Page path:

21.08.2009 What sponges, beards and the lung have in com­mon

Max Planck mathematicians and their colleagues in Poland developed a novel criterion for the calculation of mass and energy transport in porous systems
 
What sponges, beards and the lung have in common

Max Planck mathematicians and their colleagues in Poland developed a novel criterion for the calculation of mass and energy transport in porous systems

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.
Examples of different porous systems: sponge, beard, lung.
Computational analysis of the path of two particles traveling through a porous medium. Two different alignments with the gravitational field are depicted. The model system should be homogenous and should have similar properties in all directions (Isotropy). The opposite (Anisotropy) is observed. Anisotropy is used to describe the variations of properties depending on the directions. As shown here the model system is too small. Therefore, the particles travel on different paths. The model system has to be at least 100 times larger than the characteristic grain size.
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.

Manfred Schlösser




For more information please contact
Prof. Dr. Ar­zhang Khalili
+49 421 2028636
E-Mail akhalili@mpi-bre­men.de

or the press officers
Dr. Man­fred Schloesser +49 421 2028704 mschloes@mpi-bre­men.de
Dr. Susanne Borgwardt +49 421 2028704 sborgwar@mpi-bre­men.de

Original publication
Koza, Z. Matyka, M, & Khalili, A. (2009): Fi­nite-size an­iso­tropy in stat­ist­ic­ally uni­form por­ous me­dia. Phys. Rev. E. 79. 066306-1 - 066306-7.
 
Back to Top