Porous media are ubiquitous.
The sponge in the kitchen, the lung tissue, the human skin, all of them are porous. They are full of holes like a Swiss cheese and they have remarkable properties due to their structure.
Mathematicians from the Max Planck Institute for Marine Microbiology in Bremen and their colleagues from the University of Wroclaw in Poland took a close look at the characteristics of perforated matter and defined a novel criterion for the homogeneity of these systems. According to their findings a large number of old model calculations published so far do not meet this standard and are inaccurate.
Not only pure academic curiosity is the reason that scientists are interested in the mathematics of these strange materials. In nature porous surfaces are involved in the decomposition of chemical compounds and natural products. Marine aggregates in the oceans take part in the release of carbon dioxide. Today's modern industry is seeking for new technology in hydrology, oil and gas production, in textile engineering and many more applications. The calculations of heat and mass transfer through porous systems are still a challenge in process engineering. How fluids and gases flow through complex channels is a demanding task for science and engineering. The systems under consideration may be very large like the continental shelf from which almost half is made of permeable sands.
Prof. Dr. Arzhang Khalili from the Max Planck Institute for Marine Microbiology in Bremen poses the crucial question:" What is the minimum size of the model system in order to be able to predict the behavior of the particles in the real world?" The underlying basic assumption is that the porous material has to be homogeneous. Large model systems demand high computational power and therefore the systems were kept as small as possible. With many intensive numerical calculations Arzhang Khalili and his polish colleagues Zbigniew Koza and Maciej Matyka proved that most model systems published in the scientific literature were too small. " The size of the model system must be at least 100 times larger than the mean grain size. We checked old publications dating back 17 years and found that the majority of them did not fulfill this standard. According to our study almost all of them have to be recalculated", states Professor Khalili.
Dr. Manfred Schloesser | idw
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