Wu Jian, Traoré Philippe, Vázquez Pedro A, Pérez Alberto T
Institut PPRIME, Département Fluide-Thermique-Combustion, Boulevard Pierre et Marie Curie, Boîte Postale 30179, 86962 Futuroscope-Chasseneuil, France.
Departamento de Física Aplicada III, Universidad de Sevilla, ESI, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):053018. doi: 10.1103/PhysRevE.88.053018. Epub 2013 Nov 22.
This work addresses the stability of a two-dimensional plane layer of a dielectric liquid enclosed in wall bounded cavities of different aspect ratios and subjected to unipolar injection of ions. Numerical simulations have been conducted to investigate the effect of lateral walls, especially in the development of the electroconvective instability. It is found that an unexpected change of the bifurcation nature occurs for certain cavity aspect ratios. We show that above the linear stability threshold for the rest state a supercritical bifurcation arises. This bifurcation takes place at a given value T(c1) of the parameter T (the electric Rayleigh number). Then, a second subcritical bifurcation occurs at a second threshold T(c2), featuring a typical hysteresis loop with an associated nonlinear criterion T(f), which is very characteristic of the Coulomb-driven convection. This behavior has been confirmed by different numerical codes based on different numerical methods. The physical mechanism which leads to this situation is analyzed and discussed. The evolution of the bifurcation diagrams with the aspect ratio of the cavity is also provided and analyzed.
这项工作研究了封闭在不同纵横比的壁面受限腔体中的二维介电液体平面层的稳定性，并对其进行单极离子注入。进行了数值模拟，以研究侧壁的影响，特别是在电对流不稳定性的发展过程中的影响。结果发现，对于某些腔体纵横比，分岔性质会发生意想不到的变化。我们表明，在静止状态的线性稳定性阈值之上会出现超临界分岔。这种分岔发生在参数T（电瑞利数）的给定值T(c1)处。然后，在第二个阈值T(c2)处发生第二次亚临界分岔，其具有典型的滞后回线以及相关的非线性准则T(f)，这是库仑驱动对流的非常典型的特征。基于不同数值方法的不同数值代码已证实了这种行为。分析并讨论了导致这种情况的物理机制。还给出并分析了分岔图随腔体纵横比的演变。
