The effective viscosity μe 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 μe = (7.5+3.4−2.4)μf, where μf was the viscosity of the fluid. The Reynolds number, based upon the square root of the permeability, was 17.
In order to understand how a particulate plug may evolve within the flow of an essentially homogeneous suspension, we have developed a fluid-particle flow model. This theoretical model is based upon a monodisperse collection of rigid, spherical particles suspended in an incompressible, Newtonian liquid. Balance equations of mass and momentum are given for each phase within the context of a continuum mixture theory. The interactions between the phases are dominated by interfacial drag forces and unequilibrated pressure forces. The pressure associated with the solid particles is given by a phenomenological model based upon the flow dynamics. Of primary concern is the calculation of solid particle concentrations within a flow field to indicate the initiation of a particulate plug.
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