Mesoscopic, definition

The second series of models is based on the mesoscopic definition of the liquid variables, as introduced in the previous paragraph, and they focus on the collective dynanuc processes. Typically the mesoscopic variables, or their correlators, follow few equations of motion derived from the basic conservation laws [42,54,55] or the projection procedure introduced in the Mori-Zwanzig theory [42,52]. The solution of these equations determines the liquid dynamics. Recently these types of models have encountered a renewed interest, thanks to their application to visco-elastic and glassy liquids [48,49, 60-62]. 

Colloidal suspensions are, per definition, mixtures of mesoscopic particles and atomic liquids. What happens if there are several different species of particles mixed in the solvent One can invent several different sorts of mixtures small and large particles, differently charged ones, short and long rods, spheres and rods, and many more. Let us look into the literature. One important question when dealing with systems with several components is whether the species can be mixed or whether there exists a miscibility gap where the components macroscopically phase-separate. 

The terminology is not yet homogeneous. The use of the prefix nano spread out in the 1990s. Until then, the common term used to be mesoscopic structures, which continues to be used. According to a definition by IUPAC of 1985, the following classification applies to porous materials microporous, < 2 nm pore diameter mesoporous, 2-50 nm macroporous, > 50 nm. 

The presence of a low-viscosity interfacial layer makes the determination of the boundary condition even more difficult because the location of a slip plane becomes blurred. Transitional layers have been discussed in the previous section, but this is an approximate picture, since it stiU requires the definition of boundary conditions between the interfacial layers. A more accurate picture, at least from a mesoscopic standpoint, would include a continuous gradient of material properties, in the form of a viscoelastic transition from the sohd surface to the purely viscous liquid. Due to limitations of time and space, models of transitional gradient layers will be left for a future article. 

Some care in defining terms is required. On an atomic level all ionic and molecular interaction can be Interpreted as "electric . However, on the colloidal, or mesoscopic, level we may restrict the term "electric" to "Coulomblc". Consequently, all other interactions are by definition "non-electric", whatever their origin the three types of Van der Waals forces, hydrogen bonding, solvent structure-orl nated or real chemical bond formation. 

The analysis of the measurements above the critical volume concentration now made it possible to say something about whether the transport mechanism was dominated by these mesoscopic metallic regions (which we now definitely know are not interlinked by bridges of material or amorphous loops of chains, but at most display point-type physical contact above the critical volume concentration). 

Besides the simple mathematical approach of combining the rate equation and the diffusion equation, two fundamental approaches exist to derive the reaction-diffusion equation (2.3), namely a phenomenological approach based on the law of conservation and a mesoscopic approach based on a description of the underlying random motion. While it is fairly straightforward to show that the standard reaction-diffusion equation preserves positivity, the problem is much harder, not to say intractable, for other reaction-transport equations. In this context, a mesoscopic approach has definite merit. If that approach is done correctly and accounts for all reaction and transport events that particles can undergo, then by construction the resulting evolution equation preserves positivity and represents a valid reaction-transport equation. For this reason, we prefer equations based on a solid mesoscopic foundation, see Chap. 3. 

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