Hierarchical Structure of Spiral Flow-Waves Self-Organized in a Reaction-Diffusion-Convection System and Its Gravity Effect

在这项研究中，我们研究了在Belousov-Zhabotinsky(BZ)反应激发螺旋化学波的溶液层中自组织对流结构的机制。主要有两种方法：1)在反应-扩散和对流系统中引入弹性表面模型来模拟对流结构，2)流动波的微重力实验。后一项实验得到了日本空间论坛的支持。在东京都MGLAB的落塔上进行了10次微重力实验。落塔提供了4秒的微重力环境。在微重力条件下，伴随着化学波的对流模式的形成得到了一些新的发现。在以前的研究中，我们已经澄清了：奇怪的现象。它们是1)与在具有自由水-空气表面的可激发BZ溶液中触发的单个化学波有关的传播对流。(1988)，2)加速…更高等级的化学波传播伴随着强对流(A Big Wave，1993)，3)在激发螺旋化学波的溶液层中出现了振荡流动(1988)，4)在BZ溶液激发的螺旋化学波(1995，由Matthiessen和Muller提出)中自组织了一个传播流波，以及具有旋转型动力学的螺旋形流波(2003)。以前的数值实验研究从来没有成功地解释这些现象，即使是最简单的对流传播伴随着单个化学波的情况。简单的反应扩散对流系统模型很难解释单个化学波前出现的长卷状对流结构，提出了一种新的反应扩散对流系统模型。该模型假定浅层化学溶液的顶面具有弹性性质。化学物质的浓度梯度通过Marangoni对流引起弹性表面的位移。本文提出的一维模型将Oregonator模型与描述顶面位移的弹性方程联系起来。该模型成功地再现了激发单个化学波和一个化学波序列的BZ溶液层中的表面流动结构。此外，与之前的模型(Matthiessenn et al.，1996)相比，将一维模型与描述化学溶液中的对流流动的Navier-Stokes方程连接起来的二维模型也再现了可能的流动结构。我们还在MGLAB的落塔上进行了一系列微重力实验。为了弄清重力对化学波相关对流型形成的影响，重复了10次微重力实验。作为研究结果，我们得到了如下新的发现：1)即使在具有自由空气-水表面的容器中，通过保持容器底部的亲水条件，也可以进行微重力下的化学波实验；2)通过控制容器一侧的亲水或疏水的表面条件，可以抑制微重力下液体表面的变形；3)在微重力过程中，化学波似乎受到对流效应的变形；4)直到自由落体之前，才可以进行光学干涉实验来分析表面变形。较少

In this study, we investigated a mechanism to self-organize convective structures such as spiral flow waves in a solution layer of Belousov-Zhabotinsky (BZ) reaction exciting spiral chemical waves. Two main approaches are 1)numerical experiments to simulate the convective structures by introducing an elastic surface model in the reaction-diffusion and convection system., and 2)micro-gravity experiment of the flow waves. The latter experiment was supported by Japan Space Forum. 10 times of micro-gravity experiment were carried out at a fall tower in MGLAB (Toki city). The fall tower provides 4 seconds environment of micro-gravity. Several new findings were obtained on the convective pattern formation accompanied by chemical waves under micro-gravity condition.In the previous studies, we have been clarified : curious phenomena. These are1)Apropagating convection associated with a single chemical wave triggered in an excitable BZ-solution having a free water-air surface.(1988),2)An accele … More rating chemical wave propagation accompanied by a strong convection (A Big Wave, 1993),3)An oscillatory flow appeared in the solution layer exciting spiral chemical waves (1988), and4)A propagating flow wave self-organized in the BZ-solution exciting spiral chemical waves (1995, by Matthiessen and Muller), and spiral-shaped flow wave with rotating pattern dynamics (2003).All of the above phenomena were found by our research group excepting for the propagating flow wave. Previous studies of numerical experiments never succeeded to explain these phenomena even for the simplest case of the propagating convection accompanied by the single chemical wave. A simple model of reaction-diffusion and convection system is hard to explain a long roll-shaped convective structure appeared in front of the single chemical wave.We proposed a new model of the reaction-diffusion and convection system. The model assumes that the top surface of a shallow layer of a chemical solution has an elastic property. A concentration gradient of chemical species induces displacement of the elastic surface through the Marangoni convection. A one-dimension model proposed here connects the Oregonator model with an elastic equation describing displacement of the top surface. The model successfully reproduces surface flow structures organized in the BZ solution layer exciting the single chemical wave and a chemical wave train. In addition, a two-dimensional model, which connects the one-dimensional model with the Navier-Stokes equations describing convective flow in the bulk of the chemical solution, also reproduces plausible flow structures, compared with the previous model (Matthiessenn et al., 1996).We also carried out a series of micro-gravity experiment at the fall tower in MGLAB. To clarify the gravity effect on the convective pattern formation associated with chemical waves, 10 times micro-gravity experiments were repeated. As the results we obtained new findings as follows:1)Chemical wave experiment under micro-gravity is possible even in a vessel having a free air-water surface by keeping a hydrophilic condition at the bottom surface of the vessel,2)A deformation of liquid surface under micro-gravity can be suppressed by controlling the surface condition of hydrophilic or hydrophobic at the side of the vessel,3)During micro-gravity, the chemical waves seemed to be deformed by some convective effects,4)Optical interference experiment to analyze surface deformation was possible until just before the free fall. Less