Two intersection points

Table 1.1. Comparison of the mean sizes and distribution widths at the two intersecting points A and B (Fig. 1.22) of shear thinning and Newtonian rheogramms...

The phase behaviour of many polymer-solvent systems is similar to type IV and type HI phase behaviour in the classification of van Konynenburg and Scott [5]. In the first case, the most important feature is the presence of an Upper Critical Solution Temperature (UCST) and a Lower Critical Solution Temperature (LCST). The UCST is the temperature at which two liquid phases become identical (critical) if the temperature is isobarically increased. The LCST is the temperature at which two liquid phases critically merge if the system temperature is isobarically reduced. At temperatures between the UCST and the LCST a single-phase region is found, while at temperatures lower than the UCST and higher than the LCST a liquid-liquid equilibrium occurs. Both the UCST and the LCST loci end in a critical endpoint, the point of intersection of the critical curve and the liquid liquid vapour (hhg) equilibrium line. In the two intersection points the two liquid phases become critical in the presence of a... 

The dynamic method permits the purification from better soluble impurities as well as continuous solubility measurements at the same time. An adsorption effect of the stationary phase which is used to precipitate the dyestuff on its surface is not found within the experimental accuracy. The measurements of l,4-bis-(n-alkylamino)-9,10-anthraquinone (with n-alkyl = butyl, octyl) show two intersection points in the plot of pressure versus concentration. 

To account easily for the velocity distribution influence, a very simple model is adopted. It consists in a set of parallel channels (see figure 12). Each channel corresponds to a flow trajectory. All the independent lengths of these trajectories i.e. the lengths between two intersection points are assumed to be equal to a mean channel length L. Using this model, Carbonell (198I) derived an approximate expression for the area and time-averaged value of the axial dispersion coefficient... 

The free path between two intersection points along the flow trajectories is assumed to be constant and equal to L. Actually in a trickle bed, the free path varies randomJy. This simplification will require to relate somewhat empirically L to the operating conditions (see Eq. 33). 

Circle method performs a circle fitting for the detected drop profile. The static contact angle is calculated between the baseline and the tangent of flie fitted circle at the contact points, which are the two intersection points of the baseline and the fitted drop profile. 0/2 method and circle fitting method are suitable for surfaces with small contact angles or when very small drop volumes are used because they assume no gravitation effect on the drop shape. 

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