Porosity effect on the linear stability of flow overlying a porous medium
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Porosity effect on the linear stability of flow overlying a porous medium Kirill Tsiberkina Perm State University, 614990, 15 Bukirev Street, Perm, Russia Received 18 March 2020 and Received in final form 7 May 2020 Published online: 10 June 2020 c EDP Sciences / Societ` a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We study how the stability of a homogeneous incompressible fluid flow over a saturated Brinkman porous medium is affected by a change in porosity. We produce neutral curves using the shooting method in the area of bimodality. When the porosity decreases, the topology of these curves changes because of the interplay between two instability modes. The long-wave instability is dominant if the medium is highly porous. In contrast, the short-wave instability is the most significant at low porosity because of high tangential stress at the fluid-medium interface. We identify a stability gap between the neutral curve branches within a narrow range of porosity values. The calculated results show the development and disappearance of this gap when the porosity changes.
1 Introduction The interaction between flows of free fluid and a porous medium is a valuable topic in fundamental and applied mechanics. It is important for describing transport processes during metal solidification and within, for example, energy-storage systems and living tissues [1]. One of the fastest-growing research areas concerns the development of effective fuel cells and flow batteries. Fuel cells should have an intensive mass transfer of reagents through the porous electrodes to the ion-exchange membrane and counterflow of the reaction products. Therefore, flow instability is crucial for the operation of these cells. The generation of vortices within the external flow and porous medium can prevent the ion and reagent exchange, and decrease the fuel-cell efficiency, respectively [2–4]. A specific feature of these systems is a possible destabilization by two independent mechanisms that occurs for both isothermal and convective flow. The first mechanism leads to the formation of large-scale long-wavelength vortices that cover the entire system. The second mechanism results in the development of short-wave vortices localized near the interface. The interplay of these two instability modes leads to a wide range of possible mechanical phenomena in two-layer systems [5–12]. Some previous works have examined the influence of inertial terms on the flow structure. A series of experiments on the particle-image velocimetry of flow coupled with massive rods forming a highly permeable medium is a
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also known [13, 14]. These studies considered a range of factors, including the interfacial coupling of the free fluid and filtration flow with and without an inertial effect. It has been shown theoretically that the inertial terms have a major role in the formation of boundary layers [15]. It has also been shown that these terms do not affect the overall flow ins
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