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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Journal of Porous Media
Импакт фактор: 1.752 5-летний Импакт фактор: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Печать: 1091-028X
ISSN Онлайн: 1934-0508

Выпуски:
Том 23, 2020 Том 22, 2019 Том 21, 2018 Том 20, 2017 Том 19, 2016 Том 18, 2015 Том 17, 2014 Том 16, 2013 Том 15, 2012 Том 14, 2011 Том 13, 2010 Том 12, 2009 Том 11, 2008 Том 10, 2007 Том 9, 2006 Том 8, 2005 Том 7, 2004 Том 6, 2003 Том 5, 2002 Том 4, 2001 Том 3, 2000 Том 2, 1999 Том 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.v16.i1.40
pages 29-40

AN ANALYTICAL EXPRESSION FOR THE DISPERSION COEFFICIENT IN POROUS MEDIA USING CHANG'S UNIT CELL

Helen D. Lugo-Mendez
Departamento de I.P.H., Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, Mexico, D.F., Mexico
Francisco J Valdes-Parada
Universidad Autonoma, Metropolitana-Iztapalapa, Col. Vicentino, Mexico
J Alberto Ochoa-Tapia
Departamento de I.P.H., Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340, Mexico, D.F., Mexico

Краткое описание

Mathematical modeling of transport phenomena in hierarchical systems is often carried out by means of effective medium equations resulting from upscaling techniques. For the case of convection and diffusion taking place at the pore scale, the upscaled model is expressed in terms of a total dispersion tensor, which encompasses the essential features from the microscale. Several theoretical and experimental works have evidenced that the dispersion coefficient follows a power-law dependence with the particle Peclet number. In this work, we show that such functionality can be derived analytically using the method of volume averaging with Chang's unit cell. Our derivations lead to an expression for the dispersion coefficient that reduces to the classical result by Maxwell under purely diffusive conditions. Interestingly, the dispersivity is found to follow a nontrivial functionality with the particle Peclet number. The predictions from our analytical expression are compared with those obtained by solving the same closure problem in periodic unit cells showing, in general, good agreement, especially for homothetic unit cells.


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