Comprehensive three-dimensional

Figure 9.10 Three-dimensional representation of the data volume of a tryptic digest of ovalbumin. Series of planar slices through the data volume produce stacks of disks in order to show peaks. Reprinted from Analytical Chemistry, 67, A. W. Moore Jr and J. W. Jorgenson, Comprehensive three-dimensional separation of peptides using size exclusion chromatogra-phy/reversed phase liquid chromatography/optically gated capillary zone electrophoresis, pp. 3456-3463, copyright 1995, with permission from the American Chemical Society.

A. W. Moore, Jr and J. W. Jorgenson, Comprehensive three-dimensional separation of peptides using size exclusion chromatography/reversed phase liquid chromatography/ optically gated capillary zone electrophoresis . Anal. Chem. 67 3456-3463 (1995). 

A coupled analysis need not be all encompassing. For example, a two dimensional plane frame analysis of a building employing two or more degrees of freedom is considered a coupled analysis approach. Separate plane frames for each orthogonal horizontal direction can be used in lieu of a single comprehensive three dimensional model. Refer to Section 6.6.2 for a discussion on modeling considerations for this type of structure. 

Huyakorn, P. S., Wu, Y. S., and Panday, S., 1992, A Comprehensive Three-Dimensional Numerical Model for Predicting the Transport and Fate of Petroleum Hydrocarbons in the Subsurface In Proceedings of the Petroleum Hydrocarbons and Organic Chemicals in Groundwater Conference, Water Well Journal Publishing Company, Dublin, OH, pp. 239-253. 

In overcoming the shortcomings of the earlier models, Dave et al. [21,22] proposed a comprehensive three-dimensional consolidation and resin flow model that can be used to predict the following parameters during cure (1) the resin pressure and velocity profiles inside the composite as a function of position and time, (2) the consolidation profile of the laminate as a function of position and time, and (3) resin content profile as a function of position and time. 

Moore and Jorgenson combined the rapid two-dimensional separation achieved by LC-CZE with SEC to make the first comprehensive three-dimensional separation involving an electrodriven component in 1995. Size exclusion chromatography separated the analytes over a period of several hours while the reverse phase HPLC-CZE combination separated components in only 7 min. A schematic diagram of the three-dimensional SEC-reverse phase HPLC-CZE instrument is shown in Figure 9.9 (18). A dilution tee was placed between the SEC column and the reverse phase HPLC injection loop in order to dilute the eluent from the SEC column, since it contained more methanol than was optimal for the reverse phase HPLC column. 

As previously mentioned, the analysis of microfluidic systems can be rather difficult for a variety of reasons. The direct implementation of the Navier-Stokes equations toward surface-directed microfluidic systems requires careful attention when considering the advection of the free surface and the associated curvature of this surface. Consequently, sophisticated computational fluid dynamics software packages are required for a comprehensive three-dimensional analysis of the fluid transport within surface-directed microfluidic devices. However, a time-consuming comprehensive analysis may be beyond the requirements of designing and manufacturing functional surface-directed microfluidic platforms. Consequently, empirical approximations and scaling arguments are commonly used in the characterization of microfluidic physics. 

In addition to the polarization curve, the comprehensive three-dimensional model also allows for the assessment of important information about the detail of transport phenomena inside the fuel cell. These transport phenomena are the velocity flow field, variation of local concentration of gas reactants, temperature field, local current densities, and potential field. 

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