Interfacial curvature definition

It is quite noticeable that these figures are very close to those known for melted paraffins of similar chain lengths. Then the development of NMR studies of deuterated moleoules and of NMR permitted to show that the amplitude of the deformations are about the same in all structures, ordered liquid crystals as well as in disordered micellar solutions. Thus there does not appear any definite correlation between one structure and the molecular behavior in it. The chains are about equally disordered in all structures, in spite of important changes of interfacial curvature and mean area per molecule at the interface. 

FIGURE 7.27. Definition of the interfacial mean curvature (H) and Gaussian curvature (K) and the packing parameter (P). Reproduced with permission from WILEY-VCH Verlag GmbH Co.). 

Performing macro-scale experiments it has been observed that the normal surface tension force induces higher normal stresses in the fluid on the concave side of the interface than on the other fluid on the convex side of the interface. In a micro-scale view we may say that this interfacial tension force is exerted by the interfacial material lying on the convex side of the surface upon the material lying on the concave side. The normal component of the surface force is thus frequently (not always ) defined positive into the mean curvature of the surface, in line with the physical observations. The direction of the normal component of the interface force given by (3.9) is determined by two factors, the interface normal unit vector n/ which we have defined positive into the curvature, and the mean curvature variable which we have chosen to define as an absolute value. That is, the variable used here determining the mean curvature of the surface Hi = ( i + K2)/ 2) is consistent with the definition... 

Eq. (2.18) is the exact definition of the experimental relationship for the determination of surface tension by measuring the corresponding pressure differences and radii of curvature. This relationship is the basis of many experimental surface and interfacial tension methods measuring for example the volume of detaching drops (Section 5.2), the pressure inside bubbles (Section 5.3) or drops (Section 5.5), and the shape of sessile or pendent drops (Section 5.4). 

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