渗透驱动流中无搅拌层的形成
On the Formation of Unstirred Layer in Osmotically Driven Flow
摘要：
在参考以往反渗透研究的基础上，对恒静压差下渗透驱动流通过半透膜的过程进行了研究。本文介绍了几种获得近似解的数学方法，如传热学中反问题的方法，着重讨论了非线性边界条件和溶剂流速随时间的变化。结果表明，该层是在$\sim {\rm O}\bigl(\sqrt{t}\bigr)$时间尺度内由渗透作用迅速自发形成的，且该层厚度在无限时间间隔内无上限增长。在此基础上，我们还讨论了作为渗透发动机的系统在不可逆过程中的化学输出功。
英文摘要：
Osmotically driven flow across a semi-permeable membrane under a constant static pressure difference is revisited with referring to the previous reports for reverse osmosis. A few mathematical techniques for obtaining the approximate solution, such as that for inverse problems used in the field of heat transfer, are presented with an emphasis on the nonlinear boundary condition and the time-dependent solvent flow-rate. It is concluded that the layer is spontaneously formed by osmosis rapidly in the time scaled by $\sim {\rm O}\bigl(\sqrt{t}\bigr)$, and that the layer thickness grows with no upper limit in an infinite time interval. Based on the obtained solution, we will also discuss the thermodynamical output work in an irreversible process which is extracted from the system as an osmotic engine.
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