Concentric elliptical profiles

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 86). Multiple path, molecular diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral spreading. Consequently, the initially circular spots become progressively elliptical in the direction of flow. Efficiency and resolution are thus impaired. Elution must be halted before the solvent front reaches the opposite edge of the plate as the distance it has moved must be measured in order to calculate the retardation factors (Rf values) of separated components (p. 86). 

Two models of two-dimensional band broadening were established by Belenky et al. and by Mierzejewski. In these models, nonlinearity of the adsorption isotherm was neglected so that elliptical spots only, with symmetrically distributed concentration (as shown in Fig. la), could be modeled. We will now focus our attention on the effect of the adsorption mechanism on the concentration profiles of chromatographic bands. 

At deformations lower than 300-400 %, the SAXS patterns tend to assume an elliptical geometry characterized by a concentration of intensity above and below the equatorial region (Fig. 11.9b, c, b, c ). The corresponding azimuthal intensity profiles show broad maxima centred on the meridian (j = 0° and 180°) for the... 

These observations can be explained on the basis of the weak interface in the transition zone (porous layer in Figure 2.5) and the Cook-Gordon crack arrest mechanism [82] shown in Figure 3.40. The stress field ahead of the elliptical crack tip consists ofthe familiar stress concentration profile in the direction of the external tensile stress (/direction), and a tensile stress field in the... 

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