Open AccessAn approximate model for slow free-surface flows of a fluid through a highly porous medium accounting for the effect of a capillary fringe
Author(s) -
N. E. Leontiev,
E. I. Roschin
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1348/1/012012
Subject(s) - porous medium , mechanics , capillary action , free surface , capillary surface , thermal conduction , materials science , slip (aerodynamics) , porosity , thermodynamics , physics , composite material
The paper proposes a model for unconfined creeping flows of a thin fluid layer through a highly porous medium accounting for the effect of a capillary fringe at the free surface. To derive the model, we used the thin-layer approximation for the Brinkman equation with the Navier slip conditions at both the impermeable underlying surface and the free surface. The equation for the fluid layer thickness appears to be a special type of the non-linear heat conduction equation. We present similarity solutions that describe fluid propagation over a horizontal substrate.