Stress interfacial, distribution curve

Figure 4.17 Interfacial stress distribution curve of whiskers under different L/D ratios.

Figure 3.4 Distribution of interfecial shear stresses, t, and fibre tensile stresses, ay, in zones of combined elastic and frictional shear stress transfer. Po,P, Pi,and P3 indicate the distribution curves at increased stages of loading. 0, 02,03 indicate the a location of the interfacial zone v here debonding occurred.

There are different ways of counting particles to obtain the distribution. One can simply count the number of particles smaller than a specific size. This means that in the curve, a droplet of 0.1 pm will count for one, just as a droplet of size 10 pm. However, the amount of oil present in the 10-pm droplet is 100, or one million times larger. Such a distribution therefore stresses the presence of small particles. Another way is to not use the number of particles but the total interfacial area present on the particles. Since the interfacial area of a small droplet is much smaller than that of larger droplets, smaller droplets are counted less extremely, and the resulting distribution is more realistic. Remember that the amount of surfactant needed to stabilize the interface is proportional to the total interfacial area present on the droplets, and the total energy needed to put into the emulsion is proportional to the total interfacial area. As a third option, one can use the volume of the particles smaller than a specific size. In this case the distribution gives that total amount of oil that is present in small, medium or larger droplets. It depends on the application which type of distribution should be used. 

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