We perform a numerical analysis of Rayleigh-Bénard convection during solid-liquid phase change in the presence of an electric field. The objective is to examine the effects of the melting boundary and the electric field on the onset of flow motion and pattern formation. We characterize the timescale separation between the dynamics of the flow and that of the interface, which is dependent on the Rayleigh number Ra, the Prandtl number Pr, the Stefan number St, and the Fourier number Fo. It is found that (i) the delay of onset is a notable feature of the systems exhibiting phase transitions and convective instability compared to the traditional Rayleigh-Bénard convection; (ii) in the absence of the electric field, the critical Rayleigh number decreases monotonically with the timescale separation; (iii) in the presence of the electric field, the critical Rayleigh number can be lower than the classical value of ${\mathrm{Ra}}_c=1707.76$. For moderate Rayleigh number ($\mathrm{Ra}={10}^5$), we predict the robust “locked-in” effect of the topography on convection. When the electric field is strong enough, this locked-in pattern will be broken and the system will evolve to a strong nonlinear regime in an inherently time-dependent fashion.

中文翻译：

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具有熔化边界的外部电场下介电流体中的瑞利-贝纳对流

我们对存在电场的固液相变过程中的瑞利-贝纳德对流进行了数值分析。目的是检查熔化边界和电场对流动运动开始和模式形成的影响。我们描述了流动动力学和界面动力学之间的时间尺度分离，这取决于瑞利数 Ra、普朗特数 Pr、斯特凡数 St 和傅立叶数 Fo。发现 (i) 与传统的 Rayleigh-Bénard 对流相比，起始延迟是表现出相变和对流不稳定性的系统的显着特征；(ii) 在没有电场的情况下，临界瑞利数随着时间尺度的分离而单调递减；(iii) 在存在电场的情况下，${镭}_C=1707.76$. 对于中等瑞利数 ($镭={10}^5$)，我们预测了地形对对流的强大“锁定”效应。当电场足够强时，这种锁定模式将被打破，系统将以固有的时间依赖方式演变为强非线性状态。