Particle critical cracking thickness

CCT, critical cracking thickness Boltzmann constant (1.381x10 local permeability [m ] fracture resistance [N m ] average permeability in/of compact [m ] particle shape factor compact thickness [m] initial particle number concentration [m refractive index of particle material refractive index of dispersion material number density of ion i dimensionless number dimensionless number Stokes number Peclet number capillary pressure [N-m ] dynamic pressure [N m ] local liquid pressure in the compact [N-m local solid pressure in the compact [N-m ] superficial fluid velocity [m-s q gas constant [J K ] centre to centre distance [m]... 

The microstructure of a sol, in terms of the nature and concentration of sol particles, significantly affect a membrane s properties such as average pore diameter and pore size distribution. Other critical parameters are the temperature and rate of evaporation used in the drying and calcination steps. Even though it is economical to obtain the final product form quickly, too rapid a drying rate forms cracks in the membrane. Crack formation is also dependent on thickness of the membrane. The work of Cini et al. [49], who prepared supported microporous y-A C membranes as catalyst supports, illustrates many of these effects. 

The four wear mechanisms described in this section all lead to Archard s law, but the physical interpretation of the wear coefficient differs. In the adhesive wear model the wear coefficient expresses the probability that an adhesive junction leads to formation of a wear particle. In the abrasive wear model the wear coefficient depends only on the geometry of the abrasive. The wear coefficient in delamination wear characterizes the critical number of cycles leading to fatigue fracture of microscopic subsurface cracks. Finally, the wear coefficient in oxidative wear includes the growth constant and the critical thickness of a surface oxide film. 

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