Taylor-Aris theory

For axial dispersion in the micro-channel reactor, the usual relationships from Taylor-Aris theory were employed. In order to assess the performance of both reactor types, the widths of two initially delta-like concentration tracers are compared after they have passed through the flow domain. The results of this comparison are displayed in Figure 1.16. 

Thus, we recover the Danckwerts model only if no distinction is made between the cup-mixing and spatial average concentrations (with this assumption, the effective axial dispersion coefficient is given by the Taylor-Aris theory). This derivation also shows that the concept of an effective axial dispersion coefficient and lumping the macro- and micromixing effects into one parameter is valid only at steady-state, constant inlet conditions and when the deviation from plug flow is small. [Remark Even with all these constraints, the error in the model because of the assumption (cj) — cym is of the same order of magnitude as the dispersion effect ]... 

Gupta, V.K., and R.N. Bhattacharya. 1983. A new derivation of the Taylor-Aris theory of solute dispersion in a capillary. Water Resour. Res. 19 945-951. 

Edwards [105] has extended the macrotransport method, originally developed by Brenner [48] and based upon a generalization of Taylor-Aris dispersion theory, to the analysis of electrokinetic transport in spatially periodic porons media. Edwards and Langer [106] applied this methodology to transdermal dmg delivery by iontophoresis and electroporation. 

In a companion pair of contributions, Mauri and Brenner (1991a,b) introduce a novel scheme for determining the rheological properties of suspensions. Their approach extends generalized Taylor-Aris dispersion-theory moment techniques (Brenner, 1980a, 1982)—particularly as earlier addressed to the study of tracer dispersion in immobile, spatially periodic media (Brenner, 1980b Brenner and Adler, 1982)—from the realm of material... 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

The theoretical foundation for this kind of analysis was, as mentioned, originally laid by Taylor and Aris with their dispersion theory in circular tubes. Recent contributions in this area have transferred their approach to micro-reaction technology. Gobby et al. [94] studied, in 1999, a reaction in a catalytic wall micro-reactor, applying the eigenvalue method for a vertically averaged one-dimensional solution under isothermal and non-isothermal conditions. Dispersion in etched microchannels has been examined [95], and a comparison of electro-osmotic flow to pressure-driven flow in micro-channels given by Locascio et al. in 2001 [96]. 

The theoretical foundation for this kind of analysis was, as mentioned, originally laid by Taylor and Aris with their dispersion theory in circular tubes. Recent... 

The theory of diffusion in flowing fluids is first given by Taylor and Aris. According to Aris, a sharp band of solute, which is allowed to dissolve in a solvent flowing laminarly in an empty tube, can be described in the limit of a long column as a Gaussian distribution, the variance of which, o, in lengtii units is ... 

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