标题： 奇异吸引子表征渗透不稳定性 显示英文标题

标题： Strange Attractors Characterizing the Osmotic Instability

摘要： 在本文中，从第一性原理出发，推导出一个简单的动力学模型，用于计算各种复杂、非平衡情况下的渗透驱动流体流动。 使用Oberbeck-Boussinesq近似，得到了描述正向渗透过程的基本方程。 已经证明，这些方程与用于模拟自由雷利-贝纳德对流的方程非常相似。 不同之处在于，在热对流的情况下，体积膨胀由热膨胀系数驱动，而在渗透不稳定性中，起关键作用的是等温压缩系数。 此外，已经证明，渗透过程代表了随时间变化的振幅和相速度的驻波传播，其相速度等于溶剂通过半透膜的当前速度。 渗透波振幅的演化正好遵循相应控制参数的洛伦兹型奇异吸引子的动力学。 显示英文摘要

摘要： In the present paper a simple dynamical model for computing the osmotically driven fluid flow in a variety of complex, non equilibrium situations is derived from first principles. Using the Oberbeck-Boussinesq approximation, the basic equations describing the process of forward osmosis have been obtained. It has been shown that these equations are very similar to the ones used to model the free Rayleigh-Benard convection. The difference is that while in the case of thermal convection the volume expansion is driven by the coefficient of thermal expansion, the key role for the osmotic instability is played by the coefficient of isothermal compressibility. In addition, it has been shown that the osmotic process represents a propagation of standing waves with time-dependent amplitudes and phase velocity, which equals the current velocity of the solvent passing through the semi-permeable membrane. The evolution of the amplitudes of the osmotic waves is exactly following the dynamics of a strange attractor of Lorenz type with corresponding control parameters.