Onset of Rayleigh–Bénard–Marangoni convection with time-dependent nonlinear concentration profiles
Onset of Rayleigh–Bénard–Marangoni convection with time-dependent nonlinear concentration profiles
复制标题
DOI：
10.1016/j.ces.2011.10.023
复制
发表时间：
2012-01
影响因子：
4.7
通讯作者：
Zhifa Sun
中科院分区：
文献类型：
--
作者：
Zhifa Sun
考虑到瑞利-贝纳德、贝纳德-马兰戈尼和瑞利-贝纳德-马兰戈尼问题中随时间变化的非线性基浓度分布对浓度和速度扰动的影响，开发了一种受空间基分布影响的冻结时间边缘状态分析，以预测由瑞利效应（浮力）和马兰戈尼效应（表面张力梯度）引起的细胞对流的开始。已经建立了基本速度和浓度分布以及速度和浓度波动之间的关系，类似于描述非平衡系统中粒子的脉动力和速度之间关系的统计物理理论。与准静态分析和初值技术相比，这种空间基面影响的冻结时间边缘状态分析的数值计算非常简单，并且不涉及对扰动初始条件或对流起始时间标准的主观决定。利用空间基础剖面影响的冻结时间边缘状态分析，计算出的对流开始的临界参数与已发表的实验结果非常吻合。
Taking into account the effects of the time-dependent nonlinear base concentration profile on the concentration and velocity disturbances in the Rayleigh–Bénard, Bénard–Marangoni, and Rayleigh–Bénard–Marangoni problems, a spatial base-profile influenced frozen-time marginal state analysis has been developed to predict the onset of cellular convection caused by the Rayleigh effect (buoyancy) and Marangoni effect (surface tension gradient). The relations between the base velocity and concentration profiles and the velocity and concentration fluctuations have been established, analogous to the theory of statistical physics which describes the relation between the fluctuating forces and velocities for particles in non-equilibrium systems. Compared with the quasi-static analysis and the initial-value technique, the numerical calculations of this spatial base-profile influenced frozen-time marginal state analysis are straightforward and involve no subjective decisions on either the initial conditions of disturbances or the criterion for the onset time of convection. Using the spatial base-profile influenced frozen-time marginal state analysis, the calculated critical parameters for the onset of convection are in good agreement with the published experimental results.