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Analysis of nonlinear dynamics for abrupt change of interphase structure in liquid-liquid mass transfer. (English) Zbl 1186.76650

As a liquid-liquid system is far from equilibrium state, the phase thickness is variable when mass transfer process with chemical reaction occurs in interphase zone, and a dispersible transitional layer called the interphase dispersed zone (IDZ) is formed. The model composed of thermodynamically instable O/W or W/O microemulsion has reasonably explained enormous experimental phenomena in nonlinear mass transfer. In this paper the dynamical characteristics of molecular diffusion model by using the bifurcation theory of planar dynamical system, Laplace transform, and maple software are studied. Applying the Laplace transform to the model equation, the planar dynamical system is obtained and it is shown that, when bifurcation parameters \((a, b)\) cross the line \(a = \sqrt{3}/3\) and the curve \(b=1/27 t\), the interface structure will change suddenly. The phase portraits of the system in different regions are also considered. The results obtained will play an important directive role in the study of IDZ model.

MSC:

76E17 Interfacial stability and instability in hydrodynamic stability
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
74G60 Bifurcation and buckling
74H60 Dynamical bifurcation of solutions to dynamical problems in solid mechanics

Software:

Maple
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Full Text: DOI EuDML

References:

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