Chemical activity induces dynamical force with global structure in a reaction-diffusion-convection system

We found a rotating global structure induced by the dynamical force of local chemical activity in a thin solution layer of excitable Belousov-Zhabotinsky reaction coupled with diffusion. The surface flow and deformation associated with chemical spiral waves (wavelength about 1 mm) represents a global unidirectional structure and a global tilt in the entire Petri dish (100 mm in diameter), respectively. For these observations, we scanned the condition of hierarchal pattern selection. From this result, the bromomalonic acid has an important role to induce the rotating global structure. An interaction between a reaction-diffusion process and a surface-tension-driven effect leads to such hierarchal pattern with different scales.

Figure 1

Time series of flow wave patterns and flow direction on the solution surface. Pattern contrasts are emphasized so that only the flow wave pattern appears as a brighter area. The method of flow wave visualization is described in Ref. [14]. The white dots are the observation points of surface flow. The white lines indicate the direction of flow at the observation points; (a) $r=0\text{mm}$, (b) $r=33\text{mm}$, and (c) $r=66\text{mm}$. $r$ is the distance between the observation points and the chemical spiral cores. The direction of the flow wave rotation was random in each experiment. In this Rapid Communication, we used only clockwise rotating flow waves because the essential characteristics of both counterclockwise and clockwise rotating flow waves are the same. The time interval of the figures is about 8 s. The scale bar in (a-1), (b-1), and (c-1) is 10 mm. Movies of the rotating flow waves and surface flow are available [27].

Figure 2

Time series of analyzed surface deformation. The observation region is a circular region with a radius of 60 mm. The time interval of the figures is about 7.5 s. The distance between the highest and lowest parts is about $3\mu \text{m}$. The scale bar in (a) is 10 mm. Movies of the fringe pattern and surface deformation are available [27].

Figure 3

Schematic view: time evolution of surface flow structure and surface deformation. The global structure of surface flows is determined from chemical wave pattern contrasts and surface flow direction in Fig. 1.

Figure 4

Dependency of flow wave patterns on initial concentration of BrMA and MA. Regions I (△), II (○), and III $(\times )$ show a rotating flow wave, a circular flow wave, and no flow wave, respectively. Here, the circular flow wave corresponds to the faint but bright shape of a circular structure with out- or in-going propagation. The detailed demonstration is in Refs. [14, 16]. Each concentration was normalized by the experimental condition in Fig. 1.