Mixed Poiseuille-Knudsen flow model for Gas Liquid Displacement porometry data treatment

A New Interpretation of Gas Viscosity for Flow through Micro-Capillaries and Pores

The Hagen-Poiseuille equation for gas flow had never been derived theoretically; it is rather a simple analogy of the same for liquid flow, and "gas viscosity" is a measure for overall resistance to flow. In this work, experimental flow data for different gases through capillaries and porous media, reported in literature by different groups, including those measured and treated by Knudsen are treated with Hagen-Poiseuille equation, but taking "gas viscosity" as an adjustable parameter. It is found that, at constant temperature, there exists an unambiguous relation between the viscosity (µ) of a given gas, and the product of average pressure (P_av ) and capillary diameter (D). In addition, for P_{av *} D < 0.01, a universal linear relation exists between µ/M^0.5 (where M is molecular mass) for different gases and the parameter P_{av *} D. The new interpretation of gas viscosity avoids the differentiation of regimes into "Knudsen" and "viscous" flow as it is frequently done in literature. The concept can be applied to obtain a reliable data base for gas viscosities in different fields of applications, for example in microfluidic systems or the analysis of pore size distributions of filters and membranes by gas flow porometry.