Scaling methodology

This section focused on field, pilot-plant and bench-scale methodologies that can be applied to determine parameters and components for sewer process... 

Concurrent Coupling of Length Scales Methodology and Application. 

Li, Jinghai, and Mooson Kwauk, Exploring Complex Systems in Chemical Engineering - the Multi-scale Methodology, Chem. Eng. Sci., 59, 521 (2003). 

Albeit originally proposed for gas-solid fluidization, the concepts of structure resolution and compromise between dominant mechanisms embodied in the EMMS model can be generalized into the so-called variational multi-scale methodology (Li and Kwauk, 2003) and extended to other complex systems (Ge et al., 2007). One typical example out of these extensions is the Dual-Bubble-Size (DBS) model for gas-liquid two-phase flow in bubble columns (Yang et al., 2007, 2010). 

Ralf Kuriyel (Millipore Corporation) addressed some of the issues related to the use of Dean vortices, formed during the flow of fluids in curved conduits, to enhance the performance of cross-flow filters by increasing the back transport of solutes. Results were presented on coiled hollow fibers with a varying radius of curvature, fiber diameter, and solution viscosity, to characterize the relationship between the back transport of solutes and hydrodynamic parameters. A performance parameter relating back transport to the Dean number and shear rate was derived, and a simple scaling methodology was developed in terms of the performance parameter. The use of Dean vortices may result in membrane systems with less fouling and improved performance. 

Science in 2004 that have been dedicated to Complex Systems and Multi-scale Methodology, the forth issue of the 29th volume in Computers in Chemical Engineering on Multiscale Simulation published in 2005, the Springer-Verlag IMA edited book on Dispersive Transport Equations and Multiscale Models resulting from a related workshop, numerous workshops, and a topical conference on Multiscale Analysis in the 2005 AIChE meeting, just to mention a few. 

Bowman C, Newell AC (1998) Natural patterns and wavelets. Rev Modem Phys 70 289-301 Broughton JQ, Abraham FF, Bernstein N, Kaxiras E (1999) Concurrent eoupling of length scales Methodology and application. Phys Rev B 60 2391-2403 Bulatov V, Abraham FF, Kubin L, Devincre B, Yip S (1998) Connecting atomistic and mesoscale simulations of crystal plasticity. Nature 391 669-672... 

The titration method, based on rapidly varying the injection speed of reagent stock solutions into the mass spectrometer via a microreactor, offers a valuable alternative to more conventional laboratory-scale methodologies, provided that the selected supramolecular system is suitable to be studied by ESI-MS.60 The most important advantages of this approach are the limited sample... 

Since a furan ring constitutes a unique synthon (74MI1), calix[ ]furans, for which many preparative-scale methodologies are available, have been advantageously utilized for procuring some unique and often otherwise inaccessible chemical entities, particularly some targeted receptors. 

Li J, Kwauk M Exploring complex systems in chemical engineering—the multi-scale methodology, Chem Eng Sci 58 521-535, 2003. 

However, ideas from linear scaling methodologies can be used to develop ad hoc methods that are able to compute in a more approximate fashion the wavefunctimi for large systems. Essentially, aU linear scaling methods are based on the definitimi of a very localized basis set that reduces the number of matrix elements to be... 

In the last 10 years, there was a significant increase in the number of jobs that are intended to address the formation, the knowledge and molecular mechanism of these complexes, especially when involving natural polyelectrolytes. All the experience gained allowed the development of scaling methodologies applicable to macromolecules, especially enzymes with application in biotechnological processes. 

Standard multi-scale methodologies as presented in this review Chapter have developed significantly over the last 15 years. The method is able to describe the large deformation response of inelastic media with complex micro-structure, but certain key limitations exist. One such limitation is the description of shells or plates with complex micro-structure which cannot be captured in a layered-wise composite shell approach. Clearly a large munber of fiber-reinforced composite products fall into this category. This limitation exists as conventional first-order approximations can t pass second-order information, such as macroscopic deformation gradients (e.g. in bending), to the RVE boundaries. This information is required in shell theory. 

Pilch, M. and M. D. Allen, "A Scaling Methodology for Direct Containment Heating with Application to the Design and Specifications of an Experiment Program for Resolving DCH Issues," SAND 91-2784, 1991. 

---