner destruction resulting from coalescence and diffusion transfer. In real foams bubble size varies in a wide range (from micrometers to centimetres). Only by means of special methods it is possible to obtain foam in which bubble size varies in a narrow interval, i.e. foam that can be regarded as monodisperse. 

The average bubble radius (as well as the biggest and smallest size), the maximum distance between the opposite walls of the bubble (relative diameter) [8] and the specific liquid/air interface are involved in the estimation of dispersity. However, the distribution of bubbles by size, for example by radius of equivalent spheres, reveals completely the foam dispersity. Additional information about dispersity which takes into account the difference in polyhedral shapes is gathered from the number and shape of polyhedron faces (see Section 1.2). 

The capillary pressure and foam dispersity were determined simultaneously. After drying the reduced pressure under the porous plate sharply changed to lower values leading to an immediate liquid suck in from the porous plate into the foam. As a result the foam expansion ratio decreased to values at which the condition for polyhedricity was not fulfilled. The capillary pressure and the expansion ratio were measured again for the new state of the foam obtained. 

Very useful for the kinetic studies of dispersity changes in a foam is the method based on simultaneous measurement of local expansion ratio and border pressure at one and the same level in the foam column [5]. This method can be applied to polyhedral foams in which the liquid is mainly in the borders. A formula for the length of a dodecahedron edge is obtained when Eqs. (1.43), (1.45) and (4.10) are solved together... 

Considering a dodecahedral model of a polyhedral foam, the relation between its expansion ratio and dispersity is given by Eq. (4.9). The ratio between the initial foam expansion ratio and the expansion ratio at a given time is... 

An intrinsic property of a polyhedral foam is the reduced pressure in its Plateau borders. At the moment of foam formation the pressure in the borders depends mainly on the foam expansion ratio, dispersity and surface tension (see Eqs. (4.9) and (4.10)). At hydrostatic equilibrium the border pressure is expressed by Eqs. (1.37) and (1.38). 

A detailed study of emulsion behaviour in centrifugal field up to 56000 rpm has been performed by Rehfeld [74], Void and Groot [75-77] and Mittal and Void [78]. It has been shown that emulsions become rapidly polyhedral and their further destruction (the rate of separation of the dispersion medium and coalescence) depends on the concentration and type of both emulsifier and electrolyte, as well as on the acceleration of the centrifugal field. However, the technique applied in [74-78] has certain disadvantages it provides information... 

Individual structural elements of the foam, such as films and borders, can be under hydrostatic equilibrium and can correspond to a true metastable state. Therefore, when there is no diffusion expansion of bubbles in a monodisperse foam, its state can be regarded as metastable in the whole disperse system. Krotov [5-7] has performed a detailed analysis of the real hydrodynamic stability of polyhedral foam by solving two problems determination of... 

The extinction of the luminous flux passing through a foam layer occurs as a result of light scattering (in the processes of reflection, refraction, interference and diffraction from the foam elements) and light absorption by the solution. In a polyhedral foam there are three structural elements, clearly distinct by optical properties films, Plateau borders and vertexes. The optical properties of single foam films have been widely studied (see Section 2.1.3) but these of the foam as a disperse systems are poorly considered. 

The initial expansion ratio and dispersity of polyhedral foams are related through the quantitative dependence, given by Eq. (4.9). There at Ap > 103 Pa the content of the liquid phase in the films can be neglected. Thus, the connection of the structure parameters n, a and r can be expressed by the simple relation in Eq. (4.10). It follows from it that under given foaming conditions a definite expansion ratio can be reached by changing the border pressure, foam dispersity and surface tension of the foaming solution. 

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