Taylor dispersion concept

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 ]... 

When the residence time becomes shorter, this approach becomes questionable for several reasons. For example, the asymptotic state may not have been reached yet, or the peaks may be unsymmetrical. These "short-time" situations may be encountered when trying to apply chromatographic concepts to the study of dispersion in connecting tubes, or in some apphcations, such as hollow-fiber liquid chromatography. Shankar and Lenhoff [77] have derived a solution in the time domain, using series expansion. This solution can be implemented by numerical computation for the determination of concentration profiles inside a tube coated with a retentive layer, when the fluid flow is laminar. This solution is valid for systems that are either short or long after the Taylor-Aris definition. 

The concept of temporal variations in concentration at the flow-through detector explains why pronounced skewed peaks are often observed in flow analysis, especially with loop-based sample introduction. Taylor assumed that dispersion is symmetric in relation to an observer located at the dispersing zone [55,56], but in practice the recorded peaks are usually characterised by a rise time much shorter than the fall time (see also Fig. 1.3e). This skew effect is explained by the fact that the front and trailing portions of the flowing sample, which relate to the rise time and the fall time, respectively, have different residence times in the manifold and are therefore subjected to different extents of dispersion. 

We now come to the final stages of morphology development (for disperse systems). Deformation and breakup of liquid droplets in a liquid matrix was first studied in series of articles by G.I. Taylor [40, 41] in 1932. Taylor first modeled the viscosity of emulsions and in a second article studied the deformation and breakup of liquid droplets. The basis of the work ofTaylor is again the concept of the interfacial tension between immiscible liquid phases (Section 6.3.2.1). Taylor [41] subsequently described experiments with paraUel-band (for shear flow) and four roller apparatus for extensional flow using individual droplets based upon combinations of... 

Various workers have proposed theoretical models to predict the flow behavior of polymer blends. Einstein studied the shear flow behavior of a suspension of rigid spheres in Newtonian fluids. Taylor (21, 22) extended this concept to include dispersions of one liquid in another liquid based on their shear viscosities and also accounted for circulation in the droplets. According to his model, for a conq>onent 2 which is dispersed in a conq>onent 1, the blend viscosity is given by the following equation ... 

These two conditions can be combined by the concept of travel time. Thus, Taylor s comment becomes relevant dispersion will appear diffusion-like if there is sufficient (diffusive) mixing between short and long travel time pathways. If there is insufficient mixing, dispersion will be primarily due to convection and probably will not look diffusive. 

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