Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

“…Ochoa-Tapia and Whitaker [23,24] deduced a discontinuity condition of the shearing stress at a liquid-porous layer interface. The derivation of the latter condition, which the authors refer to as "jump momentum boundary condition at a fluid-porous dividing surface" based on a averaging procedure of Navier-Stokes equations, velocity field, pressure and stress tensor over liquid outside the porous layer, the liquid inside the porous layer, and the boundary in between.…”

“…The derivation of the latter condition, which the authors refer to as "jump momentum boundary condition at a fluid-porous dividing surface" based on a averaging procedure of Navier-Stokes equations, velocity field, pressure and stress tensor over liquid outside the porous layer, the liquid inside the porous layer, and the boundary in between. Ochoa-Tapia and Whitaker [23,24] defined superficial and intrinsic (actual) velocities of the liquid. Similarly they introduced superficial and intrinsic pressures and stress tensors.…”

“…It is easy to see that the ratio of «superficial» and «intrinsic» values is equal to the porosity. The derivations of "jump momentum boundary condition" has been undertaken in [23,24] in parallel with the derivation of Brinkman's equation. In the case of cylindrical interface the jump boundary condition of intrinsic tangential stress on the liquid-porous layer interface takes the following form [23,24]:…”

Macroscopic modeling of columnar dendritic solidification

“…For small evolving heterogeneities, the dendritic layer can be viewed as homogeneous and therefore averaged properties are constant whatever the size of the averaging volume. For large τ , scale separation is not satisfied, and more theoretical work is needed to explore alternative descriptions using for instance deforming averaging volume [29] or jump boundary condition [30][31][32]. Between these two limiting situations, i.e.…”

“…However, if we consider the length scale constraint (18), we can estimate that the two last terms in equation (30) are small compared to the area integral friction term, leading to a classical boundary value problem [37]. This is obviously an approximation since, due to evolving heterogeneities, (18) is not valid everywhere along the dendrites.…”