Abstract
A one-dimensional model to determine the laminar flow of a fluid in a porous channel with wall suction or injection is proposed. The approach is based on the integration of the Navier–Stokes equations using the analytical solutions for the two-dimensional local velocity and pressure fields obtained from the asymptotic developments at low filtration Reynolds number proposed by Berman (J. Appl. Phys. 24 (1953) 1232) and Yuan and Finkelstein (Trans. ASME 74 (1956) 719). It is noticeable that the resulting one-dimensional model preserves the whole flow properties, in particular the inertial terms which can affect the wall suction conditions and the spatial distribution of the growing particle cake layer at the wall encountered in filtration processes. The model is validated in the case of a single porous channel of rectangular or circular cross-section with uniform or variable wall suction. Then the model is applied to a two-dimensional multi-channel system which consists of a great number of adjacent entrance and exit channels connected by a filter porous medium. It is shown that the effect of non-uniform boundary conditions and the influence of heterogeneous geometrical characteristics on the heterogeneity of the fluid flow structure can be studied using such a model.
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