Mrazík Lukáš, Kříž Pavel
Department of Computing and Control Engineering, University of Chemistry and Technology Prague, 166 28 Prague, Czech Republic.
Department of Mathematics, University of Chemistry and Technology Prague, 166 28 Prague, Czech Republic.
Membranes (Basel). 2021 Aug 29;11(9):665. doi: 10.3390/membranes11090665.
Membrane performance in gas separation is quantified by its selectivity, determined as a ratio of measured gas permeabilities of given gases at fixed pressure difference. In this manuscript a nonlinear dependence of gas permeability on pressure difference observed in the measurements of gas permeability of graphene oxide membrane on a manometric integral permeameter is reported. We show that after reasoned assumptions and simplifications in the mathematical description of the experiment, only static properties of any proposed governing equation can be studied, in order to analyze the permeation rate for different pressure differences. Porous Medium Equation is proposed as a suitable governing equation for the gas permeation, as it manages to predict a nonlinear behavior which is consistent with the measured data. A coefficient responsible for the nonlinearity, the polytropic exponent, is determined to be gas-specific-implications on selectivity are discussed, alongside possible hints to a deeper physical interpretation of its actual value.
气体分离中膜的性能通过其选择性来量化，选择性定义为在固定压差下给定气体的测量气体渗透率之比。在本手稿中，报道了在压力计积分渗透仪上测量氧化石墨烯膜气体渗透率时观察到的气体渗透率与压差的非线性关系。我们表明，在对实验的数学描述进行合理假设和简化后，为了分析不同压差下的渗透速率，只能研究任何提出的控制方程的静态特性。提出多孔介质方程作为气体渗透的合适控制方程，因为它能够预测与测量数据一致的非线性行为。确定了负责非线性的系数，即多方指数，讨论了其对选择性的影响，以及对其实际值进行更深入物理解释的可能线索。
