Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan.
Sci Rep. 2016 Jun 29;6:28960. doi: 10.1038/srep28960.
Patterns are often formed when particles cluster: Since patterns reflect the connectivity of different types of material, the emergence of patterns affects the physical and chemical properties of systems and shares a close relationship to their macroscopic functions. A radial dendritic pattern (RDP) is observed in many systems such as snow crystals, polymer crystals and biological systems. Although most of these systems are considered as dense particle suspensions, the mechanism of RDP formation in dense particle systems is not yet understood. It should be noted that the diffusion limited aggregation model is not applicable to RDP formation in dense systems, but in dilute particle systems. Here, we propose a simple model that exhibits RDP formation in a dense particle system. The model potential for the inter-particle interaction is composed of two parts, a repulsive and an attractive force. The repulsive force is applied to all the particles all the time and the attractive force is exerted only among particles inside a circular domain, which expands at a certain speed as a wave front propagating from a preselected centre. It is found that an RDP is formed if the velocity of the wave front that triggers the attractive interaction is of the same order of magnitude as the time scale defined by the aggregation speed.
当粒子聚集时，通常会形成图案：由于图案反映了不同类型物质的连接性，因此图案的出现会影响系统的物理和化学性质，并与其宏观功能密切相关。在许多系统中都观察到了径向枝晶图案（RDP），例如雪花晶体、聚合物晶体和生物系统。尽管这些系统大多被认为是密集的粒子悬浮液，但密集粒子系统中 RDP 形成的机制尚不清楚。应该注意的是，扩散限制聚集模型不适用于密集系统中的 RDP 形成，而适用于稀粒子系统。在这里，我们提出了一个简单的模型，该模型在密集粒子系统中表现出 RDP 的形成。粒子间相互作用的模型势由两部分组成，即排斥力和吸引力。排斥力一直作用于所有粒子上，吸引力仅在圆形域内的粒子之间施加，该圆形域以波前的形式以一定的速度扩展，从预选的中心向前传播。结果发现，如果触发吸引力相互作用的波前速度与由聚集速度定义的时间尺度处于同一数量级，则会形成 RDP。
