Permeability, tortuosity, and attenuation of waves in porous materials

Wilmański, K.

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Tytuł artykułu

Permeability, tortuosity, and attenuation of waves in porous materials

Autorzy

Wilmański K.

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Warianty tytułu

Dyfuzyjność, krętność i tłumienie fal w materiałach porowatych

Języki publikacji

Abstrakty

The paper contains a consistent presentation of the construction of a linear poroelastic model and its applications in the theory of acoustic waves. The main purpose of this presentation is the discussion of material parameters describing the diffusion. This concerns particularly the permeability and tortuosity. In Section 2 we mention a few examples of porous systems in which diffusion processes play an important role. Section 3 contains a concise description of the two-component model describing saturated porous materials with diffusion. We point out the main features of such a system with the special emphasis of relative motion of components and changes of porosity. As a special case the governing equations of Biot's model are presented. In Section 4 we discuss the notions of permeability, hydraulic conductivity and tortuosity. In particular the notion of the tortuosity tensor is introduced. Section 5 is the primer of the nuclear magnetic resonance method of experimental determination of permeability and tortuosity in various porous materials. Finally, Section 6 contains some issues concerning the propagation of monochromatic waves and, in particular, an influence of tortuosity on speeds and attenuation.

Praca zawiera zwięzłą prezentację konstrukcji liniowego modelu porospężystego i jego zastosowania w teorii fal akustycznych. Głównym celem tej prezentacji jest dyskusja parametrów materiałowych opisujących dyfuzję. Dotyczy to w szczególności dyfuzyjności i krętności. W rozdziale 2 przytaczamy kilka przykładów ośrodków porowatych, w których dyfuzja odgrywa ważną rolę. Rozdział 3 zawiera zwięzły opis modelu dwuskładnikowego dla nasyconych ośrodków porowatych z dyfuzją. Uwypuklamy główne cechy takiego układu ze szczególnym uwzględnieniem ruchu względnego składników i zmian porowatości. Jako przypadek szczególny przedstwiane są równania modelu Biota. W rozdziale 4 dyskutujemy pojęcia dyfuzyjności, przewodnictwa hydraulicznego i krętności. W szczególności wprowadzamy pojęcie tensora krętności. Rozdział 5 zawiera elementarne wiadomości dotyczące metody nuklearnego rezonansu magnetycznego w zastosowaniu do eksperymentów określających dyfuzyjność i krętność w różnych materiałach porowatych. Wreszcie rozdział 6 zawiera pewne zagadnienia związane z propagacją fal monochromatycznych, a w szczególności wpływu krętności na prędkości propagacji i tłumienie.

Słowa kluczowe

porous media diffusion permeability tortuosity acoustic waves

ośrodki porowate dyfuzja przepuszczalność krętność fale akustyczne

Wydawca

Oficyna Wydawnicza Uniwersytetu Zielonogórskiego

Czasopismo

Civil and Environmental Engineering Reports

Rocznik

2010

Tom

No. 5

Strony

9--52

Opis fizyczny

Bibliogr. 91 poz., rys., tab., wykr.

Twórcy

autor

Wilmański K.

ROSE School, c/o Eucentre, Via Ferrata 1, 27100 Pavia, Italy Institut für Thermodynamik und Verfahrenstechnik, TU Berlin, Str. des 17. Juni 135, 10623 Berlin, Germany, krzysztof_wilmanski@t-online.de

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