Linearized description of the non-isothermal flow of a saturated vapor through a micro-porous membrane

The one-dimensional flow of a fluid near saturation through a micro-porous membrane is considered. Upstream of the porous membrane the fluid is in a state of saturated vapor. Downstream, the fluid is in a state of unsaturated vapor. Due to the Joule-Thomson effect, the fluid is cooler at the downstream side of the membrane than at the upstream side. Due to the temperature difference and the heat conduction in downstream direction, the saturated vapor condenses fully or partially and the fluid re-evaporates further downstream within the membrane. The flow process is described taking into account (i) the temperature difference due to the Joule-Thomson effect, (ii) the capillary pressure across a curved meniscus in the porous medium and (iii) the vapor pressure reduction at a curved meniscus given by Kelvin’s equation. Depending on the material properties of the fluid and the membrane and on the pressure difference, different types of flow occur. These flow types are analyzed, expressions for the mass flux are given for each case and a flow map is drawn to show the conditions under which the different types of flow occur. A comparison is made with isothermal models and with experimental data from the Preprint submitted to Elsevier Science 30th May 2007 Manuscript