Dispersion Taylor-Aris

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. 

As mentioned earlier, in curved channels a secondary flow pattern of two counter-rotating vortices is formed. Similarly to the situation depicted in Figrue 2.43, these vortices redistribute fluid volumes in a plane perpendicular to the main flow direction. Such a transversal mass transfer reduces the dispersion, a fact reflected in the dependence in Eq. (108) at large Dean numbers. For small Dean numbers, the secondary flow is negligible, and the dispersion in curved ducts equals the Taylor-Aris dispersion of straight ducts. 

Commenge et al. extended the one-dimensional model of reacting flows to include Taylor-Aris dispersion, i.e. they considered an equation of the form... 

Pe Modified Peclet number containing the Taylor-Aris dispersion... 

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... 

Despite the small dimensions, conventional models for dispersion have been applied to microreactors. Since flow is laminar, a Taylor-Aris or shear-induced dispersion model generally describes dispersion. Beard has applied the Taylor-Aris dispersion model to... 

Ghosal has also examined electrophoretic flow in microchannels using a Taylor-Aris dispersion model. In both of the above cases Taylor-Aiis models were reported to work well. On the other hand, Ni, Seebauer and Masel found that at high flow rales over... 

Hoagland, D.A., and R.K. Prud homme. 1985. Taylor-Aris dispersion arising from flow in a sinusoidal tube. AlChEJ. 31 236-244. 

This is termed the Taylor-Aris dispersion coefficient, and is simply the sum of the axial molecular diffusion coefficient and the Taylor radial dispersion coefficient. As can be seen, at large Peclet numbers D ffD increases as the square of the Peclet number (the Taylor dispersion limit), and at small Peclet numbers D ifD approaches 1 (the convective axial diffusion limit). 

This 1-D convection-diffusion equation has features of the Taylor-Aris dispersion equation. However, in contrast to Taylor-Aris, here >eff is a function of temperature and the axial coordinate, as it depends on both D and Up. When/ is a linear function of the axial dimension. Equation 38.39 can be solved in closed form subject to the form of D s. IfT>eff is uniform, the solution is a Gaussian with peak variance = 2Deffrfoc, where Tfoc = l/2 ovo d//dJc. If Detr is also a linear function of X, the solution is... 

Huber, D.E. and Santiago, J.G., Taylor-Aris dispersion in temperature gradient focusing. Electrophoresis, 2007, 28 2333-2344. 

Hydrodynamic dispersion refers to the stretching of a solute band in the flow direction during its transport by an advecting fluid. Variation in the fluid velocity across the channel cross section leads to such band broadening which is often quantified in terms of the Taylor-Aris dispersion coefficient. 

The process of solutal spreading in pressure-driven flows was first analyzed by Sir Geoffrey Taylor in 1953. He showed that the variation in the fluid velocity over the channel cross section in these systems spreads out an analyte band as advection proceeds in the flow direction. This advective spreading is ultimately limited by molecular diffusion across streamlines and may be described in terms of an effective dispersivity [3], often referred to as the Taylor-Aris dispersivity (K). The Taylor-Aris dispersivity determines the rate at which the spatial variance of the solute slug grows in the axial direction ([Pg.1314]

It is important to note that the Taylor-Aris dispersion hmit for band broadening described above is reached only after solute molecules have a chance to diffuse across the wider channel... 

Under these steady-state conditions, the solute slug acquires a constant velocity in the channel and hence grows linearly in time yielding the following expression for the Taylor-Aris dispersivity ... 

Diffusion coefficients of solids into fluids can conveniently be measured by capillary evaporation [109-111] or evaporation from flat plates or surfaces of one sort or another. The Taylor Aris dispersion technique [112-115] can be used not only for solids but also for any component which will dissolve in the solvent of interest. The above two techniques are probably the ones most frequently used in connection with near-critical solvents. 

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