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

Abstract

A comprehensive methodology has been developed for treating Gas Liquid Displacement (GLD) porometry data with a flow model called Weber model (WM) describing mixed Poiseuille-Knudsen flow regime. The model has been applied in two options: i) considering that the gas viscosity in porometry experiments is the same as that available in reference books for Poiseuille flow regime and ii) equating the expression for Darcy coefficient in gas flow to that obtained in additional liquid permeability experiments and thus leaving the gas viscosity to be an adaptable parameter. In the analysis of GLD porometry data for a range of different microfiltration membranes, it is found that with the WM in both options identical relative pore-number distribution is estimated; and this distribution satisfactorily reproduces both dry and wet flow data from the GLD experiments. The absolute pore-number distributions obtained by the two options are quite similar, but differ in the absolute value of the pore numbers. The pore-number distribution obtained by the second option describes the liquid permeability well, while the first option fails. The WM as a method of GLD porometry data treatment is quite similar to the earlier introduced variable viscosity Poiseuille model (VVPM), and the variable viscosity from the latter model appears to be a combined effect of an uncertainty about actual gas viscosity and the contribution of Knudsen flow. It is concluded that a standard test method for determining pore-size distribution by GLD porometry must include prediction or description of liquid permeability of the membrane. Then, any acceptable gas flow model with adjusted Darcy coefficient obtained from liquid permeability experiment will be suitable for advanced GLD porometry data treatment, beyond the methods typically implemented in gas flow-based porometers, currently used in academia and industry.