Compressible Advection Through an Elastomer Seal: A Porous Media Approach to Seals for Space Applications

Gas permeability characterization is of the utmost importance in space seals applications. Space seals must maintain acceptable mass losses in harsh environments where temperatures widely vary under vacuum conditions. Silicone elastomers are commonly used in space as they offer significant sealing performance at temperature extremes and are capable of meeting stringent outgassing requirements necessary for vacuum environments. Traditional models of leak rates solely rely on a diffusive transport mechanism; mass is transported across a membrane through molecular flow induced by a concentration gradient under isostatic conditions. In the application of space seals, the pressure gradients are large, resulting in advection dominated transport. Conventional applications of advection utilize Darcy’s law; however, the fluid is assumed incompressible and fails to capture the nonlinear pressure gradient under compressible situations. Consequently, employing Darcy’s law incorrectly predicts the leak rate. A novel model in compressible advection through an elastomer seal is presented. A phenomenological approach is taken to determine the specific discharge. Through the conservation of mass, the governing equation for pressure is derived. An exact analytical solution exists for one-dimensional flow in the form of a Generalized Emden-Fowler equation and as a result, an analytical expression for mass flow is developed. A series of experiments is presented to deduce permeability constants and Klinkenberg parameter of silicone S0383-70 under one-dimensional flow conditions. The leak rates of the model and experiments are compared. Through the presented compressible advection model, the mass leak rate of any candidate seal geometry can be evaluated.