Modeling convection/diffusion processes in porous textiles with inclusion of humidity-dependent air permeability

A set of partial differential equations describing time-dependent heat and mass transfer through porous hygroscopic materials was developed. Water in a hygroscopic porous solid may exist in vapor or liquid form in the pore spaces or in bound form when it has been absorbed by the solid, which is typically some kind of hydrophilic polymer. Factors such as the swelling of the solid due to water imbibition, and the heat of sorption evolved when the water is absorbed by the polymeric matrix, were incorporated into the appropriate conservation and transport equations. A numerical code to solve the set of nonlinear coupled equations was developed, and applied to an experimental apparatus designed to simulate transient and steady-state convection/diffusion conditions for textile materials. Experimental measurements of air permeability and diffusion properties as a function of relative humidity provided fundamental data on the changes in transport properties as hygroscopic textiles fibers swell and decrease the free gas phase volume within the porous structure. When these relations were incorporated into the numerical model, it was possible to directly compare the predictions of the numerical code with results generated in the experimental apparatus. Results are shown for hygroscopic porous textiles under several conditions. Under pure diffusion, with no convective flows across the sample, the temperature changes of hygroscopic textiles subjected to step changes in environmental relative humidity are shown to agree with the numerical predictions. These temperature changes are due to sorption of water vapor from the flows on the two sides of the material, and relate to textile fiber equilibrium sorption isotherms and sorption kinetics, as well as the physical structure and thermal properties of the textile. Under conditions of both a concentration gradient and a pressure gradient across the fabric, which results in combined diffusion and convection, it is shown that the effect of fiber swelling, which results in significant changes in the resistance to convective flow, also has an effect on the resulting total mass flux across the textile layer.