Cylinder, infinite absence

Assuming isothermal samples and the absence of external heat and mass transport resistances, Pick s second law may be used to calculate the diffusion coefficient for the species in the pores as they are being taken up. Solutions of the equation describing the diffusion have been developed for various cases (33). In many instances adsorbent particles are not uniform spheres, and it is therefore pertinent to consider the extent to which the solution of the diffusion equation may be affected by the particle shape. The expressions for a parallel-sided slab, an infinite cylinder, and a cube have been considered. 

The subj t of adhesive contact mechanics may be said to have started when Kendall (//), solving the problem of the adhesive contact of a rigid flat cylinder punch indenting the smooth plane surface of an elastic medium, demonstrated that the border of the contact area can be considered as a crack tip. The more complex problem of a spherical punch was solved in 1971 by Johnson, KendaU and Roberts (72). The JKR theory predicts the existence of contact area greater then that ven by the elastic contact Hertz s theory. The molecular attractive forces are responsible for this increase and, even in the absence of external compressive loading, the contact area has a finite size. Separating the two solids requires the application of an adherence force despite the existence of infinite normal stresses in the border of the contact area. 

This general expression, which applies to infinite slabs, long cylinders, and spheres, is analogous to Eq. (3.2.29) obtained for shrinking particles. It is again seen that the time required to reach a certain conversion is the sum of the time to reach the same conversion in the absence of diffusional resistance [Eq. (3.3.1)] and that for pure diffusion control [Eq. (3.3.17)]. 

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