Lima D, D'Onofrio A, De Wit A
Service de Chimie Physique and Centre for Nonlinear Phenomena and Complex Systems, CP231, Université Libre de Bruxelles, Campus Plaine, 1050 Brussels, Belgium.
J Chem Phys. 2006 Jan 7;124(1):14509. doi: 10.1063/1.2145746.
Nonlinear interactions between chemical reactions and buoyancy-driven Rayleigh-Taylor instability of reaction-diffusion acidity fronts of the chlorite-tetrathionate (CT) reaction are studied theoretically in a vertical Hele-Shaw cell or a porous medium. To do so, we perform a numerical integration of a two-variable reaction-diffusion model of the CT system coupled through an advection term to Darcy's law ruling the evolution of the velocity field of the fluid. The fingering dynamics of these chemical fronts is characterized by the appearance of several fingers at onset. These fingers then undergo coarsening and eventually merge to form one single symmetric finger. We study this asymptotic dynamics as a function of the three dimensionless parameters of the problem, i.e., the Damkohler number Da, the diffusivity ratio delta of the two chemical species, and the Rayleigh number Ra constructed here on the basis of the width L(y) of the system. For moderate values of Ra, the asymptotic single finger is shown to have self-similar scaling properties while above a given value of Ra, which depends on the other values of the parameters, tip splitting comes into play. Increasing the difference of diffusivities of the two chemical species (i.e., increasing delta) leads to more efficient coarsening and smaller asymptotic fingers. Experimental procedures to verify our predictions are proposed.
在垂直的赫勒肖池或多孔介质中，从理论上研究了化学反应与亚氯酸盐 - 连四硫酸盐（CT）反应的反应扩散酸度前沿的浮力驱动瑞利 - 泰勒不稳定性之间的非线性相互作用。为此，我们对CT系统的双变量反应扩散模型进行了数值积分，该模型通过一个平流项与达西定律耦合，达西定律控制着流体速度场的演化。这些化学前沿的指进动力学的特征是在起始时出现多个指状物。然后这些指状物经历粗化并最终合并形成一个单一的对称指状物。我们研究这种渐近动力学作为问题的三个无量纲参数的函数，即达姆科勒数Da、两种化学物质的扩散率比δ以及在此基于系统宽度L(y)构建的瑞利数Ra。对于适中的Ra值，渐近单指状物显示出具有自相似缩放特性，而在高于给定的Ra值时（该值取决于其他参数值），尖端分裂开始起作用。增加两种化学物质扩散率的差异（即增加δ）会导致更有效的粗化和更小的渐近指状物。本文还提出了验证我们预测的实验程序。
