A determination of the effective viscosity for the Brinkman–Forchheimer flow model

Abstract

The effective viscosity μ e for the Brinkman–Forchheimer flow (BFF) model has been determined experimentally for steady flow through a wall-bounded porous medium. Nuclear magnetic resonance (NMR) techniques were used to measure non-invasively the ensemble-average velocity profile of water flowing through a tube filled with an open-cell rigid foam of high porosity (ϕ = 0.972). By comparing these data with the BFF model, for which all remaining parameters were measured independently, it was determined that μ e = (7.5 +3.4 −2.4 )μ f , where μ f was the viscosity of the fluid. The Reynolds number, based upon the square root of the permeability, was 17.