描述渗透不稳定性的奇异吸引子
Strange Attractors Characterizing the Osmotic Instability
摘要：
本文从第一性原理出发，导出了一个简单的动力学模型，用于计算在各种复杂的非平衡情况下的磁驱动流体流动。采用Oberbeck-Boussinesq近似，得到了描述正渗透过程的基本方程。它已被证明，这些方程是非常相似的用于模拟自由Rayleigh-Benard对流。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，而对于渗透不稳定性起关键作用的是等温压缩系数。此外，已经表明，渗透过程表示具有时间依赖性振幅和相速度的驻波的传播，其等于溶剂通过半透膜的流速。渗透波振幅的演化完全遵循具有相应控制参数的Lorenz型奇异吸引子的动力学过程。
英文摘要：
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.
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