Dynamic equilibrium microstructures

Frequently, however, the stability and, more generally, the microstructure and the macroscopic states of dispersions are determined by kinetic and thermodynamic considerations. Thermodynamics dictates what the equilibrium state will be, but it is often the kinetics that determines if that equilibrium state will be reached and how fast. This becomes a consideration of special importance in practice since most processing operations involve dynamic variables such as flow, sedimentation, buoyancy, and the like. Although a detailed discussion of this is beyond our scope here, it is important that we consider at least one example so that we can place some of the topics we discuss in this chapter in proper context. 

The relationship between the structure of the disordered heterogeneous material (e.g., composite and porous media) and the effective physical properties (e.g., elastic moduli, thermal expansion coefficient, and failure characteristics) can also be addressed by the concept of the reconstructed porous/multiphase media (Torquato, 2000). For example, it is of great practical interest to understand how spatial variability in the microstructure of composites affects the failure characteristics of heterogeneous materials. The determination of the deformation under the stress of the porous material is important in porous packing of beds, mechanical properties of membranes (where the pressure applied in membrane separations is often large), mechanical properties of foams and gels, etc. Let us restrict our discussion to equilibrium mechanical properties in static deformations, e.g., effective Young s modulus and Poisson s ratio. The calculation of the impact resistance and other dynamic mechanical properties can be addressed by discrete element models (Thornton et al., 1999, 2004). 

As for pure phosphoric acid, the transport properties of PBI and phosphoric acid also depend on the water activity, this is on the degree of condensation (polyphosphate formation) and hydrolysis. There is even indication that these reactions do not necessarily lead to thermodynamic equilibrium, and hydrated orthophos-phoric acid may coexist with polyphosphates in heterogeneous gel-like microstructures [99]. There is not much known on the mechanism of proton transport in polymer adducts with polyphosphates and/or low hydrates of orthophosphoric acid. Whether the increased conductivity at high water activities is the result of the plasticizing effect of the water on the phosphate dynamics, thereby assisting proton transfer from one phosphate to the other, or whether the water is directly involved in the conduction mechanism has not been elucidated. 

Emphasizing equilibrium phenomena, flow, transport, and stability, Intcrfacial Phenomena Equilibrium and Dynamic Effects, Second Edition presents a concise and current summary of the fundamental principles governing interfacial interactions. This new edition features updated and expanded topics in every chapter. It highlights key experimental techniques that have expanded the scope of our understanding, such as in mass transfer, microstructure determination in colloidal dispersions, and surfactant-polymer interactions. 

The rheological properties of the suspension are strongly influenced by the spatial distributiOTi of the particles. The relationship between microstructure and rheology of suspensions has been smdied extensively (Brader 2010 Morris 2009 Vermant and Solomon 2005). Most of earlier smdies dealt with the simplest form of suspensions, in which dilute hard-sphere suspensions are subjected only to hydro-dynamic and thermal forces near the equilibrium state (i.e., Peclet number << 1) (Bergenholtz et al. 2002 Brady 1993 Brady and Vicic 1995). In shear flows of such suspensions, the structure is governed only by the particle volume fraction and the ratio of hydrodynamic to thermal forces, as given by the Peclet number. 

It is difficult to summarize all the phenomena discussed in this volume. However, major topics include ultralow interfacial tension, phase behavior, microstructure of surfactant systems, optimal salinity concept, middle-phase microemuIsions, interfacial rheology, flow of emulsions in porous media, wettability of rocks, rock-fluid interactions, surfactant loss mechanisms, precipitation and redissolution of surfactants, coalescence of drops in emulsions and in porous media, surfactant mass transfer across interfaces, equilibrium dynamic properties of surfactant/oil/brine systems, mechanisms of oil displacement in porous media, ion-... 

The microstructure characterization of porous membranes is of great importance for understanding the separation process mechanism. Due to the complexity of the structural effects on the membrane performance, a combination of independent equilibrium and dynamic methods is required, applied on the same model membrane systems. 

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