Determination of the Darcy Permeability of Porous Media Including Sintered Metal Plugs

Abstract

Porous media have become of increasing importance in low temperature applications. In contrast to the usual Newtonian fluid flow near room temperature, the mass throughput characterization appears to be less certain at liquid He⁴ temperatures, in particular, in the superfluid He II range. In the present work, the Darcy permeability has been evaluated for laminar flow at very small velocities in Newtonian fluids. However, in the non-Newtonian He II superfluid, the Darcy permeability is not so readily obtainable from simple fluid flow experiments. In our experiments, sintered metal porous plugs with a nominal (filtration rating) size of the order 1 µm to 10 µm have been used. The characteristic length diagram for the equivalent Ergun particle diameter, the filtration rating, and the characteristic throughput length has been evaluated as a function of the Darcy permeability. This set of functions is seen to give a comprehensive picture of porous media throughput properties. In non-Newtonian super- fluid He II, the present work relies on the two-fluid model as the frame of reference. It is found that there exists an analog of Darcy’s law for the flow of the normal fluid component of He II. In this analog, the pressure gradient, mass flux, and the shear viscosity are replaced by the thermomechanical pressure gradient, normal fluid mass flux, and the normal fluid shear viscosity.