Eur. Phys. J. Special Topics 143, 95–100 (2007) c  EDP Sciences, Springer-Verlag 2007 DOI: 10.1140/epjst/e2007-00076-0 T HE EUROPEAN P HYSICAL JOURNAL SPECIAL TOPICS Maximizing the dynamic permeability during occlusions R. Collepardo 1 and E. Corvera Poir´ e 1 1 Departamento de F´ ısica y Qu´ ımica Te´ orica, Facultad de Qu´ ımica, UNAM, Ciudad Universitaria, M´ exico D.F. 04510, M´ exico Abstract. We study the dynamic permeability of a viscoelastic fluid flowing in an occluded tube due to either central or peripheral obstructions. We find that for occluded systems, the dynamic permeability decreases. We also find that the value of the dynamic permeability for the occluded systems, can be made as large as the dynamic permeability for the non-occluded system when the proper frequency is imposed to the flow. 1 Introduction Occlusion of tubes have always represented a problem in a wide range of fields. From engines and filters to arteries and bronchia we can find a countless amount of systems in which the lack of movement of a fluid due to the presence of an obstacle results in the partial or total failure of a process. In particular, the occlusion of bio-tubes in the human body represent an important issue in many diseases. For instance, during the occlusion of arteries, blood decreases its velocity and, in critical cases, is effectively unable to flow through the remaining space. Such a lack of movement prevents irrigation and, in many cases, results in the eventual death of tissues. Recent experimental and theoretical work on viscoelastic fluids [1–6] have found that the dynamic permeability can increase orders of magnitude at certain frequencies. Since the dynamic permeability is a measurement of how easily a fluid can flow, the later results imply that it is possible to increase or decrease the resistance to flow by driving the fluid at certain frequencies. Based on this work, we model two types of occlusions. We predict that the dynamic permeability of a viscoelastic fluid, flowing through an obstructed tube, can largely be increased by imposing the right frequency to the flow. We compare the results obtained for the two types of occlusions studied, namely central occlusions and peripheral occlusions. 2 Model We consider occlusions that results from the partial obstruction of flow in two different ways. The first type of obstruction is one in which the walls of a tube have been internally engrossed and the fluid circulates through a tube that has effectively a smaller radius. We call this peripheral occlusion and we model the space of flow as the one inside a cylinder with a radius smaller than the one of the unobstructed tube. The second type of obstruction consid- ered is one in which the fluid has to flow between the walls of a tube and an obstacle inside it. We call this central occlusion and we model the space of flow as the one between two concentric cylinders.