Studia Geotechnica et Mechanica, Vol. XXVII, No. 1–2, 2005 CORIOLIS EFFECTS DURING FLUID FLOW THROUGH ROTATING GRANULAR POROUS MEDIA EUGENIUSZ SAWICKI, CHRISTIAN GEINDREAU, JEAN-LOUIS AURIAULT Laboratoire Sols, Solides, Structures Domaine Universitaire, BP53, 38041 Grenoble Cedex 9, Prance. E-mails: Jean-Louis.Aurialut@hmg.inpg.fr. Tel. +33 4 76 82 51 68. Fax: +33 4 76 82 70 43 Christian.Geindreau@hgm.inpg. fr. Tel. +33 4 7682 51 76. Fax: +33 4 76 82 70 43 Abstract: Recently, the filtration law of an incompressible viscous Newtonian fluid flowing through a rigid non-inertial porous medium (e.g. a soil sample placed in a centrifuge basket) which takes into account the Criolis effects was developed by using an upscaling technique [2], [3], [7]. The structure of the law obtained is similar to that of the Darcy’s law but the permeability tensor depends on the angular velocity ω of the porous matrix, i.e. on the Ekman number Ek. It satisfies the Hall–Onsager’s relation and is a non-symmetric tensor. The present study aims at quantifying more precisely the Coriolis effects in a porous medium. For this purpose we performed some 3D numerical simulations for the flow through rotating periodic array of spheres. Our numerical results clearly show the influ- ence of the Coriolis effects on the permeability at large Ekman number ε << Ek –1 << 1 and Ekman number O(l ). These results are analyzed according to the geometrical properties of the packings of spheres: soild volume fraction, arrangement and size. Under particular conditions, we finally show that in the first approximation the flow through rotating granular media can be described by a modi- fied Darcy’s law including a “macroscopic Coriolis force” which brakes and deviates the flow. 1. INTRODUCTION In the absence of external forces, the steady-state slow flow of an incompressible liquid through a rigid inertial porous matrix is described by the well-known Darcy’s law, in which the tensor of intrinsic permeability K [m 2 ] is positive and symmetri- cal. In many practical applications in engineering and geophysics [8], [9], [11], [12], [13], the rigid porous matrix rotates with an angular velocity ω with respect to a Galilean frame. The main issue is to determine the consequences of the angular ve- locity in Darcy’s law. Recently, [2], [3], [7], the filtration law in a rotating porous medium was rigorously derived by upscaling the physics at the pore scale. A deter- ministic upscaling technique was used, namely the homogenisation method of mul- tiple scale expansion for periodic structures [1], [4], [10]. Due to this the steady- state slow flow of an incompressible liquid through a rigid porous matrix within a non-Galilean framework is described by Darcy’s law, but the permeability tensor K rot presents the following remarkable properties: it depends upon the angular ve- locity of the porous medium through the Ekman number Ek = µ (2ρω l 2 ) which measures the ratio of the viscous term to the Coriolis term in the Navier–Stokes equations, where l is a characteristic length of the porous medium and ρ is the fluid