Extension of Darcy-Brinkman Equations to Unsaturated Domain

Abstract

The objective of this paper is to extend the conventional Darcy-Brinkman equations, which are applicable only to saturated porous region, to unsaturated region because the Darcy-Brinkman equations for the unsaturated region have not be proposed yet. The conventional equations are derived by spatially averaging the Navier-Stokes equations over the saturated domain. Similarly, the extension of the Darcy-Brinkman equations to the unsaturated domain is achieved by spatially averaging the Navier-Stokes equations over the partially saturated porous domain. The extended equations include the time-derivative of volumetric water content in the continuity equation and reveal that viscous and inertia terms and the term derived from the Darcy's law in the equation of motion reflect the characteristics of partial saturation of voids in porous media.