The application of percolation theory in powder technology

It is about 10 years ago since the author of this invited paper started to apply percolation theory in the held of (pharmaceutical) powder technology. Thus the invited paper summarizes 10 years of experience in the applicatio n of percolation theory. The goal of the paper is to share this experience and to stimulate a broader use of percolation theory. The application of pe rcolation theory is a fast growing held in very different areas of science and technology. However, percolation theory has nor yet reached as broad an application in the held of powder technology as it should deserve. For thi s purpose, within this article a strong emphasis is put on a condensed but still rigorous introduction to the concepts of percolation theory to facili tate a broader application in powder technology. In this respect it is impo rtant to get a deeper knowledge and understanding of the basic power law of percolation theory to describe a desired property X = S*(p - p(c))(q), whe re S* is the scaling factor, p is the (bond or site) occupation probability , p(c) is the percolation threshold and q is the critical exponent, close t o the percolation threshold. A prerequisite is a geometrical or a physical phase transition at p(c). An explicit statement about the nature of the per colation threshold phenomenon should be part of the system and model analyz ed. The question of the universal character of a critical exponent q, which depends only on the dimensionality d of a system, plays an important role as well as the concept of percolation threshold p(c). which reflects the mi crostructure of a system. Different tramples illustrate the successful appl ication of percolation theory in (pharmaceutical) powder technology, coveri ng important unit operations such as the compression of powder and the diss olution of an active substance from a binary powder compact, etc. Percolati on theory provides key tools for a more rational design of pharmaceutical d osage forms and for the development of robust formulations. Thus the develo pment time can be speeded up and time to market can be reduced. The trample s presented show the range of application and possible limitations of perco lation theory. An outlook is given for a broader application as well as for a possible fruitful application of percolation theory in nanoscience and n anotechnology.