Scale-Dependent Slip at Porous Interfaces: micro-PIV Measurements of Beavers–Joseph and Saffman Coefficients

Abstract

The interaction between a free-flow and a porous medium is frequently modeled using interfacial slip conditions, such as the Beavers–Joseph formulation. Despite extensive theoretical and numerical studies, the experimental determination of slip coefficients and their dependence on pore-scale geometry and averaging procedures remains insufficiently constrained. In this work, flow coupling at a fluid–porous interface is investigated using μPIV measurements in Hele-Shaw-type microfluidic models. Both ordered and disordered porous media are examined, with bulk porosities of 55%, 75%, and 85%.  Pore-scale velocity fields are systematically upscaled via spatial averaging to the representative elementary volume (REV) scale, enabling direct quantification of slip velocities, interfacial velocity gradients, and the corresponding slip coefficients. The 
interfacial slip velocity is governed primarily by local pore geometry, whereas the Darcy velocity within the porous matrix depends strongly on bulk porosity and structural disorder. Both the Beavers–Joseph and Saffman slip coefficients vary not only with porosity but also with the size and shape of the averaging filter. At local and sub-REV scales, the two coefficients can differ by more than 100%, with convergence observed only after REV-scale averaging in low-permeability systems. In highly permeable ordered media, insufficient averaging can even yield non-physical negative slip coefficients. These findings show that slip coefficients are scale-dependent parameters rather than intrinsic material properties. Robust estimation therefore requires consistent REV-scale averaging and explicit reporting of the averaging procedure. More broadly, the results motivate standardized, geometry-aware protocols for determining and comparing interfacial slip conditions in porous media.