Solid macroscale

In summary, it is clear that the micromechanical shock response of single crystal LiF is extremely complex. These results certainly temper the initial enthusiasm associated with Taylor s [9] study of Armco iron as a eomplete explanation for the relationship between the microscale and the macroscale in shock-loaded solids. 

Underlying all continuum and mesoscale descriptions of shock-wave compression of solids is the microscale. Physical processes on the microscale control observed dynamic material behavior in subtle ways sometimes in ways that do not fit nicely with simple preconceived macroscale ideas. The repeated cycle of experiment and theory slowly reveals the micromechanical nature of the shock-compression process. 

Application of SPE to sample clean-up started in 1977 with the introduction of disposable cartridges packed with silica-based bonded phase sorbents. The solid phase extraction term was devised in 1982. The most commonly cited advantages of SPE over liquid-liquid extraction (LLE) as practiced on a macroscale include the reduced time and labor requirements, use of much lower volumes of solvents, minimal risk of emulsion formation, selectivity achievable when desired, wide choices of sorbents, and amenability to automation. The principle of operation consists of four steps (1) conditioning of the sorbent with a solvent and water or buffer, (2) loading of the sample in an aqueous or aqueous low organic medium, (3) washing away unwanted components with a suitable combination of solvents, and (4) elution of the desired compound with an appropriate organic solvent. 

Ivers-Tiffee E., Weber A., Schmid K., Krebs V. (2004) Macroscale modeling of cathode formation in SOFC. Solid State Ionics 174, 223-232. 

On the macroscale gels do not flow and hence a simple test for a gel is to invert its container - if it lands on the floor with a splash it is probably not a gel On the microscale the solid-like component generally comprises fibrillar bundles of high aspect ratio and in the case of chiral gelators can adopt... 

To simplify the presentation, we limit this discussion to two phases, liquid and solid, with N constituents per phase, and restrict our discussion to results pertaining to the continuity equations and momenta balance. Interfacial effects are assumed negligible, although these effects have been incorporated into HMT [1, 12], In [4] the following macroscale equations are derived. 

The hydrodynamics of a circulating fluidized bed can be analyzed from both the macroscopic and mesoscopic points of view. The nonuniformity of the solids concentration in the radial and axial directions represents macroscopic behavior. The existence of solid clusters characterizes mesoscopic behavior (see 10.5). The hydrodynamic behavior in a macroscale is discussed in the following. 

Radial flow impellers have a much lower pumping capacity and a much higher macroscale shear rate. Therefore they consume more horsepower for blending or solids suspension requirements. However, when used for mass transfer types of processes, the additional interfacial area produced by these impellers becomes a very important factor in the performance of the overall process. Radial flow turbines are primarily used in gas-liquid, liquid-solid, or liquid-liquid mass transfer systems or any combinations of those. 

Empirical approaches are useful when macroscale HRR measurements are available but little or no information is available regarding the thermophysical properties, kinetic parameters, and heats of reaction that would be necessary to apply a more comprehensive pyrolysis model. Although these modeling approaches are crude in comparison with some of the more refined solid-phase treatments, one advantage is that all required input parameters can be obtained from widely used bench-scale fire tests using well-established data reduction techniques. As greater levels of complexity are added, establishing the required input parameters (or material properties ) for different materials becomes an onerous task. 

Initially, the adhesive must be either a liquid or a readily deformed solid so that it can be applied and formed to the required geometry within the assembled joint. It is necessary for the adhesive to flow and conform to the surface of the adherends on both micro- and macroscales. Small air pockets caused by the roughness of the substrate must be easily displaced with adhesive. 

Continuum models encompass both micro and macro scales and in li-ion models the microscale is governed by the solid phase diffusion equation. The coupling of the microscale and the macroscale variables pose computational limitations. 

Macroporous VPO Phases. - The macroscale templating of bulk mixed metal oxide phases in the presence of colloidal sphere arrays typically consists of three steps shown in Figure 18. First, the interstitial voids of the monodisperse sphere arrays are filled with metal oxide precursors. In the second step, the precursors condense and form a solid framework around the spheres. Finally, the spheres are removed by either calcination or solvent extraction leading to the formation of 3D ordered macroporous structures [137]. 

A variety of well-established macroscale SPE methods for nucleic acid extraction have been successfully transferred to microscale devices [10, 31-57]. Although the physical principles of these methods may be different (e.g., chaotropic interactions, electrostatic interactions, affinity interactions, etc.), micro-SPE protocols typically consist of three steps (1) selective adsorption of nucleic acids onto a solid phase (2) removal of contaminants by a washing step and (3) elution of the preconcentrated nucleic acids from the solid support using water or a low salt buffer [31]. Like their macroscale counterparts, micro-SPE devices possess a loading level of target material that is dependent upon the available surface area within the extraction bed and, thus, are manufactured either by packing the solid phase... 

Both microscale and macroscale phenomena have the potential to control bioreactor performance. These are illustrated in Fig. 3 for an aerobic process. These processes occur within a spatially heterogeneous physical system, as was demonstrated in Fig. 1, a substrate bed consisting of moist solid particles between which are gas-filled voids. During the fermentation the bulk of the growth occurs at the particle surfaces. 

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