Hexagonal system dispersion

The shear modulus of polydisperse hexagonal systems of the type depleted in Fig. 8b is still given by Eq. (72) when R is replaeed by R = (X R2 /n)j/2characteristic drop radius that is based on the average drop area (44). However, as expected, the elastie limit , i.e., the stress and strain where the first T1 rearrangement oeeurs, is reduced relative to that of the mono-disperse ease of the same volume fraction. 

Another major drawback stems from the disperse nature of the system itself involving a size distribution of the bubbles in the continuous liquid, which can be broad. The interface is not as defined as for two-phase continuous reactors, as described in Section 5.1.1. However, in the case of making foams, regular micro flow structures, such as hexagon flow, were described [22]. 

Surfactants are amphiphilic molecules which, when dispersed in a solvent, spontaneously self-assemble to form a wide variety of structures, including spherical and asymmetric micelles, hexagonal, lamellar, and a plethora of cubic phases. With the exception of the lamellar phase, each of these phase structures can exist in both normal and reverse orientations with the hydrophobic chains on the exterior of the aggregate, in contact with solvent or vice versa orientation. The range of structures a particular surfactant forms and the concentration range over which they form, depends upon the molecular architecture of the surfactant, its concentration, and the solvent in which it is dispersed. For example, some solvents such as ethanol do not support the formation of aggregates. As most pharmaceutical systems use water as their solvent, this entry will concentrate on aqueous-based systems, although other solvent systems, particularly other non-aqueous polar systems, will be mentioned where appropriate. 

A liquid crystal is a general term used to describe a variety of anisotropic structures formed by amphiphilic molecules, typically but not exclusively at high concentrations. Hexagonal, lamellar, and cubic phases are all examples of liquid crystalline phases. These phases have been examined as drug delivery systems because of their stability, broad solubilization potential, ability to delay the release of encapsulated drug, and, in the case of lamellar phases, their ability to form closed, spherical bilayer structures known as vesicles, which can entrap both hydrophobic and hydrophilic drug. This section will review SANS studies performed on all liquid crystalline phases, except vesicles, which will be considered separately. Vesicles will be considered separately because, with a few exceptions, generally mixed systems, vesicles (unlike the other liquid crystalline phases mentioned) do not form spontaneously upon dispersal of the surfactant in water and because there have been many more SANS studies performed on these systems. 

With solid-in-liquid dispersions, such a highly ordered structure - which is close to the maximum packing fraction (q> = 0.74 for hexagonally closed packed array of monodisperse particles) - is referred to as a soHd suspension. In such a system, any particle in the system interacts with many neighbours and the vibrational amplitude is small relative to particle size thus, the properties of the system are essentially time-independent [30-32]. In between the random arrangement of particles in dilute suspensions and the highly ordered structure of solid suspensions, concentrated suspensions may be easily defined. In this case, the particle interactions occur by many body collisions and the translational motion of the particles is restricted. However, this reduced translational motion is less than with solid suspensions - that is, the vibrational motion of the particles is large compared to the particle size. Consequently, a time-dependent system arises in which there will be both spatial and temporal correlation. 

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