The modeling description of basic transport phenomena of either liquid, gas or vapor molecules in dense polymeric membranes is of tremendous impact for the separation industry, which relies on solid models for the design of optimal process conditions, for the selection of the most suitable membrane materials as well as for the development of novel ones. Such models need to deal with several physical aspects and phenomena, spanning over broad time and length scales, thus requiring multiple approaches. The solid frameworks now available mainly rely on the solution–diffusion theory, in which equation of state models and free volume theories are applied for the description of thermodynamic and kinetic properties, to be coupled in appropriate transport schemes.

致密聚合物膜中液体，气体或蒸气分子的基本传输现象的建模描述对分离行业具有巨大影响，分离行业依赖于固体模型来设计最佳工艺条件，以选择最合适的膜材料以及开发新颖的产品。这样的模型需要处理多个物理方面和现象，跨越很宽的时间和长度范围，因此需要多种方法。现在可用的固体框架主要依靠溶液扩散理论，在该理论中，状态方程模型和自由体积理论被用于描述热力学和动力学性质，并与适当的传输方案相结合。